%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET137-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 : Tue May 21 03:16:27 EDT 2024

% Result   : Unsatisfiable 24.73s 3.92s
% Output   : Refutation 24.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1289
% Syntax   : Number of formulae    : 4512 ( 121 unt;   0 def)
%            Number of atoms       : 18237 (1744 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives : 24648 (10923   ~;12526   |;   0   &)
%                                         (1199 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   28 (   4 avg)
%            Number of predicates  : 1210 (1208 usr;1200 prp; 0-3 aty)
%            Number of functors    :   38 (  38 usr;  12 con; 0-3 aty)
%            Number of variables   : 6132 (6132   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f37685,plain,
    $false,
    inference(avatar_sat_refutation,[],[f175,f180,f185,f190,f195,f199,f204,f208,f212,f216,f220,f225,f230,f234,f238,f243,f247,f251,f255,f259,f263,f267,f271,f277,f282,f286,f290,f294,f298,f302,f306,f310,f314,f319,f337,f341,f345,f349,f354,f381,f385,f389,f398,f402,f406,f410,f414,f418,f422,f426,f452,f456,f460,f465,f473,f477,f481,f485,f490,f494,f498,f502,f511,f518,f522,f536,f540,f551,f556,f560,f568,f573,f577,f587,f593,f597,f602,f618,f624,f631,f635,f639,f645,f652,f657,f664,f675,f680,f684,f688,f703,f712,f716,f730,f735,f744,f748,f752,f756,f810,f815,f819,f823,f846,f850,f854,f863,f872,f876,f880,f884,f897,f923,f927,f931,f935,f939,f958,f997,f1001,f1005,f1050,f1054,f1058,f1062,f1100,f1104,f1111,f1135,f1139,f1143,f1147,f1169,f1173,f1204,f1214,f1218,f1227,f1231,f1235,f1274,f1278,f1282,f1286,f1294,f1298,f1339,f1344,f1357,f1363,f1370,f1375,f1396,f1409,f1421,f1427,f1445,f1463,f1467,f1507,f1514,f1519,f1547,f1572,f1588,f1598,f1602,f1656,f1663,f1671,f1681,f1691,f1696,f1751,f1759,f1763,f1805,f1819,f1823,f1836,f1840,f1853,f1861,f1865,f1879,f1884,f1899,f1909,f1918,f1923,f1927,f1933,f1938,f1942,f1969,f1987,f1991,f1994,f1995,f2076,f2104,f2108,f2113,f2126,f2152,f2157,f2161,f2168,f2184,f2195,f2199,f2236,f2240,f2244,f2248,f2252,f2260,f2269,f2273,f2277,f2281,f2285,f2304,f2371,f2387,f2396,f2402,f2413,f2431,f2440,f2471,f2512,f2638,f2644,f2648,f2650,f2672,f2676,f2680,f2684,f2688,f2747,f2751,f2755,f2759,f2764,f2808,f2855,f2858,f2873,f2877,f2881,f2959,f2964,f2965,f2969,f2982,f2986,f2990,f2994,f2998,f3002,f3006,f3011,f3015,f3019,f3032,f3037,f3041,f3045,f3200,f3204,f3219,f3223,f3241,f3245,f3258,f3264,f3268,f3272,f3276,f3280,f3285,f3289,f3293,f3297,f3301,f3379,f3492,f3496,f3500,f3504,f3508,f3512,f3516,f3520,f3524,f3528,f3532,f3536,f3540,f3544,f3548,f3574,f3578,f3582,f3586,f3590,f3615,f4120,f4124,f4128,f4132,f4136,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4178,f4186,f4639,f4644,f4651,f4655,f4659,f4660,f4664,f4668,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4700,f4705,f4709,f4710,f4754,f4760,f4764,f4779,f4783,f4798,f4801,f5407,f5412,f5421,f5427,f5431,f5439,f5443,f5448,f5515,f5519,f5523,f5527,f5531,f5540,f6109,f6113,f6117,f6124,f6193,f6197,f6201,f6430,f6443,f6473,f6477,f6482,f6488,f6499,f6503,f6507,f6512,f6516,f6521,f6580,f6730,f6734,f6739,f6758,f6762,f6766,f6770,f6774,f6778,f6782,f6786,f6790,f6799,f6802,f6814,f7280,f7284,f7289,f7298,f7302,f7306,f7310,f7315,f7446,f7450,f7454,f7458,f7462,f7466,f7470,f7475,f7487,f7492,f7503,f7579,f7586,f8200,f8202,f8266,f8278,f8283,f8287,f8291,f8304,f8320,f8324,f8328,f8332,f8336,f8341,f8409,f8413,f8418,f8497,f9082,f9088,f9096,f9100,f9104,f9108,f9144,f9150,f9159,f9163,f9167,f9172,f9184,f9188,f9192,f9196,f9200,f9204,f9240,f9244,f9248,f9252,f9256,f9261,f9429,f9701,f9705,f9710,f9715,f9780,f9786,f9819,f9831,f9839,f9873,f9877,f9881,f9886,f9924,f9930,f9934,f9938,f9997,f10001,f10006,f10019,f10024,f10116,f10124,f10131,f10139,f10145,f10149,f10153,f10157,f10189,f10282,f10286,f10290,f10295,f10309,f10313,f10318,f10339,f10344,f10364,f10369,f10459,f10463,f10467,f10471,f10476,f10563,f10568,f10573,f10577,f10685,f10691,f10732,f10809,f10812,f10817,f10822,f10862,f10867,f10881,f10886,f10900,f10906,f10919,f10923,f10927,f11032,f11036,f11041,f11056,f11061,f11077,f11081,f11085,f11091,f11130,f11134,f11139,f11155,f11160,f11223,f11228,f11232,f11288,f11293,f11356,f11361,f11415,f11420,f11427,f11487,f11492,f11554,f11559,f11620,f11624,f11628,f11640,f11646,f11689,f11696,f11700,f11704,f11773,f11938,f11942,f11948,f12098,f12103,f12108,f12109,f12426,f12431,f12436,f12441,f12446,f12447,f12461,f12465,f12591,f12595,f12599,f12608,f12702,f12706,f12881,f12901,f12918,f12927,f12933,f12937,f12938,f13061,f13066,f13072,f13079,f13085,f13090,f13095,f13101,f13106,f13112,f13122,f13126,f13147,f13153,f13161,f13167,f13233,f13299,f13304,f13308,f13361,f13383,f13390,f13395,f13406,f13411,f13480,f13648,f13716,f13784,f13789,f13848,f13853,f13866,f13940,f13974,f13978,f13984,f14056,f14193,f14199,f14378,f14382,f14423,f14912,f14918,f14923,f15008,f15013,f15024,f15028,f15032,f15036,f15040,f15045,f15049,f15543,f15547,f15564,f15568,f15678,f15682,f15690,f15697,f15703,f15743,f15750,f15757,f15761,f15769,f15784,f15790,f15796,f15815,f15819,f15823,f15827,f15832,f15844,f15849,f15887,f15898,f15970,f15975,f15989,f15993,f15997,f16002,f16080,f16101,f16105,f16109,f16113,f16193,f16206,f16210,f16214,f16218,f16521,f16527,f16531,f16550,f16555,f16574,f16578,f16582,f16586,f16590,f16640,f16936,f16942,f16947,f16951,f16964,f16977,f17019,f17032,f17059,f17072,f17105,f17109,f17114,f17136,f17140,f17145,f17166,f17171,f17197,f17237,f17242,f17269,f17273,f17277,f17282,f17547,f17552,f17567,f17571,f17584,f17613,f17623,f17725,f17735,f17769,f17773,f17778,f17798,f17808,f17814,f17819,f17824,f17847,f18027,f18031,f18036,f18106,f18110,f18114,f18120,f18317,f18322,f18352,f18357,f18362,f18367,f18375,f18411,f18470,f18478,f18495,f18500,f18532,f18609,f18613,f18617,f18621,f18627,f18633,f18658,f18807,f18887,f18893,f18899,f18904,f18931,f18944,f18948,f18952,f18957,f18983,f18988,f19038,f19042,f19046,f19051,f19074,f19079,f19094,f19099,f19103,f19107,f19112,f19117,f19184,f19189,f19208,f19220,f19231,f19236,f19244,f19249,f19254,f19270,f19275,f19279,f19333,f19337,f19352,f19377,f19429,f19435,f19453,f19459,f19480,f19485,f19506,f19511,f19515,f19536,f19541,f19562,f19567,f19585,f19590,f19594,f19612,f19617,f19638,f19643,f19664,f19669,f19710,f19718,f19723,f19749,f19754,f19780,f19785,f19812,f19816,f19824,f19842,f19850,f19875,f19879,f19883,f20060,f20064,f20068,f20129,f20137,f20141,f20169,f20183,f20188,f20204,f20208,f20284,f20304,f20309,f20329,f20334,f20354,f20362,f20367,f20388,f20392,f20396,f20401,f20433,f20438,f20470,f20476,f20480,f20497,f20502,f20534,f20539,f20696,f20700,f20705,f20726,f20731,f20776,f20781,f20867,f20872,f20976,f20981,f20997,f21013,f21017,f21080,f21085,f21090,f21094,f21151,f21156,f21161,f21227,f21232,f21237,f21278,f21283,f21324,f21329,f21375,f21379,f21384,f21425,f21430,f21435,f21440,f21445,f21482,f21487,f21524,f21529,f21566,f21571,f21608,f21615,f21652,f21659,f21694,f21699,f21716,f21721,f21739,f21743,f21748,f21765,f21770,f21804,f21809,f21829,f21835,f21856,f21863,f21904,f21909,f21933,f21940,f21944,f21985,f21989,f22004,f22035,f22044,f22066,f22074,f22078,f22082,f22086,f22140,f22145,f22266,f22286,f22290,f22295,f22331,f22336,f22369,f22375,f22380,f22385,f22390,f22395,f22414,f22427,f22441,f22445,f22455,f22476,f22508,f22513,f22540,f22544,f22548,f22604,f22609,f22614,f22624,f22636,f22699,f22731,f22736,f22742,f22753,f22757,f22758,f22759,f22785,f23736,f24080,f24168,f24172,f24234,f24749,f24808,f24815,f24821,f24828,f24833,f24836,f24840,f24845,f24851,f24935,f24967,f24985,f24989,f24990,f25050,f25054,f25217,f25222,f25234,f25441,f25462,f25541,f25782,f25789,f25829,f25929,f25941,f25946,f25951,f26209,f26663,f26720,f26725,f26790,f26802,f26808,f26925,f26930,f26986,f27042,f27045,f27046,f27077,f27101,f27113,f27119,f27120,f27199,f27200,f27201,f27249,f27254,f27259,f27261,f27633,f27637,f27699,f27704,f27709,f27714,f27794,f27799,f27800,f27827,f27843,f27847,f27864,f27869,f27874,f27875,f27897,f28193,f28199,f28213,f28216,f28222,f28246,f28325,f28404,f28436,f28476,f28477,f28496,f28613,f28921,f29066,f29101,f29114,f29123,f29705,f29908,f29916,f29920,f29937,f30112,f30125,f30142,f30146,f30151,f30195,f30199,f30484,f30773,f30999,f31039,f31043,f31117,f31128,f31132,f31165,f31456,f31888,f31890,f31941,f31943,f31984,f32005,f32056,f32060,f32064,f32073,f32261,f32265,f32270,f32350,f32354,f32355,f32391,f32412,f32418,f32423,f32428,f32434,f32448,f32459,f32464,f32468,f32472,f32476,f32480,f32504,f32509,f32513,f32517,f32521,f32615,f32633,f32638,f32641,f33065,f33070,f33079,f33128,f33258,f33590,f33594,f33615,f33648,f33650,f33785,f34035,f34241,f34256,f34346,f34943,f35071,f35221,f35238,f35553,f35617,f35665,f35755,f35788,f35842,f35864,f35896,f35947,f36672,f37031,f37061,f37065,f37209,f37210,f37230,f37684]) ).

fof(f37684,plain,
    ( ~ spl0_361
    | ~ spl0_1
    | ~ spl0_894 ),
    inference(avatar_split_clause,[],[f20210,f20139,f172,f4702]) ).

fof(f4702,plain,
    ( spl0_361
  <=> member(u,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f172,plain,
    ( spl0_1
  <=> member(u,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f20139,plain,
    ( spl0_894
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,x) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).

fof(f20210,plain,
    ( ~ member(u,null_class)
    | ~ spl0_1
    | ~ spl0_894 ),
    inference(resolution,[],[f20140,f174]) ).

fof(f174,plain,
    ( member(u,x)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f172]) ).

fof(f20140,plain,
    ( ! [X0] :
        ( ~ member(X0,x)
        | ~ member(X0,null_class) )
    | ~ spl0_894 ),
    inference(avatar_component_clause,[],[f20139]) ).

fof(f37230,plain,
    ( spl0_1199
    | ~ spl0_37
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f37222,f1336,f339,f37228]) ).

fof(f37228,plain,
    ( spl0_1199
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f339,plain,
    ( spl0_37
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1336,plain,
    ( spl0_155
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f37222,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0) )
    | ~ spl0_37
    | ~ spl0_155 ),
    inference(resolution,[],[f1338,f340]) ).

fof(f340,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f339]) ).

fof(f1338,plain,
    ( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1336]) ).

fof(f37210,plain,
    ( spl0_361
    | ~ spl0_8
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f9109,f7452,f206,f4702]) ).

fof(f206,plain,
    ( spl0_8
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f7452,plain,
    ( spl0_433
  <=> ! [X0] :
        ( ~ subclass(null_class,X0)
        | member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f9109,plain,
    ( member(u,null_class)
    | ~ spl0_8
    | ~ spl0_433 ),
    inference(resolution,[],[f7453,f207]) ).

fof(f207,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f7453,plain,
    ( ! [X0] :
        ( ~ subclass(null_class,X0)
        | member(u,X0) )
    | ~ spl0_433 ),
    inference(avatar_component_clause,[],[f7452]) ).

fof(f37209,plain,
    ( spl0_1198
    | ~ spl0_849
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f32803,f21854,f19371,f37207]) ).

fof(f37207,plain,
    ( spl0_1198
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,null_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f19371,plain,
    ( spl0_849
  <=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f21854,plain,
    ( spl0_984
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f32803,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,null_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_849
    | ~ spl0_984 ),
    inference(forward_demodulation,[],[f21855,f19373]) ).

fof(f19373,plain,
    ( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
    | ~ spl0_849 ),
    inference(avatar_component_clause,[],[f19371]) ).

fof(f21855,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_984 ),
    inference(avatar_component_clause,[],[f21854]) ).

fof(f37065,plain,
    ( spl0_1197
    | ~ spl0_849
    | ~ spl0_967 ),
    inference(avatar_split_clause,[],[f32805,f21606,f19371,f37063]) ).

fof(f37063,plain,
    ( spl0_1197
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f21606,plain,
    ( spl0_967
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f32805,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_849
    | ~ spl0_967 ),
    inference(forward_demodulation,[],[f21607,f19373]) ).

fof(f21607,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_967 ),
    inference(avatar_component_clause,[],[f21606]) ).

fof(f37061,plain,
    ( spl0_1196
    | ~ spl0_849
    | ~ spl0_969 ),
    inference(avatar_split_clause,[],[f32804,f21650,f19371,f37059]) ).

fof(f37059,plain,
    ( spl0_1196
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f21650,plain,
    ( spl0_969
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).

fof(f32804,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_849
    | ~ spl0_969 ),
    inference(forward_demodulation,[],[f21651,f19373]) ).

fof(f21651,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_969 ),
    inference(avatar_component_clause,[],[f21650]) ).

fof(f37031,plain,
    ( spl0_606
    | ~ spl0_162
    | ~ spl0_612 ),
    inference(avatar_split_clause,[],[f36174,f12597,f1372,f12438]) ).

fof(f12438,plain,
    ( spl0_606
  <=> member(u,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f1372,plain,
    ( spl0_162
  <=> member(u,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f12597,plain,
    ( spl0_612
  <=> ! [X0] :
        ( member(X0,element_relation)
        | ~ member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f36174,plain,
    ( member(u,element_relation)
    | ~ spl0_162
    | ~ spl0_612 ),
    inference(resolution,[],[f1373,f12598]) ).

fof(f12598,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,element_relation) )
    | ~ spl0_612 ),
    inference(avatar_component_clause,[],[f12597]) ).

fof(f1373,plain,
    ( member(u,subset_relation)
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1372]) ).

fof(f36672,plain,
    ( spl0_606
    | ~ spl0_8
    | ~ spl0_644 ),
    inference(avatar_split_clause,[],[f13413,f13306,f206,f12438]) ).

fof(f13306,plain,
    ( spl0_644
  <=> ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f13413,plain,
    ( member(u,element_relation)
    | ~ spl0_8
    | ~ spl0_644 ),
    inference(resolution,[],[f13307,f207]) ).

fof(f13307,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(u,X0) )
    | ~ spl0_644 ),
    inference(avatar_component_clause,[],[f13306]) ).

fof(f35947,plain,
    ( spl0_162
    | ~ spl0_8
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f8949,f8407,f206,f1372]) ).

fof(f8407,plain,
    ( spl0_460
  <=> ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f8949,plain,
    ( member(u,subset_relation)
    | ~ spl0_8
    | ~ spl0_460 ),
    inference(resolution,[],[f8408,f207]) ).

fof(f8408,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(u,X0) )
    | ~ spl0_460 ),
    inference(avatar_component_clause,[],[f8407]) ).

fof(f35896,plain,
    ( spl0_1195
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(avatar_split_clause,[],[f32809,f20352,f19371,f35894]) ).

fof(f35894,plain,
    ( spl0_1195
  <=> ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f20352,plain,
    ( spl0_908
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f32809,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f32808,f19373]) ).

fof(f32808,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f32807,f19373]) ).

fof(f32807,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f20353,f19373]) ).

fof(f20353,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_908 ),
    inference(avatar_component_clause,[],[f20352]) ).

fof(f35864,plain,
    ( spl0_864
    | ~ spl0_114
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f29838,f1757,f874,f19583]) ).

fof(f19583,plain,
    ( spl0_864
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f874,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1757,plain,
    ( spl0_188
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f29838,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | null_class = X3
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(regular(X3)))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_114
    | ~ spl0_188 ),
    inference(resolution,[],[f875,f1758]) ).

fof(f1758,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_188 ),
    inference(avatar_component_clause,[],[f1757]) ).

fof(f875,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,null_class)
        | null_class = X0 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f874]) ).

fof(f35842,plain,
    ( spl0_869
    | ~ spl0_114
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f29837,f1761,f874,f19636]) ).

fof(f19636,plain,
    ( spl0_869
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f1761,plain,
    ( spl0_189
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f29837,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | null_class = X3
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_114
    | ~ spl0_189 ),
    inference(resolution,[],[f875,f1762]) ).

fof(f1762,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_189 ),
    inference(avatar_component_clause,[],[f1761]) ).

fof(f35788,plain,
    ( spl0_1194
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(avatar_split_clause,[],[f32812,f20127,f19371,f35786]) ).

fof(f35786,plain,
    ( spl0_1194
  <=> ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f20127,plain,
    ( spl0_892
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).

fof(f32812,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f32811,f19373]) ).

fof(f32811,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f32810,f19373]) ).

fof(f32810,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f20128,f19373]) ).

fof(f20128,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_892 ),
    inference(avatar_component_clause,[],[f20127]) ).

fof(f35755,plain,
    ( spl0_1193
    | ~ spl0_686
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f35677,f19371,f15688,f35753]) ).

fof(f35753,plain,
    ( spl0_1193
  <=> ! [X0] :
        ( ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X0),universal_class)))))
        | member(null_class,compose(X0,regular(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f15688,plain,
    ( spl0_686
  <=> ! [X0] :
        ( member(null_class,compose(X0,regular(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class))))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f35677,plain,
    ( ! [X0] :
        ( ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X0),universal_class)))))
        | member(null_class,compose(X0,regular(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class)))) )
    | ~ spl0_686
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f15689,f19373]) ).

fof(f15689,plain,
    ( ! [X0] :
        ( member(null_class,compose(X0,regular(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class))))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_686 ),
    inference(avatar_component_clause,[],[f15688]) ).

fof(f35665,plain,
    ( ~ spl0_70
    | spl0_361
    | ~ spl0_27
    | ~ spl0_1079 ),
    inference(avatar_split_clause,[],[f27176,f27099,f288,f4702,f553]) ).

fof(f553,plain,
    ( spl0_70
  <=> member(u,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f288,plain,
    ( spl0_27
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f27099,plain,
    ( spl0_1079
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,null_class)
        | ~ member(X0,unordered_pair(u,u)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f27176,plain,
    ( member(u,null_class)
    | ~ member(u,universal_class)
    | ~ spl0_27
    | ~ spl0_1079 ),
    inference(duplicate_literal_removal,[],[f27123]) ).

fof(f27123,plain,
    ( member(u,null_class)
    | ~ member(u,universal_class)
    | ~ member(u,universal_class)
    | ~ spl0_27
    | ~ spl0_1079 ),
    inference(resolution,[],[f27100,f289]) ).

fof(f289,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f288]) ).

fof(f27100,plain,
    ( ! [X0] :
        ( ~ member(X0,unordered_pair(u,u))
        | member(X0,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_1079 ),
    inference(avatar_component_clause,[],[f27099]) ).

fof(f35617,plain,
    ( spl0_1192
    | ~ spl0_841
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32818,f19371,f19247,f35615]) ).

fof(f35615,plain,
    ( spl0_1192
  <=> ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),null_class)
        | member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

fof(f19247,plain,
    ( spl0_841
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f32818,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),null_class)
        | member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_841
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f19248,f19373]) ).

fof(f19248,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_841 ),
    inference(avatar_component_clause,[],[f19247]) ).

fof(f35553,plain,
    ( spl0_1191
    | ~ spl0_833
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32819,f19371,f19182,f35551]) ).

fof(f35551,plain,
    ( spl0_1191
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f19182,plain,
    ( spl0_833
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f32819,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_833
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f19183,f19373]) ).

fof(f19183,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_833 ),
    inference(avatar_component_clause,[],[f19182]) ).

fof(f35238,plain,
    ( spl0_1190
    | ~ spl0_823
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32822,f19371,f19044,f35236]) ).

fof(f35236,plain,
    ( spl0_1190
  <=> ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f19044,plain,
    ( spl0_823
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f32822,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_823
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f19045,f19373]) ).

fof(f19045,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_823 ),
    inference(avatar_component_clause,[],[f19044]) ).

fof(f35221,plain,
    ( spl0_1189
    | ~ spl0_811
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32825,f19371,f18897,f35219]) ).

fof(f35219,plain,
    ( spl0_1189
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f18897,plain,
    ( spl0_811
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f32825,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_811
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f18898,f19373]) ).

fof(f18898,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_811 ),
    inference(avatar_component_clause,[],[f18897]) ).

fof(f35071,plain,
    ( spl0_1188
    | ~ spl0_804
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32831,f19371,f18619,f35069]) ).

fof(f35069,plain,
    ( spl0_1188
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f18619,plain,
    ( spl0_804
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f32831,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_804
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f18620,f19373]) ).

fof(f18620,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_804 ),
    inference(avatar_component_clause,[],[f18619]) ).

fof(f34943,plain,
    ( spl0_1187
    | ~ spl0_797
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32834,f19371,f18493,f34941]) ).

fof(f34941,plain,
    ( spl0_1187
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,null_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f18493,plain,
    ( spl0_797
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f32834,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,null_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_797
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f18494,f19373]) ).

fof(f18494,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_797 ),
    inference(avatar_component_clause,[],[f18493]) ).

fof(f34346,plain,
    ( spl0_1186
    | ~ spl0_780
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32841,f19371,f18029,f34344]) ).

fof(f34344,plain,
    ( spl0_1186
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f18029,plain,
    ( spl0_780
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f32841,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
    | ~ spl0_780
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f18030,f19373]) ).

fof(f18030,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
    | ~ spl0_780 ),
    inference(avatar_component_clause,[],[f18029]) ).

fof(f34256,plain,
    ( spl0_1185
    | ~ spl0_749
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32855,f19371,f17107,f34254]) ).

fof(f34254,plain,
    ( spl0_1185
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(null_class,universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f17107,plain,
    ( spl0_749
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f32855,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(null_class,universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_749
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f17108,f19373]) ).

fof(f17108,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_749 ),
    inference(avatar_component_clause,[],[f17107]) ).

fof(f34241,plain,
    ( spl0_1184
    | ~ spl0_739
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32858,f19371,f16940,f34239]) ).

fof(f34239,plain,
    ( spl0_1184
  <=> ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f16940,plain,
    ( spl0_739
  <=> ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f32858,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_739
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f16941,f19373]) ).

fof(f16941,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_739 ),
    inference(avatar_component_clause,[],[f16940]) ).

fof(f34035,plain,
    ( spl0_1183
    | ~ spl0_800
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f32830,f19371,f18530,f34033]) ).

fof(f34033,plain,
    ( spl0_1183
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(null_class,universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f18530,plain,
    ( spl0_800
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f32830,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(null_class,universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_800
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f32829,f19373]) ).

fof(f32829,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(null_class,universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) )
    | ~ spl0_800
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f18531,f19373]) ).

fof(f18531,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) )
    | ~ spl0_800 ),
    inference(avatar_component_clause,[],[f18530]) ).

fof(f33785,plain,
    ( ~ spl0_1181
    | ~ spl0_1182
    | spl0_297
    | ~ spl0_101
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1449,f1443,f754,f3255,f33782,f33778]) ).

fof(f33778,plain,
    ( spl0_1181
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f33782,plain,
    ( spl0_1182
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f3255,plain,
    ( spl0_297
  <=> null_class = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f754,plain,
    ( spl0_101
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1443,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f1449,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_101
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f755]) ).

fof(f755,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f754]) ).

fof(f1444,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
        | complement(X0) = null_class
        | ~ member(complement(X0),universal_class) )
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f1443]) ).

fof(f33650,plain,
    ( spl0_1180
    | ~ spl0_686
    | ~ spl0_748
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f33649,f19371,f17102,f15688,f33646]) ).

fof(f33646,plain,
    ( spl0_1180
  <=> ! [X0] :
        ( ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X0),universal_class)))))
        | member(null_class,compose(X0,regular(cross_product(u,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f17102,plain,
    ( spl0_748
  <=> u = unordered_pair(first(null_class),first(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f33649,plain,
    ( ! [X0] :
        ( ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X0),universal_class)))))
        | member(null_class,compose(X0,regular(cross_product(u,universal_class)))) )
    | ~ spl0_686
    | ~ spl0_748
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f17668,f19373]) ).

fof(f17668,plain,
    ( ! [X0] :
        ( member(null_class,compose(X0,regular(cross_product(u,universal_class))))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_686
    | ~ spl0_748 ),
    inference(forward_demodulation,[],[f15689,f17104]) ).

fof(f17104,plain,
    ( u = unordered_pair(first(null_class),first(null_class))
    | ~ spl0_748 ),
    inference(avatar_component_clause,[],[f17102]) ).

fof(f33648,plain,
    ( spl0_1180
    | ~ spl0_688
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f33629,f19371,f15701,f33646]) ).

fof(f15701,plain,
    ( spl0_688
  <=> ! [X0] :
        ( member(null_class,compose(X0,regular(cross_product(u,universal_class))))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f33629,plain,
    ( ! [X0] :
        ( ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X0),universal_class)))))
        | member(null_class,compose(X0,regular(cross_product(u,universal_class)))) )
    | ~ spl0_688
    | ~ spl0_849 ),
    inference(forward_demodulation,[],[f15702,f19373]) ).

fof(f15702,plain,
    ( ! [X0] :
        ( ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class)))))
        | member(null_class,compose(X0,regular(cross_product(u,universal_class)))) )
    | ~ spl0_688 ),
    inference(avatar_component_clause,[],[f15701]) ).

fof(f33615,plain,
    ( spl0_1150
    | ~ spl0_541
    | ~ spl0_1149 ),
    inference(avatar_split_clause,[],[f32404,f32386,f10571,f32389]) ).

fof(f32389,plain,
    ( spl0_1150
  <=> ! [X0,X1] : ~ member(null_class,compose(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f10571,plain,
    ( spl0_541
  <=> ! [X0,X1] :
        ( member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(u,universal_class),X1),universal_class)))),universal_class),X0),universal_class)))))
        | ~ member(null_class,compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f32386,plain,
    ( spl0_1149
  <=> ! [X2] : ~ member(second(null_class),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f32404,plain,
    ( ! [X0,X1] : ~ member(null_class,compose(X0,X1))
    | ~ spl0_541
    | ~ spl0_1149 ),
    inference(resolution,[],[f32387,f10572]) ).

fof(f10572,plain,
    ( ! [X0,X1] :
        ( member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(u,universal_class),X1),universal_class)))),universal_class),X0),universal_class)))))
        | ~ member(null_class,compose(X0,X1)) )
    | ~ spl0_541 ),
    inference(avatar_component_clause,[],[f10571]) ).

fof(f32387,plain,
    ( ! [X2] : ~ member(second(null_class),X2)
    | ~ spl0_1149 ),
    inference(avatar_component_clause,[],[f32386]) ).

fof(f33594,plain,
    ( spl0_1179
    | ~ spl0_96
    | ~ spl0_188
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f32780,f26983,f1757,f728,f33592]) ).

fof(f33592,plain,
    ( spl0_1179
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f728,plain,
    ( spl0_96
  <=> ! [X0] :
        ( member(X0,null_class)
        | member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f26983,plain,
    ( spl0_1076
  <=> universal_class = complement(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f32780,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_188
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f23106,f26985]) ).

fof(f26985,plain,
    ( universal_class = complement(null_class)
    | ~ spl0_1076 ),
    inference(avatar_component_clause,[],[f26983]) ).

fof(f23106,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_188 ),
    inference(resolution,[],[f729,f1758]) ).

fof(f729,plain,
    ( ! [X0] :
        ( member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | member(X0,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f728]) ).

fof(f33590,plain,
    ( spl0_1178
    | ~ spl0_96
    | ~ spl0_189
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f32779,f26983,f1761,f728,f33588]) ).

fof(f33588,plain,
    ( spl0_1178
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f32779,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_189
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f23105,f26985]) ).

fof(f23105,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_189 ),
    inference(resolution,[],[f729,f1762]) ).

fof(f33258,plain,
    ( spl0_1177
    | ~ spl0_268
    | ~ spl0_1142 ),
    inference(avatar_split_clause,[],[f32257,f32062,f2871,f33255]) ).

fof(f33255,plain,
    ( spl0_1177
  <=> null_class = intersection(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f2871,plain,
    ( spl0_268
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f32062,plain,
    ( spl0_1142
  <=> ! [X0] :
        ( null_class = intersection(universal_class,X0)
        | ~ member(regular(intersection(universal_class,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f32257,plain,
    ( null_class = intersection(universal_class,identity_relation)
    | ~ spl0_268
    | ~ spl0_1142 ),
    inference(duplicate_literal_removal,[],[f32234]) ).

fof(f32234,plain,
    ( null_class = intersection(universal_class,identity_relation)
    | null_class = intersection(universal_class,identity_relation)
    | ~ spl0_268
    | ~ spl0_1142 ),
    inference(resolution,[],[f32063,f2872]) ).

fof(f2872,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),subset_relation)
        | null_class = intersection(X0,identity_relation) )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f2871]) ).

fof(f32063,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(universal_class,X0)),subset_relation)
        | null_class = intersection(universal_class,X0) )
    | ~ spl0_1142 ),
    inference(avatar_component_clause,[],[f32062]) ).

fof(f33128,plain,
    ( spl0_1176
    | ~ spl0_119
    | ~ spl0_1142 ),
    inference(avatar_split_clause,[],[f32255,f32062,f925,f33125]) ).

fof(f33125,plain,
    ( spl0_1176
  <=> null_class = intersection(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f925,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f32255,plain,
    ( null_class = intersection(universal_class,subset_relation)
    | ~ spl0_119
    | ~ spl0_1142 ),
    inference(duplicate_literal_removal,[],[f32236]) ).

fof(f32236,plain,
    ( null_class = intersection(universal_class,subset_relation)
    | null_class = intersection(universal_class,subset_relation)
    | ~ spl0_119
    | ~ spl0_1142 ),
    inference(resolution,[],[f32063,f926]) ).

fof(f926,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f925]) ).

fof(f33079,plain,
    ( spl0_1175
    | ~ spl0_556
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f32783,f26983,f10904,f33077]) ).

fof(f33077,plain,
    ( spl0_1175
  <=> ! [X0] :
        ( subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f10904,plain,
    ( spl0_556
  <=> ! [X0] :
        ( subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f32783,plain,
    ( ! [X0] :
        ( subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) )
    | ~ spl0_556
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f32782,f26985]) ).

fof(f32782,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0) )
    | ~ spl0_556
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f10905,f26985]) ).

fof(f10905,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0) )
    | ~ spl0_556 ),
    inference(avatar_component_clause,[],[f10904]) ).

fof(f33070,plain,
    ( spl0_1174
    | ~ spl0_264
    | ~ spl0_1141 ),
    inference(avatar_split_clause,[],[f32145,f32058,f2757,f33067]) ).

fof(f33067,plain,
    ( spl0_1174
  <=> null_class = intersection(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f2757,plain,
    ( spl0_264
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f32058,plain,
    ( spl0_1141
  <=> ! [X0] :
        ( null_class = intersection(X0,universal_class)
        | ~ member(regular(intersection(X0,universal_class)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f32145,plain,
    ( null_class = intersection(identity_relation,universal_class)
    | ~ spl0_264
    | ~ spl0_1141 ),
    inference(duplicate_literal_removal,[],[f32119]) ).

fof(f32119,plain,
    ( null_class = intersection(identity_relation,universal_class)
    | null_class = intersection(identity_relation,universal_class)
    | ~ spl0_264
    | ~ spl0_1141 ),
    inference(resolution,[],[f32059,f2758]) ).

fof(f2758,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f2757]) ).

fof(f32059,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,universal_class)),subset_relation)
        | null_class = intersection(X0,universal_class) )
    | ~ spl0_1141 ),
    inference(avatar_component_clause,[],[f32058]) ).

fof(f33065,plain,
    ( ~ spl0_1173
    | spl0_550
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f32781,f26983,f10819,f33062]) ).

fof(f33062,plain,
    ( spl0_1173
  <=> member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f10819,plain,
    ( spl0_550
  <=> member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f32781,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation)
    | spl0_550
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f10821,f26985]) ).

fof(f10821,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation)
    | spl0_550 ),
    inference(avatar_component_clause,[],[f10819]) ).

fof(f32641,plain,
    ( ~ spl0_1147
    | ~ spl0_110
    | ~ spl0_1076
    | spl0_1172 ),
    inference(avatar_split_clause,[],[f32640,f32635,f26983,f856,f32267]) ).

fof(f32267,plain,
    ( spl0_1147
  <=> subclass(identity_relation,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f856,plain,
    ( spl0_110
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f32635,plain,
    ( spl0_1172
  <=> subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f32640,plain,
    ( ~ subclass(identity_relation,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_1076
    | spl0_1172 ),
    inference(forward_demodulation,[],[f32639,f858]) ).

fof(f858,plain,
    ( element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f856]) ).

fof(f32639,plain,
    ( ~ subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_1076
    | spl0_1172 ),
    inference(forward_demodulation,[],[f32636,f26985]) ).

fof(f32636,plain,
    ( ~ subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | spl0_1172 ),
    inference(avatar_component_clause,[],[f32635]) ).

fof(f32638,plain,
    ( spl0_1172
    | ~ spl0_230
    | ~ spl0_544 ),
    inference(avatar_split_clause,[],[f10725,f10689,f2242,f32635]) ).

fof(f2242,plain,
    ( spl0_230
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f10689,plain,
    ( spl0_544
  <=> ! [X0] :
        ( subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f10725,plain,
    ( subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_544 ),
    inference(duplicate_literal_removal,[],[f10692]) ).

fof(f10692,plain,
    ( subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_544 ),
    inference(resolution,[],[f10690,f2243]) ).

fof(f2243,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_230 ),
    inference(avatar_component_clause,[],[f2242]) ).

fof(f10690,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_544 ),
    inference(avatar_component_clause,[],[f10689]) ).

fof(f32633,plain,
    ( spl0_1171
    | ~ spl0_37
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1887,f1882,f339,f32631]) ).

fof(f32631,plain,
    ( spl0_1171
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,null_class)
        | ~ subclass(complement(unordered_pair(u,u)),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f1882,plain,
    ( spl0_199
  <=> ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,universal_class)
        | member(X0,complement(unordered_pair(u,u))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f1887,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,null_class)
        | ~ subclass(complement(unordered_pair(u,u)),X1)
        | member(X0,X1) )
    | ~ spl0_37
    | ~ spl0_199 ),
    inference(resolution,[],[f1883,f340]) ).

fof(f1883,plain,
    ( ! [X0] :
        ( member(X0,complement(unordered_pair(u,u)))
        | ~ member(X0,universal_class)
        | member(X0,null_class) )
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f1882]) ).

fof(f32615,plain,
    ( spl0_1170
    | ~ spl0_118
    | ~ spl0_1141 ),
    inference(avatar_split_clause,[],[f32143,f32058,f921,f32612]) ).

fof(f32612,plain,
    ( spl0_1170
  <=> null_class = intersection(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f921,plain,
    ( spl0_118
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f32143,plain,
    ( null_class = intersection(subset_relation,universal_class)
    | ~ spl0_118
    | ~ spl0_1141 ),
    inference(duplicate_literal_removal,[],[f32121]) ).

fof(f32121,plain,
    ( null_class = intersection(subset_relation,universal_class)
    | null_class = intersection(subset_relation,universal_class)
    | ~ spl0_118
    | ~ spl0_1141 ),
    inference(resolution,[],[f32059,f922]) ).

fof(f922,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f921]) ).

fof(f32521,plain,
    ( spl0_1169
    | ~ spl0_281
    | ~ spl0_1107 ),
    inference(avatar_split_clause,[],[f28430,f28402,f3004,f32519]) ).

fof(f32519,plain,
    ( spl0_1169
  <=> ! [X0] : subclass(intersection(identity_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f3004,plain,
    ( spl0_281
  <=> ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f28402,plain,
    ( spl0_1107
  <=> ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f28430,plain,
    ( ! [X0] : subclass(intersection(identity_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_281
    | ~ spl0_1107 ),
    inference(duplicate_literal_removal,[],[f28407]) ).

fof(f28407,plain,
    ( ! [X0] :
        ( subclass(intersection(identity_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(intersection(identity_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_281
    | ~ spl0_1107 ),
    inference(resolution,[],[f28403,f3005]) ).

fof(f3005,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation)
        | subclass(intersection(identity_relation,X0),X1) )
    | ~ spl0_281 ),
    inference(avatar_component_clause,[],[f3004]) ).

fof(f28403,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_1107 ),
    inference(avatar_component_clause,[],[f28402]) ).

fof(f32517,plain,
    ( spl0_1168
    | ~ spl0_283
    | ~ spl0_1107 ),
    inference(avatar_split_clause,[],[f28429,f28402,f3013,f32515]) ).

fof(f32515,plain,
    ( spl0_1168
  <=> ! [X0] : subclass(intersection(X0,identity_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f3013,plain,
    ( spl0_283
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f28429,plain,
    ( ! [X0] : subclass(intersection(X0,identity_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_283
    | ~ spl0_1107 ),
    inference(duplicate_literal_removal,[],[f28408]) ).

fof(f28408,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,identity_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(intersection(X0,identity_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_283
    | ~ spl0_1107 ),
    inference(resolution,[],[f28403,f3014]) ).

fof(f3014,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation)
        | subclass(intersection(X0,identity_relation),X1) )
    | ~ spl0_283 ),
    inference(avatar_component_clause,[],[f3013]) ).

fof(f32513,plain,
    ( spl0_1167
    | ~ spl0_124
    | ~ spl0_1107 ),
    inference(avatar_split_clause,[],[f28427,f28402,f995,f32511]) ).

fof(f32511,plain,
    ( spl0_1167
  <=> ! [X0] : subclass(intersection(subset_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f995,plain,
    ( spl0_124
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f28427,plain,
    ( ! [X0] : subclass(intersection(subset_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_124
    | ~ spl0_1107 ),
    inference(duplicate_literal_removal,[],[f28410]) ).

fof(f28410,plain,
    ( ! [X0] :
        ( subclass(intersection(subset_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(intersection(subset_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_124
    | ~ spl0_1107 ),
    inference(resolution,[],[f28403,f996]) ).

fof(f996,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f995]) ).

fof(f32509,plain,
    ( ~ spl0_1166
    | ~ spl0_668
    | ~ spl0_1138 ),
    inference(avatar_split_clause,[],[f31993,f31982,f14915,f32506]) ).

fof(f32506,plain,
    ( spl0_1166
  <=> member(not_subclass_element(element_relation,successor_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f14915,plain,
    ( spl0_668
  <=> not_subclass_element(element_relation,successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,successor_relation)),first(not_subclass_element(element_relation,successor_relation))),unordered_pair(first(not_subclass_element(element_relation,successor_relation)),unordered_pair(second(not_subclass_element(element_relation,successor_relation)),second(not_subclass_element(element_relation,successor_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f31982,plain,
    ( spl0_1138
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f31993,plain,
    ( ~ member(not_subclass_element(element_relation,successor_relation),subset_relation)
    | ~ spl0_668
    | ~ spl0_1138 ),
    inference(superposition,[],[f31983,f14917]) ).

fof(f14917,plain,
    ( not_subclass_element(element_relation,successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,successor_relation)),first(not_subclass_element(element_relation,successor_relation))),unordered_pair(first(not_subclass_element(element_relation,successor_relation)),unordered_pair(second(not_subclass_element(element_relation,successor_relation)),second(not_subclass_element(element_relation,successor_relation)))))
    | ~ spl0_668 ),
    inference(avatar_component_clause,[],[f14915]) ).

fof(f31983,plain,
    ( ! [X0,X1] : ~ member(unordered_pair(X0,X1),subset_relation)
    | ~ spl0_1138 ),
    inference(avatar_component_clause,[],[f31982]) ).

fof(f32504,plain,
    ( spl0_1165
    | ~ spl0_125
    | ~ spl0_1107 ),
    inference(avatar_split_clause,[],[f28425,f28402,f999,f32502]) ).

fof(f32502,plain,
    ( spl0_1165
  <=> ! [X0] : subclass(intersection(X0,subset_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f999,plain,
    ( spl0_125
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f28425,plain,
    ( ! [X0] : subclass(intersection(X0,subset_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_125
    | ~ spl0_1107 ),
    inference(duplicate_literal_removal,[],[f28412]) ).

fof(f28412,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,subset_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(intersection(X0,subset_relation),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_125
    | ~ spl0_1107 ),
    inference(resolution,[],[f28403,f1000]) ).

fof(f1000,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f999]) ).

fof(f32480,plain,
    ( spl0_1164
    | ~ spl0_1077
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_342
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28105,f26983,f25938,f4167,f1202,f921,f856,f27039,f32478]) ).

fof(f32478,plain,
    ( spl0_1164
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f27039,plain,
    ( spl0_1077
  <=> subclass(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f1202,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f4167,plain,
    ( spl0_342
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f25938,plain,
    ( spl0_1063
  <=> member(regular(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f28105,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,universal_class)
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_342
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28104,f26985]) ).

fof(f28104,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(null_class))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_342
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24337,f25952]) ).

fof(f25952,plain,
    ( null_class = intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_118
    | spl0_1063 ),
    inference(resolution,[],[f25940,f922]) ).

fof(f25940,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),element_relation)
    | spl0_1063 ),
    inference(avatar_component_clause,[],[f25938]) ).

fof(f24337,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_342 ),
    inference(forward_demodulation,[],[f4570,f858]) ).

fof(f4570,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation) )
    | ~ spl0_140
    | ~ spl0_342 ),
    inference(resolution,[],[f4168,f1203]) ).

fof(f1203,plain,
    ( ! [X0] :
        ( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1202]) ).

fof(f4168,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | ~ member(X1,universal_class)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_342 ),
    inference(avatar_component_clause,[],[f4167]) ).

fof(f32476,plain,
    ( spl0_1163
    | ~ spl0_379
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f27802,f8271,f5441,f32474]) ).

fof(f32474,plain,
    ( spl0_1163
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,subset_relation))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f5441,plain,
    ( spl0_379
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f8271,plain,
    ( spl0_446
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f27802,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,subset_relation))),X1) )
    | ~ spl0_379
    | ~ spl0_446 ),
    inference(resolution,[],[f8272,f5442]) ).

fof(f5442,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,universal_class)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
    | ~ spl0_379 ),
    inference(avatar_component_clause,[],[f5441]) ).

fof(f8272,plain,
    ( member(subset_relation,universal_class)
    | ~ spl0_446 ),
    inference(avatar_component_clause,[],[f8271]) ).

fof(f32472,plain,
    ( spl0_1162
    | ~ spl0_97
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f13245,f5441,f732,f32470]) ).

fof(f32470,plain,
    ( spl0_1162
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,w))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f732,plain,
    ( spl0_97
  <=> member(w,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f13245,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,w))),X1) )
    | ~ spl0_97
    | ~ spl0_379 ),
    inference(resolution,[],[f5442,f734]) ).

fof(f734,plain,
    ( member(w,universal_class)
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f732]) ).

fof(f32468,plain,
    ( spl0_1161
    | ~ spl0_86
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f13244,f5441,f654,f32466]) ).

fof(f32466,plain,
    ( spl0_1161
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,v))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f654,plain,
    ( spl0_86
  <=> member(v,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f13244,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,v))),X1) )
    | ~ spl0_86
    | ~ spl0_379 ),
    inference(resolution,[],[f5442,f656]) ).

fof(f656,plain,
    ( member(v,universal_class)
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f654]) ).

fof(f32464,plain,
    ( spl0_1160
    | ~ spl0_70
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f13243,f5441,f553,f32462]) ).

fof(f32462,plain,
    ( spl0_1160
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,u))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f13243,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,u))),X1) )
    | ~ spl0_70
    | ~ spl0_379 ),
    inference(resolution,[],[f5442,f555]) ).

fof(f555,plain,
    ( member(u,universal_class)
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f553]) ).

fof(f32459,plain,
    ( spl0_367
    | ~ spl0_1159
    | spl0_1158
    | ~ spl0_110
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f12404,f8264,f856,f32445,f32456,f4776]) ).

fof(f4776,plain,
    ( spl0_367
  <=> element_relation = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f32456,plain,
    ( spl0_1159
  <=> member(regular(element_relation),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f32445,plain,
    ( spl0_1158
  <=> member(first(regular(element_relation)),second(regular(element_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f8264,plain,
    ( spl0_445
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),null_class)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f12404,plain,
    ( member(first(regular(element_relation)),second(regular(element_relation)))
    | ~ member(regular(element_relation),null_class)
    | element_relation = null_class
    | ~ spl0_110
    | ~ spl0_445 ),
    inference(superposition,[],[f8265,f858]) ).

fof(f8265,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(regular(cross_product(X0,X1)),null_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_445 ),
    inference(avatar_component_clause,[],[f8264]) ).

fof(f32448,plain,
    ( spl0_1156
    | ~ spl0_1157
    | spl0_1158
    | ~ spl0_110
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f12403,f7584,f856,f32445,f32441,f32437]) ).

fof(f32437,plain,
    ( spl0_1156
  <=> element_relation = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f32441,plain,
    ( spl0_1157
  <=> member(regular(element_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f7584,plain,
    ( spl0_443
  <=> ! [X0,X1] :
        ( cross_product(X0,X1) = subset_relation
        | ~ member(regular(cross_product(X0,X1)),subset_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f12403,plain,
    ( member(first(regular(element_relation)),second(regular(element_relation)))
    | ~ member(regular(element_relation),subset_relation)
    | element_relation = subset_relation
    | ~ spl0_110
    | ~ spl0_443 ),
    inference(superposition,[],[f7585,f858]) ).

fof(f7585,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(regular(cross_product(X0,X1)),subset_relation)
        | cross_product(X0,X1) = subset_relation )
    | ~ spl0_443 ),
    inference(avatar_component_clause,[],[f7584]) ).

fof(f32434,plain,
    ( ~ spl0_1155
    | ~ spl0_110
    | spl0_549 ),
    inference(avatar_split_clause,[],[f12351,f10814,f856,f32431]) ).

fof(f32431,plain,
    ( spl0_1155
  <=> null_class = complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f10814,plain,
    ( spl0_549
  <=> null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f12351,plain,
    ( null_class != complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_110
    | spl0_549 ),
    inference(superposition,[],[f10816,f858]) ).

fof(f10816,plain,
    ( null_class != complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | spl0_549 ),
    inference(avatar_component_clause,[],[f10814]) ).

fof(f32428,plain,
    ( spl0_1154
    | ~ spl0_110
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f12340,f6485,f856,f32425]) ).

fof(f32425,plain,
    ( spl0_1154
  <=> member(regular(subset_relation),intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f6485,plain,
    ( spl0_400
  <=> member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f12340,plain,
    ( member(regular(subset_relation),intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_400 ),
    inference(superposition,[],[f6487,f858]) ).

fof(f6487,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_400 ),
    inference(avatar_component_clause,[],[f6485]) ).

fof(f32423,plain,
    ( spl0_1153
    | ~ spl0_88
    | ~ spl0_380 ),
    inference(avatar_split_clause,[],[f5451,f5446,f668,f32421]) ).

fof(f32421,plain,
    ( spl0_1153
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(intersection(null_class,cross_product(universal_class,null_class))),X1)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f668,plain,
    ( spl0_88
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f5446,plain,
    ( spl0_380
  <=> ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,X1))),X2)
        | ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f5451,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(intersection(null_class,cross_product(universal_class,null_class))),X1)
        | ~ subclass(X0,X1) )
    | ~ spl0_88
    | ~ spl0_380 ),
    inference(resolution,[],[f5447,f669]) ).

fof(f669,plain,
    ( member(null_class,universal_class)
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f668]) ).

fof(f5447,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,universal_class)
        | ~ subclass(universal_class,X0)
        | member(domain_of(intersection(null_class,cross_product(universal_class,X1))),X2)
        | ~ subclass(X0,X2) )
    | ~ spl0_380 ),
    inference(avatar_component_clause,[],[f5446]) ).

fof(f32418,plain,
    ( spl0_1152
    | ~ spl0_230
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f24963,f24933,f2242,f32415]) ).

fof(f32415,plain,
    ( spl0_1152
  <=> subclass(identity_relation,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f24933,plain,
    ( spl0_1048
  <=> ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f24963,plain,
    ( subclass(identity_relation,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_1048 ),
    inference(duplicate_literal_removal,[],[f24936]) ).

fof(f24936,plain,
    ( subclass(identity_relation,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | subclass(identity_relation,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_1048 ),
    inference(resolution,[],[f24934,f2243]) ).

fof(f24934,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_1048 ),
    inference(avatar_component_clause,[],[f24933]) ).

fof(f32412,plain,
    ( ~ spl0_1151
    | ~ spl0_110
    | spl0_506 ),
    inference(avatar_split_clause,[],[f12347,f9927,f856,f32409]) ).

fof(f32409,plain,
    ( spl0_1151
  <=> subclass(universal_class,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f9927,plain,
    ( spl0_506
  <=> subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f12347,plain,
    ( ~ subclass(universal_class,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_110
    | spl0_506 ),
    inference(superposition,[],[f9929,f858]) ).

fof(f9929,plain,
    ( ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | spl0_506 ),
    inference(avatar_component_clause,[],[f9927]) ).

fof(f32391,plain,
    ( spl0_694
    | spl0_1149
    | spl0_1150
    | ~ spl0_250
    | ~ spl0_541 ),
    inference(avatar_split_clause,[],[f10580,f10571,f2469,f32389,f32386,f15763]) ).

fof(f15763,plain,
    ( spl0_694
  <=> member(second(null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f2469,plain,
    ( spl0_250
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f10580,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(null_class,compose(X0,X1))
        | ~ member(second(null_class),X2)
        | member(second(null_class),universal_class) )
    | ~ spl0_250
    | ~ spl0_541 ),
    inference(resolution,[],[f10572,f2470]) ).

fof(f2470,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,universal_class) )
    | ~ spl0_250 ),
    inference(avatar_component_clause,[],[f2469]) ).

fof(f32355,plain,
    ( ~ spl0_89
    | spl0_1057
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f32175,f26983,f25438,f672]) ).

fof(f672,plain,
    ( spl0_89
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f25438,plain,
    ( spl0_1057
  <=> inductive(complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f32175,plain,
    ( ~ inductive(universal_class)
    | spl0_1057
    | ~ spl0_1076 ),
    inference(superposition,[],[f25440,f26985]) ).

fof(f25440,plain,
    ( ~ inductive(complement(null_class))
    | spl0_1057 ),
    inference(avatar_component_clause,[],[f25438]) ).

fof(f32354,plain,
    ( ~ spl0_249
    | spl0_1148
    | ~ spl0_400
    | ~ spl0_493 ),
    inference(avatar_split_clause,[],[f9718,f9708,f6485,f32352,f2437]) ).

fof(f2437,plain,
    ( spl0_249
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f32352,plain,
    ( spl0_1148
  <=> ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f9708,plain,
    ( spl0_493
  <=> ! [X0,X1] :
        ( ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f9718,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
        | member(regular(subset_relation),X0) )
    | ~ spl0_400
    | ~ spl0_493 ),
    inference(resolution,[],[f9709,f6487]) ).

fof(f9709,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | member(X1,X0) )
    | ~ spl0_493 ),
    inference(avatar_component_clause,[],[f9708]) ).

fof(f32350,plain,
    ( spl0_716
    | ~ spl0_118
    | ~ spl0_230
    | ~ spl0_661
    | spl0_1063 ),
    inference(avatar_split_clause,[],[f26641,f25938,f13976,f2242,f921,f16077]) ).

fof(f16077,plain,
    ( spl0_716
  <=> subclass(identity_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f13976,plain,
    ( spl0_661
  <=> ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f26641,plain,
    ( subclass(identity_relation,null_class)
    | ~ spl0_118
    | ~ spl0_230
    | ~ spl0_661
    | spl0_1063 ),
    inference(forward_demodulation,[],[f26640,f25952]) ).

fof(f26640,plain,
    ( subclass(identity_relation,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_661 ),
    inference(duplicate_literal_removal,[],[f26613]) ).

fof(f26613,plain,
    ( subclass(identity_relation,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | subclass(identity_relation,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_661 ),
    inference(resolution,[],[f13977,f2243]) ).

fof(f13977,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_661 ),
    inference(avatar_component_clause,[],[f13976]) ).

fof(f32270,plain,
    ( spl0_1147
    | ~ spl0_230
    | ~ spl0_1107 ),
    inference(avatar_split_clause,[],[f28432,f28402,f2242,f32267]) ).

fof(f28432,plain,
    ( subclass(identity_relation,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_1107 ),
    inference(duplicate_literal_removal,[],[f28405]) ).

fof(f28405,plain,
    ( subclass(identity_relation,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | subclass(identity_relation,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_230
    | ~ spl0_1107 ),
    inference(resolution,[],[f28403,f2243]) ).

fof(f32265,plain,
    ( spl0_1146
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_320
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28008,f26983,f25938,f3534,f1202,f921,f856,f32263]) ).

fof(f32263,plain,
    ( spl0_1146
  <=> ! [X0,X1] :
        ( subclass(intersection(universal_class,X0),X1)
        | ~ member(not_subclass_element(intersection(universal_class,X0),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f3534,plain,
    ( spl0_320
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f28008,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(universal_class,X0),X1)
        | ~ member(not_subclass_element(intersection(universal_class,X0),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_320
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28007,f26985]) ).

fof(f28007,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(null_class),X0),X1)
        | ~ member(not_subclass_element(intersection(universal_class,X0),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_320
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28006,f25952]) ).

fof(f28006,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(universal_class,X0),X1),subset_relation)
        | subclass(intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_320
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28005,f26985]) ).

fof(f28005,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(null_class),X0),X1),subset_relation)
        | subclass(intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_320
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24270,f25952]) ).

fof(f24270,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1),subset_relation)
        | subclass(intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_320 ),
    inference(forward_demodulation,[],[f24269,f858]) ).

fof(f24269,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1)
        | ~ member(not_subclass_element(intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_320 ),
    inference(forward_demodulation,[],[f3834,f858]) ).

fof(f3834,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1)
        | ~ member(not_subclass_element(intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1),subset_relation) )
    | ~ spl0_140
    | ~ spl0_320 ),
    inference(resolution,[],[f3535,f1203]) ).

fof(f3535,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_320 ),
    inference(avatar_component_clause,[],[f3534]) ).

fof(f32261,plain,
    ( spl0_1145
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_321
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28004,f26983,f25938,f3538,f1202,f921,f856,f32259]) ).

fof(f32259,plain,
    ( spl0_1145
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,universal_class),X1)
        | ~ member(not_subclass_element(intersection(X0,universal_class),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f3538,plain,
    ( spl0_321
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f28004,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,universal_class),X1)
        | ~ member(not_subclass_element(intersection(X0,universal_class),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_321
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28003,f26985]) ).

fof(f28003,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(null_class)),X1)
        | ~ member(not_subclass_element(intersection(X0,universal_class),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_321
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28002,f25952]) ).

fof(f28002,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,universal_class),X1),subset_relation)
        | subclass(intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_321
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28001,f26985]) ).

fof(f28001,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(null_class)),X1),subset_relation)
        | subclass(intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_321
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24266,f25952]) ).

fof(f24266,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1),subset_relation)
        | subclass(intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_321 ),
    inference(forward_demodulation,[],[f24265,f858]) ).

fof(f24265,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_321 ),
    inference(forward_demodulation,[],[f3871,f858]) ).

fof(f3871,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1),subset_relation) )
    | ~ spl0_140
    | ~ spl0_321 ),
    inference(resolution,[],[f3539,f1203]) ).

fof(f3539,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f3538]) ).

fof(f32073,plain,
    ( ~ spl0_1143
    | spl0_1123
    | ~ spl0_1144
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_408
    | spl0_1063
    | ~ spl0_1110 ),
    inference(avatar_split_clause,[],[f29157,f28493,f25938,f6728,f921,f856,f533,f32070,f30148,f32066]) ).

fof(f32066,plain,
    ( spl0_1143
  <=> member(regular(universal_class),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f30148,plain,
    ( spl0_1123
  <=> universal_class = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f32070,plain,
    ( spl0_1144
  <=> member(regular(universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f533,plain,
    ( spl0_67
  <=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f6728,plain,
    ( spl0_408
  <=> ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f28493,plain,
    ( spl0_1110
  <=> universal_class = complement(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f29157,plain,
    ( ~ member(regular(universal_class),element_relation)
    | universal_class = null_class
    | ~ member(regular(universal_class),null_class)
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_408
    | spl0_1063
    | ~ spl0_1110 ),
    inference(forward_demodulation,[],[f29156,f28495]) ).

fof(f28495,plain,
    ( universal_class = complement(subset_relation)
    | ~ spl0_1110 ),
    inference(avatar_component_clause,[],[f28493]) ).

fof(f29156,plain,
    ( ~ member(regular(complement(subset_relation)),element_relation)
    | universal_class = null_class
    | ~ member(regular(universal_class),null_class)
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_408
    | spl0_1063
    | ~ spl0_1110 ),
    inference(forward_demodulation,[],[f29155,f858]) ).

fof(f29155,plain,
    ( universal_class = null_class
    | ~ member(regular(universal_class),null_class)
    | ~ member(regular(complement(subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_408
    | spl0_1063
    | ~ spl0_1110 ),
    inference(forward_demodulation,[],[f29154,f28495]) ).

fof(f29154,plain,
    ( ~ member(regular(universal_class),null_class)
    | null_class = complement(subset_relation)
    | ~ member(regular(complement(subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_408
    | spl0_1063
    | ~ spl0_1110 ),
    inference(forward_demodulation,[],[f27067,f28495]) ).

fof(f27067,plain,
    ( ~ member(regular(complement(subset_relation)),null_class)
    | null_class = complement(subset_relation)
    | ~ member(regular(complement(subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_408
    | spl0_1063 ),
    inference(forward_demodulation,[],[f27066,f25952]) ).

fof(f27066,plain,
    ( ~ member(regular(complement(subset_relation)),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = complement(subset_relation)
    | ~ member(regular(complement(subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_408 ),
    inference(forward_demodulation,[],[f6834,f858]) ).

fof(f6834,plain,
    ( ~ member(regular(complement(subset_relation)),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = complement(subset_relation)
    | ~ member(regular(complement(subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_67
    | ~ spl0_408 ),
    inference(superposition,[],[f6729,f535]) ).

fof(f535,plain,
    ( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f533]) ).

fof(f6729,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(complement(intersection(X0,X1))),X1)
        | complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_408 ),
    inference(avatar_component_clause,[],[f6728]) ).

fof(f32064,plain,
    ( spl0_1142
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_303
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28118,f26983,f25938,f3283,f1202,f921,f856,f32062]) ).

fof(f3283,plain,
    ( spl0_303
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f28118,plain,
    ( ! [X0] :
        ( null_class = intersection(universal_class,X0)
        | ~ member(regular(intersection(universal_class,X0)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_303
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28117,f26985]) ).

fof(f28117,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(null_class),X0)
        | ~ member(regular(intersection(universal_class,X0)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_303
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28116,f25952]) ).

fof(f28116,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(universal_class,X0)),subset_relation)
        | null_class = intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_303
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28115,f26985]) ).

fof(f28115,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(complement(null_class),X0)),subset_relation)
        | null_class = intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_303
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24366,f25952]) ).

fof(f24366,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)),subset_relation)
        | null_class = intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_303 ),
    inference(forward_demodulation,[],[f24365,f858]) ).

fof(f24365,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)
        | ~ member(regular(intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_303 ),
    inference(forward_demodulation,[],[f3386,f858]) ).

fof(f3386,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)
        | ~ member(regular(intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)),subset_relation) )
    | ~ spl0_140
    | ~ spl0_303 ),
    inference(resolution,[],[f3284,f1203]) ).

fof(f3284,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(complement(X0),X1)),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_303 ),
    inference(avatar_component_clause,[],[f3283]) ).

fof(f32060,plain,
    ( spl0_1141
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_304
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28113,f26983,f25938,f3287,f1202,f921,f856,f32058]) ).

fof(f3287,plain,
    ( spl0_304
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f28113,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,universal_class)
        | ~ member(regular(intersection(X0,universal_class)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_304
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28112,f26985]) ).

fof(f28112,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(null_class))
        | ~ member(regular(intersection(X0,universal_class)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_304
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28111,f25952]) ).

fof(f28111,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,universal_class)),subset_relation)
        | null_class = intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_304
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28110,f26985]) ).

fof(f28110,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,complement(null_class))),subset_relation)
        | null_class = intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_304
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24361,f25952]) ).

fof(f24361,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))),subset_relation)
        | null_class = intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_304 ),
    inference(forward_demodulation,[],[f24360,f858]) ).

fof(f24360,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(regular(intersection(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_304 ),
    inference(forward_demodulation,[],[f3412,f858]) ).

fof(f3412,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(regular(intersection(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))),subset_relation) )
    | ~ spl0_140
    | ~ spl0_304 ),
    inference(resolution,[],[f3288,f1203]) ).

fof(f3288,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,complement(X1))),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_304 ),
    inference(avatar_component_clause,[],[f3287]) ).

fof(f32056,plain,
    ( spl0_1140
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_278
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28010,f26983,f25938,f2992,f1202,f921,f856,f32054]) ).

fof(f32054,plain,
    ( spl0_1140
  <=> ! [X0,X1] :
        ( ~ subclass(X0,universal_class)
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f2992,plain,
    ( spl0_278
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f28010,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,universal_class)
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_278
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28009,f26985]) ).

fof(f28009,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(null_class))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_278
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24272,f25952]) ).

fof(f24272,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_278 ),
    inference(forward_demodulation,[],[f3094,f858]) ).

fof(f3094,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_140
    | ~ spl0_278 ),
    inference(resolution,[],[f2993,f1203]) ).

fof(f2993,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f2992]) ).

fof(f32005,plain,
    ( spl0_1139
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_263
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28109,f26983,f25938,f2753,f1202,f921,f856,f32003]) ).

fof(f32003,plain,
    ( spl0_1139
  <=> ! [X0] :
        ( ~ subclass(X0,universal_class)
        | null_class = X0
        | ~ member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f2753,plain,
    ( spl0_263
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f28109,plain,
    ( ! [X0] :
        ( ~ subclass(X0,universal_class)
        | null_class = X0
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_263
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28108,f26985]) ).

fof(f28108,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(null_class))
        | null_class = X0
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_263
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24357,f25952]) ).

fof(f24357,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | null_class = X0
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_263 ),
    inference(forward_demodulation,[],[f2903,f858]) ).

fof(f2903,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_140
    | ~ spl0_263 ),
    inference(resolution,[],[f2754,f1203]) ).

fof(f2754,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2753]) ).

fof(f31984,plain,
    ( spl0_1138
    | ~ spl0_1077
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_247
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28053,f26983,f25938,f2429,f1202,f921,f856,f27039,f31982]) ).

fof(f2429,plain,
    ( spl0_247
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f28053,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,universal_class)
        | ~ member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_247
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28052,f26985]) ).

fof(f28052,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(null_class))
        | ~ member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_247
    | spl0_1063 ),
    inference(forward_demodulation,[],[f24312,f25952]) ).

fof(f24312,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_247 ),
    inference(forward_demodulation,[],[f2482,f858]) ).

fof(f2482,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_140
    | ~ spl0_247 ),
    inference(resolution,[],[f2430,f1203]) ).

fof(f2430,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f2429]) ).

fof(f31943,plain,
    ( ~ spl0_828
    | ~ spl0_118
    | spl0_634
    | spl0_711 ),
    inference(avatar_split_clause,[],[f31942,f15972,f13109,f921,f19096]) ).

fof(f19096,plain,
    ( spl0_828
  <=> member(regular(subset_relation),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f13109,plain,
    ( spl0_634
  <=> member(regular(subset_relation),intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f15972,plain,
    ( spl0_711
  <=> member(regular(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f31942,plain,
    ( ~ member(regular(subset_relation),null_class)
    | ~ spl0_118
    | spl0_634
    | spl0_711 ),
    inference(forward_demodulation,[],[f13110,f15981]) ).

fof(f15981,plain,
    ( null_class = intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_118
    | spl0_711 ),
    inference(resolution,[],[f15974,f922]) ).

fof(f15974,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),element_relation)
    | spl0_711 ),
    inference(avatar_component_clause,[],[f15972]) ).

fof(f13110,plain,
    ( ~ member(regular(subset_relation),intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_634 ),
    inference(avatar_component_clause,[],[f13109]) ).

fof(f31941,plain,
    ( spl0_248
    | ~ spl0_1137
    | ~ spl0_118
    | ~ spl0_263
    | ~ spl0_634
    | spl0_711
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27987,f26983,f15972,f13109,f2753,f921,f31885,f2433]) ).

fof(f2433,plain,
    ( spl0_248
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f31885,plain,
    ( spl0_1137
  <=> subclass(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f27987,plain,
    ( ~ subclass(subset_relation,universal_class)
    | null_class = subset_relation
    | ~ spl0_118
    | ~ spl0_263
    | ~ spl0_634
    | spl0_711
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f24483,f26985]) ).

fof(f24483,plain,
    ( ~ subclass(subset_relation,complement(null_class))
    | null_class = subset_relation
    | ~ spl0_118
    | ~ spl0_263
    | ~ spl0_634
    | spl0_711 ),
    inference(forward_demodulation,[],[f13114,f15981]) ).

fof(f13114,plain,
    ( null_class = subset_relation
    | ~ subclass(subset_relation,complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
    | ~ spl0_263
    | ~ spl0_634 ),
    inference(resolution,[],[f13111,f2754]) ).

fof(f13111,plain,
    ( member(regular(subset_relation),intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_634 ),
    inference(avatar_component_clause,[],[f13109]) ).

fof(f31890,plain,
    ( ~ spl0_6
    | spl0_1137 ),
    inference(avatar_contradiction_clause,[],[f31889]) ).

fof(f31889,plain,
    ( $false
    | ~ spl0_6
    | spl0_1137 ),
    inference(resolution,[],[f31887,f198]) ).

fof(f198,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f197]) ).

fof(f197,plain,
    ( spl0_6
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f31887,plain,
    ( ~ subclass(subset_relation,universal_class)
    | spl0_1137 ),
    inference(avatar_component_clause,[],[f31885]) ).

fof(f31888,plain,
    ( spl0_1136
    | ~ spl0_1137
    | ~ spl0_118
    | ~ spl0_278
    | ~ spl0_646
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27950,f26983,f25938,f13381,f2992,f921,f31885,f31882]) ).

fof(f31882,plain,
    ( spl0_1136
  <=> ! [X0] : subclass(subset_relation,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f13381,plain,
    ( spl0_646
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f27950,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,universal_class)
        | subclass(subset_relation,X0) )
    | ~ spl0_118
    | ~ spl0_278
    | ~ spl0_646
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f26195,f26985]) ).

fof(f26195,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,complement(null_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_118
    | ~ spl0_278
    | ~ spl0_646
    | spl0_1063 ),
    inference(forward_demodulation,[],[f26191,f25952]) ).

fof(f26191,plain,
    ( ! [X0] :
        ( subclass(subset_relation,X0)
        | ~ subclass(subset_relation,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) )
    | ~ spl0_278
    | ~ spl0_646 ),
    inference(duplicate_literal_removal,[],[f26177]) ).

fof(f26177,plain,
    ( ! [X0] :
        ( subclass(subset_relation,X0)
        | subclass(subset_relation,X0)
        | ~ subclass(subset_relation,complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) )
    | ~ spl0_278
    | ~ spl0_646 ),
    inference(resolution,[],[f13382,f2993]) ).

fof(f13382,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_646 ),
    inference(avatar_component_clause,[],[f13381]) ).

fof(f31456,plain,
    ( ~ spl0_1135
    | spl0_670
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29348,f26983,f15005,f31453]) ).

fof(f31453,plain,
    ( spl0_1135
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f15005,plain,
    ( spl0_670
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f29348,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))))))),subset_relation)
    | spl0_670
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f15007,f26985]) ).

fof(f15007,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),subset_relation)
    | spl0_670 ),
    inference(avatar_component_clause,[],[f15005]) ).

fof(f31165,plain,
    ( ~ spl0_361
    | ~ spl0_858
    | ~ spl0_1066 ),
    inference(avatar_split_clause,[],[f26667,f26206,f19509,f4702]) ).

fof(f19509,plain,
    ( spl0_858
  <=> ! [X0] :
        ( ~ member(u,X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f26206,plain,
    ( spl0_1066
  <=> subclass(universal_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f26667,plain,
    ( ~ member(u,null_class)
    | ~ spl0_858
    | ~ spl0_1066 ),
    inference(resolution,[],[f26208,f19510]) ).

fof(f19510,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(u,X0) )
    | ~ spl0_858 ),
    inference(avatar_component_clause,[],[f19509]) ).

fof(f26208,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_1066 ),
    inference(avatar_component_clause,[],[f26206]) ).

fof(f31132,plain,
    ( spl0_1134
    | ~ spl0_514
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29451,f26983,f10114,f31130]) ).

fof(f31130,plain,
    ( spl0_1134
  <=> ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f10114,plain,
    ( spl0_514
  <=> ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f29451,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_514
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29450,f26985]) ).

fof(f29450,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class)
        | null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_514
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29449,f26985]) ).

fof(f29449,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_514
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f10115,f26985]) ).

fof(f10115,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_514 ),
    inference(avatar_component_clause,[],[f10114]) ).

fof(f31128,plain,
    ( spl0_1133
    | ~ spl0_516
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29438,f26983,f10129,f31126]) ).

fof(f31126,plain,
    ( spl0_1133
  <=> ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f10129,plain,
    ( spl0_516
  <=> ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f29438,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_516
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29437,f26985]) ).

fof(f29437,plain,
    ( ! [X0] :
        ( ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class)
        | null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_516
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29436,f26985]) ).

fof(f29436,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_516
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f10130,f26985]) ).

fof(f10130,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_516 ),
    inference(avatar_component_clause,[],[f10129]) ).

fof(f31117,plain,
    ( spl0_1130
    | ~ spl0_1131
    | ~ spl0_1132
    | ~ spl0_74
    | ~ spl0_1114 ),
    inference(avatar_split_clause,[],[f29712,f29703,f575,f31114,f31110,f31106]) ).

fof(f31106,plain,
    ( spl0_1130
  <=> null_class = intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f31110,plain,
    ( spl0_1131
  <=> member(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f31114,plain,
    ( spl0_1132
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)),universal_class))))))),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f575,plain,
    ( spl0_74
  <=> ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f29703,plain,
    ( spl0_1114
  <=> ! [X0] :
        ( ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(X0,null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f29712,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)),universal_class))))))),null_class)
    | ~ member(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),universal_class)
    | null_class = intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))
    | ~ spl0_74
    | ~ spl0_1114 ),
    inference(resolution,[],[f29704,f576]) ).

fof(f576,plain,
    ( ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f575]) ).

fof(f29704,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(X0,null_class) )
    | ~ spl0_1114 ),
    inference(avatar_component_clause,[],[f29703]) ).

fof(f31043,plain,
    ( spl0_1129
    | ~ spl0_515
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29426,f26983,f10122,f31041]) ).

fof(f31041,plain,
    ( spl0_1129
  <=> ! [X0] :
        ( null_class = intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)
        | ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f10122,plain,
    ( spl0_515
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f29426,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)
        | ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_515
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29425,f26985]) ).

fof(f29425,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),universal_class)
        | ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_515
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29424,f26985]) ).

fof(f29424,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),intersection(X0,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_515
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f10123,f26985]) ).

fof(f10123,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_515 ),
    inference(avatar_component_clause,[],[f10122]) ).

fof(f31039,plain,
    ( spl0_1128
    | ~ spl0_517
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29422,f26983,f10137,f31037]) ).

fof(f31037,plain,
    ( spl0_1128
  <=> ! [X0] :
        ( null_class = intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),universal_class)
        | ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f10137,plain,
    ( spl0_517
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f29422,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),universal_class)
        | ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_517
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29421,f26985]) ).

fof(f29421,plain,
    ( ! [X0] :
        ( ~ member(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),universal_class)
        | ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_517
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29420,f26985]) ).

fof(f29420,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),intersection(intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_517
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f10138,f26985]) ).

fof(f10138,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_517 ),
    inference(avatar_component_clause,[],[f10137]) ).

fof(f30999,plain,
    ( spl0_743
    | ~ spl0_118
    | spl0_1063
    | ~ spl0_1070 ),
    inference(avatar_split_clause,[],[f29174,f26723,f25938,f921,f16975]) ).

fof(f16975,plain,
    ( spl0_743
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,null_class)),subset_relation)
        | subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f26723,plain,
    ( spl0_1070
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | subclass(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f29174,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1)
        | subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),subset_relation) )
    | ~ spl0_118
    | spl0_1063
    | ~ spl0_1070 ),
    inference(forward_demodulation,[],[f29173,f25952]) ).

fof(f29173,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),subset_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_118
    | spl0_1063
    | ~ spl0_1070 ),
    inference(forward_demodulation,[],[f26726,f25952]) ).

fof(f26726,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,null_class)),subset_relation)
        | subclass(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_118
    | spl0_1063
    | ~ spl0_1070 ),
    inference(forward_demodulation,[],[f26724,f25952]) ).

fof(f26724,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | subclass(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_1070 ),
    inference(avatar_component_clause,[],[f26723]) ).

fof(f30773,plain,
    ( spl0_1127
    | ~ spl0_346
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29468,f26983,f4637,f30771]) ).

fof(f30771,plain,
    ( spl0_1127
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ compatible(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f4637,plain,
    ( spl0_346
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f29468,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ compatible(X0,X1,X2) )
    | ~ spl0_346
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f4638,f26985]) ).

fof(f4638,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ operation(X2)
        | ~ compatible(X0,X1,X2) )
    | ~ spl0_346 ),
    inference(avatar_component_clause,[],[f4637]) ).

fof(f30484,plain,
    ( spl0_1126
    | ~ spl0_347
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29467,f26983,f4642,f30482]) ).

fof(f30482,plain,
    ( spl0_1126
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f4642,plain,
    ( spl0_347
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f29467,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(universal_class,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2) )
    | ~ spl0_347
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f4643,f26985]) ).

fof(f4643,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ subclass(domain_of(X1),intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_347 ),
    inference(avatar_component_clause,[],[f4642]) ).

fof(f30199,plain,
    ( spl0_1125
    | ~ spl0_293
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29503,f26983,f3221,f30197]) ).

fof(f30197,plain,
    ( spl0_1125
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),X1),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f3221,plain,
    ( spl0_293
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f29503,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),X1),null_class) )
    | ~ spl0_293
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29502,f26985]) ).

fof(f29502,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),X1),null_class)
        | subclass(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1) )
    | ~ spl0_293
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f3222,f26985]) ).

fof(f3222,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1),null_class)
        | subclass(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1) )
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f3221]) ).

fof(f30195,plain,
    ( spl0_1124
    | ~ spl0_292
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29500,f26983,f3217,f30193]) ).

fof(f30193,plain,
    ( spl0_1124
  <=> ! [X0,X1] :
        ( subclass(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),X1)
        | ~ member(not_subclass_element(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),X1),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f3217,plain,
    ( spl0_292
  <=> ! [X0,X1] :
        ( subclass(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1)
        | ~ member(not_subclass_element(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f29500,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),X1)
        | ~ member(not_subclass_element(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),X1),null_class) )
    | ~ spl0_292
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29499,f26985]) ).

fof(f29499,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),X1),null_class)
        | subclass(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1) )
    | ~ spl0_292
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f3218,f26985]) ).

fof(f3218,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1),null_class)
        | subclass(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1) )
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f3217]) ).

fof(f30151,plain,
    ( ~ spl0_1123
    | spl0_500
    | ~ spl0_1110 ),
    inference(avatar_split_clause,[],[f29087,f28493,f9870,f30148]) ).

fof(f9870,plain,
    ( spl0_500
  <=> null_class = complement(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f29087,plain,
    ( universal_class != null_class
    | spl0_500
    | ~ spl0_1110 ),
    inference(superposition,[],[f9871,f28495]) ).

fof(f9871,plain,
    ( null_class != complement(subset_relation)
    | spl0_500 ),
    inference(avatar_component_clause,[],[f9870]) ).

fof(f30146,plain,
    ( spl0_1122
    | ~ spl0_291
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29405,f26983,f3202,f30144]) ).

fof(f30144,plain,
    ( spl0_1122
  <=> ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(regular(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f3202,plain,
    ( spl0_291
  <=> ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(regular(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f29405,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(regular(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),null_class) )
    | ~ spl0_291
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29404,f26985]) ).

fof(f29404,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))),null_class)
        | null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_291
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f3203,f26985]) ).

fof(f3203,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f3202]) ).

fof(f30142,plain,
    ( spl0_1121
    | ~ spl0_290
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29395,f26983,f3198,f30140]) ).

fof(f30140,plain,
    ( spl0_1121
  <=> ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(regular(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f3198,plain,
    ( spl0_290
  <=> ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)
        | ~ member(regular(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f29395,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(regular(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),null_class) )
    | ~ spl0_290
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29394,f26985]) ).

fof(f29394,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)),null_class)
        | null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_290
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f3199,f26985]) ).

fof(f3199,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),null_class)
        | null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_290 ),
    inference(avatar_component_clause,[],[f3198]) ).

fof(f30125,plain,
    ( spl0_1120
    | ~ spl0_274
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29466,f26983,f2967,f30123]) ).

fof(f30123,plain,
    ( spl0_1120
  <=> ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f2967,plain,
    ( spl0_274
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f29466,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_274
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f2968,f26985]) ).

fof(f2968,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2967]) ).

fof(f30112,plain,
    ( spl0_1119
    | ~ spl0_273
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29508,f26983,f2962,f30110]) ).

fof(f30110,plain,
    ( spl0_1119
  <=> ! [X0] :
        ( subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(not_subclass_element(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f2962,plain,
    ( spl0_273
  <=> ! [X0] :
        ( ~ member(not_subclass_element(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),null_class)
        | subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f29508,plain,
    ( ! [X0] :
        ( subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0)
        | ~ member(not_subclass_element(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),null_class) )
    | ~ spl0_273
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f29507,f26985]) ).

fof(f29507,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),X0),null_class)
        | subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_273
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f2963,f26985]) ).

fof(f2963,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),null_class)
        | subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_273 ),
    inference(avatar_component_clause,[],[f2962]) ).

fof(f29937,plain,
    ( spl0_1118
    | ~ spl0_225
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29497,f26983,f2182,f29935]) ).

fof(f29935,plain,
    ( spl0_1118
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f2182,plain,
    ( spl0_225
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f29497,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),null_class) )
    | ~ spl0_225
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f2183,f26985]) ).

fof(f2183,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),null_class) )
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f2182]) ).

fof(f29920,plain,
    ( spl0_1117
    | ~ spl0_223
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29418,f26983,f2159,f29918]) ).

fof(f29918,plain,
    ( spl0_1117
  <=> ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | null_class = X0
        | ~ member(regular(X0),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f2159,plain,
    ( spl0_223
  <=> ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | null_class = X0
        | ~ member(regular(X0),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f29418,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | null_class = X0
        | ~ member(regular(X0),null_class) )
    | ~ spl0_223
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f2160,f26985]) ).

fof(f2160,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | null_class = X0
        | ~ member(regular(X0),null_class) )
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2159]) ).

fof(f29916,plain,
    ( ~ spl0_1116
    | spl0_215
    | ~ spl0_99
    | ~ spl0_1114 ),
    inference(avatar_split_clause,[],[f29737,f29703,f746,f2098,f29913]) ).

fof(f29913,plain,
    ( spl0_1116
  <=> subclass(universal_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f2098,plain,
    ( spl0_215
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f746,plain,
    ( spl0_99
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f29737,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),null_class)
        | ~ subclass(universal_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))) )
    | ~ spl0_99
    | ~ spl0_1114 ),
    inference(resolution,[],[f29704,f747]) ).

fof(f747,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f746]) ).

fof(f29908,plain,
    ( ~ spl0_1115
    | spl0_272
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29393,f26983,f2956,f29905]) ).

fof(f29905,plain,
    ( spl0_1115
  <=> member(regular(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f2956,plain,
    ( spl0_272
  <=> member(regular(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f29393,plain,
    ( ~ member(regular(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),null_class)
    | spl0_272
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f2958,f26985]) ).

fof(f2958,plain,
    ( ~ member(regular(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
    | spl0_272 ),
    inference(avatar_component_clause,[],[f2956]) ).

fof(f29705,plain,
    ( spl0_1114
    | ~ spl0_93
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f29519,f26983,f701,f29703]) ).

fof(f701,plain,
    ( spl0_93
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f29519,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))))
        | ~ member(X0,null_class) )
    | ~ spl0_93
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f702,f26985]) ).

fof(f702,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(X0,null_class) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f701]) ).

fof(f29123,plain,
    ( ~ spl0_1024
    | ~ spl0_1113 ),
    inference(avatar_contradiction_clause,[],[f29119]) ).

fof(f29119,plain,
    ( $false
    | ~ spl0_1024
    | ~ spl0_1113 ),
    inference(resolution,[],[f29113,f22547]) ).

fof(f22547,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_1024 ),
    inference(avatar_component_clause,[],[f22546]) ).

fof(f22546,plain,
    ( spl0_1024
  <=> ! [X0] : ~ member(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f29113,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),null_class)
    | ~ spl0_1113 ),
    inference(avatar_component_clause,[],[f29111]) ).

fof(f29111,plain,
    ( spl0_1113
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f29114,plain,
    ( ~ spl0_446
    | spl0_248
    | spl0_1113
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_170
    | spl0_1063 ),
    inference(avatar_split_clause,[],[f27911,f25938,f1461,f921,f856,f533,f29111,f2433,f8271]) ).

fof(f1461,plain,
    ( spl0_170
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f27911,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),null_class)
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_170
    | spl0_1063 ),
    inference(forward_demodulation,[],[f27910,f25952]) ).

fof(f27910,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_170 ),
    inference(forward_demodulation,[],[f1485,f858]) ).

fof(f1485,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_67
    | ~ spl0_170 ),
    inference(superposition,[],[f1462,f535]) ).

fof(f1462,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class) )
    | ~ spl0_170 ),
    inference(avatar_component_clause,[],[f1461]) ).

fof(f29101,plain,
    ( ~ spl0_446
    | spl0_248
    | spl0_1112
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f27909,f1465,f856,f533,f29098,f2433,f8271]) ).

fof(f29098,plain,
    ( spl0_1112
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f1465,plain,
    ( spl0_171
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f27909,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),element_relation)
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_67
    | ~ spl0_110
    | ~ spl0_171 ),
    inference(forward_demodulation,[],[f1503,f858]) ).

fof(f1503,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_67
    | ~ spl0_171 ),
    inference(superposition,[],[f1466,f535]) ).

fof(f1466,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1465]) ).

fof(f29066,plain,
    ( ~ spl0_898
    | ~ spl0_118
    | spl0_1061
    | spl0_1063 ),
    inference(avatar_split_clause,[],[f28085,f25938,f25786,f921,f20180]) ).

fof(f20180,plain,
    ( spl0_898
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(null_class,null_class),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f25786,plain,
    ( spl0_1061
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f28085,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(null_class,null_class),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_118
    | spl0_1061
    | spl0_1063 ),
    inference(forward_demodulation,[],[f25788,f25952]) ).

fof(f25788,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
    | spl0_1061 ),
    inference(avatar_component_clause,[],[f25786]) ).

fof(f28921,plain,
    ( ~ spl0_1111
    | spl0_1058
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28058,f26983,f25459,f28918]) ).

fof(f28918,plain,
    ( spl0_1111
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),unordered_pair(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f25459,plain,
    ( spl0_1058
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(null_class),complement(null_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f28058,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class))))))),unordered_pair(universal_class,universal_class))),subset_relation)
    | spl0_1058
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f25461,f26985]) ).

fof(f25461,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(null_class),complement(null_class)))),subset_relation)
    | spl0_1058 ),
    inference(avatar_component_clause,[],[f25459]) ).

fof(f28613,plain,
    ( spl0_1053
    | ~ spl0_118
    | ~ spl0_647
    | spl0_1063 ),
    inference(avatar_split_clause,[],[f27991,f25938,f13388,f921,f25052]) ).

fof(f25052,plain,
    ( spl0_1053
  <=> ! [X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f13388,plain,
    ( spl0_647
  <=> ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f27991,plain,
    ( ! [X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_118
    | ~ spl0_647
    | spl0_1063 ),
    inference(forward_demodulation,[],[f13389,f25952]) ).

fof(f13389,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_647 ),
    inference(avatar_component_clause,[],[f13388]) ).

fof(f28496,plain,
    ( spl0_1110
    | ~ spl0_91
    | ~ spl0_1078 ),
    inference(avatar_split_clause,[],[f27080,f27074,f682,f28493]) ).

fof(f682,plain,
    ( spl0_91
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f27074,plain,
    ( spl0_1078
  <=> subclass(universal_class,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f27080,plain,
    ( universal_class = complement(subset_relation)
    | ~ spl0_91
    | ~ spl0_1078 ),
    inference(resolution,[],[f27076,f683]) ).

fof(f683,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f682]) ).

fof(f27076,plain,
    ( subclass(universal_class,complement(subset_relation))
    | ~ spl0_1078 ),
    inference(avatar_component_clause,[],[f27074]) ).

fof(f28477,plain,
    ( spl0_1051
    | ~ spl0_118
    | ~ spl0_661
    | spl0_1063 ),
    inference(avatar_split_clause,[],[f28035,f25938,f13976,f921,f24987]) ).

fof(f24987,plain,
    ( spl0_1051
  <=> ! [X0] :
        ( subclass(X0,null_class)
        | ~ member(not_subclass_element(X0,null_class),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f28035,plain,
    ( ! [X0] :
        ( subclass(X0,null_class)
        | ~ member(not_subclass_element(X0,null_class),subset_relation) )
    | ~ spl0_118
    | ~ spl0_661
    | spl0_1063 ),
    inference(forward_demodulation,[],[f28034,f25952]) ).

fof(f28034,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,null_class),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_118
    | ~ spl0_661
    | spl0_1063 ),
    inference(forward_demodulation,[],[f13977,f25952]) ).

fof(f28476,plain,
    ( spl0_1109
    | ~ spl0_110
    | ~ spl0_259 ),
    inference(avatar_split_clause,[],[f27929,f2682,f856,f28474]) ).

fof(f28474,plain,
    ( spl0_1109
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),element_relation)
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f2682,plain,
    ( spl0_259
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f27929,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),element_relation)
        | subclass(subset_relation,X0) )
    | ~ spl0_110
    | ~ spl0_259 ),
    inference(forward_demodulation,[],[f2683,f858]) ).

fof(f2683,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_259 ),
    inference(avatar_component_clause,[],[f2682]) ).

fof(f28436,plain,
    ( spl0_1108
    | ~ spl0_1049
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27994,f26983,f24965,f28434]) ).

fof(f28434,plain,
    ( spl0_1108
  <=> ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f24965,plain,
    ( spl0_1049
  <=> ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f27994,plain,
    ( ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) )
    | ~ spl0_1049
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27993,f26985]) ).

fof(f27993,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0) )
    | ~ spl0_1049
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f24966,f26985]) ).

fof(f24966,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0) )
    | ~ spl0_1049 ),
    inference(avatar_component_clause,[],[f24965]) ).

fof(f28404,plain,
    ( spl0_1107
    | ~ spl0_1048
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28033,f26983,f24933,f28402]) ).

fof(f28033,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation) )
    | ~ spl0_1048
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28032,f26985]) ).

fof(f28032,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_1048
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f24934,f26985]) ).

fof(f28325,plain,
    ( spl0_1106
    | ~ spl0_118
    | ~ spl0_641
    | spl0_1063 ),
    inference(avatar_split_clause,[],[f27990,f25938,f13231,f921,f28323]) ).

fof(f28323,plain,
    ( spl0_1106
  <=> ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f13231,plain,
    ( spl0_641
  <=> ! [X0] :
        ( member(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f27990,plain,
    ( ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,subset_relation) )
    | ~ spl0_118
    | ~ spl0_641
    | spl0_1063 ),
    inference(forward_demodulation,[],[f13232,f25952]) ).

fof(f13232,plain,
    ( ! [X0] :
        ( member(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_641 ),
    inference(avatar_component_clause,[],[f13231]) ).

fof(f28246,plain,
    ( ~ spl0_1105
    | spl0_839
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28103,f26983,f19233,f28243]) ).

fof(f28243,plain,
    ( spl0_1105
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f19233,plain,
    ( spl0_839
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(null_class),complement(null_class)),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f28103,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation)
    | spl0_839
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f19235,f26985]) ).

fof(f19235,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(null_class),complement(null_class)),universal_class)),universal_class))))))),subset_relation)
    | spl0_839 ),
    inference(avatar_component_clause,[],[f19233]) ).

fof(f28222,plain,
    ( spl0_1104
    | ~ spl0_110
    | ~ spl0_410
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27935,f26983,f6737,f856,f28220]) ).

fof(f28220,plain,
    ( spl0_1104
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f6737,plain,
    ( spl0_410
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f27935,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_110
    | ~ spl0_410
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27934,f858]) ).

fof(f27934,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_410
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f6738,f26985]) ).

fof(f6738,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_410 ),
    inference(avatar_component_clause,[],[f6737]) ).

fof(f28216,plain,
    ( ~ spl0_1043
    | ~ spl0_118
    | spl0_1063
    | spl0_1064 ),
    inference(avatar_split_clause,[],[f28114,f25943,f25938,f921,f24825]) ).

fof(f24825,plain,
    ( spl0_1043
  <=> member(regular(null_class),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f25943,plain,
    ( spl0_1064
  <=> member(regular(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f28114,plain,
    ( ~ member(regular(null_class),subset_relation)
    | ~ spl0_118
    | spl0_1063
    | spl0_1064 ),
    inference(forward_demodulation,[],[f25945,f25952]) ).

fof(f25945,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | spl0_1064 ),
    inference(avatar_component_clause,[],[f25943]) ).

fof(f28213,plain,
    ( ~ spl0_1103
    | spl0_1042
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28128,f26983,f24818,f28210]) ).

fof(f28210,plain,
    ( spl0_1103
  <=> member(regular(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f24818,plain,
    ( spl0_1042
  <=> member(regular(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f28128,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation)
    | spl0_1042
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f24820,f26985]) ).

fof(f24820,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation)
    | spl0_1042 ),
    inference(avatar_component_clause,[],[f24818]) ).

fof(f28199,plain,
    ( spl0_1102
    | ~ spl0_118
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27998,f26983,f25938,f14191,f921,f28197]) ).

fof(f28197,plain,
    ( spl0_1102
  <=> ! [X0] :
        ( subclass(universal_class,X0)
        | ~ member(not_subclass_element(universal_class,X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f14191,plain,
    ( spl0_663
  <=> ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f27998,plain,
    ( ! [X0] :
        ( subclass(universal_class,X0)
        | ~ member(not_subclass_element(universal_class,X0),subset_relation) )
    | ~ spl0_118
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27997,f26985]) ).

fof(f27997,plain,
    ( ! [X0] :
        ( subclass(complement(null_class),X0)
        | ~ member(not_subclass_element(universal_class,X0),subset_relation) )
    | ~ spl0_118
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27996,f25952]) ).

fof(f27996,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(universal_class,X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_118
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27995,f26985]) ).

fof(f27995,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(null_class),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_118
    | ~ spl0_663
    | spl0_1063 ),
    inference(forward_demodulation,[],[f14192,f25952]) ).

fof(f14192,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_663 ),
    inference(avatar_component_clause,[],[f14191]) ).

fof(f28193,plain,
    ( ~ spl0_1101
    | ~ spl0_118
    | spl0_637
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f28130,f26983,f25938,f13144,f921,f28190]) ).

fof(f28190,plain,
    ( spl0_1101
  <=> member(regular(universal_class),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f13144,plain,
    ( spl0_637
  <=> member(regular(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f28130,plain,
    ( ~ member(regular(universal_class),subset_relation)
    | ~ spl0_118
    | spl0_637
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f28129,f26985]) ).

fof(f28129,plain,
    ( ~ member(regular(complement(null_class)),subset_relation)
    | ~ spl0_118
    | spl0_637
    | spl0_1063 ),
    inference(forward_demodulation,[],[f13146,f25952]) ).

fof(f13146,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | spl0_637 ),
    inference(avatar_component_clause,[],[f13144]) ).

fof(f27897,plain,
    ( ~ spl0_89
    | ~ spl0_91
    | ~ spl0_248
    | spl0_1057
    | ~ spl0_1078 ),
    inference(avatar_split_clause,[],[f27629,f27074,f25438,f2433,f682,f672]) ).

fof(f27629,plain,
    ( ~ inductive(universal_class)
    | ~ spl0_91
    | ~ spl0_248
    | spl0_1057
    | ~ spl0_1078 ),
    inference(forward_demodulation,[],[f27562,f27080]) ).

fof(f27562,plain,
    ( ~ inductive(complement(subset_relation))
    | ~ spl0_248
    | spl0_1057 ),
    inference(superposition,[],[f25440,f2435]) ).

fof(f2435,plain,
    ( null_class = subset_relation
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f2433]) ).

fof(f27875,plain,
    ( spl0_716
    | ~ spl0_230
    | ~ spl0_1051 ),
    inference(avatar_split_clause,[],[f25046,f24987,f2242,f16077]) ).

fof(f25046,plain,
    ( subclass(identity_relation,null_class)
    | ~ spl0_230
    | ~ spl0_1051 ),
    inference(duplicate_literal_removal,[],[f25019]) ).

fof(f25019,plain,
    ( subclass(identity_relation,null_class)
    | subclass(identity_relation,null_class)
    | ~ spl0_230
    | ~ spl0_1051 ),
    inference(resolution,[],[f24988,f2243]) ).

fof(f24988,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,null_class),subset_relation)
        | subclass(X0,null_class) )
    | ~ spl0_1051 ),
    inference(avatar_component_clause,[],[f24987]) ).

fof(f27874,plain,
    ( ~ spl0_1100
    | ~ spl0_248
    | spl0_286 ),
    inference(avatar_split_clause,[],[f23732,f3029,f2433,f27871]) ).

fof(f27871,plain,
    ( spl0_1100
  <=> member(subset_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f3029,plain,
    ( spl0_286
  <=> member(null_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f23732,plain,
    ( ~ member(subset_relation,identity_relation)
    | ~ spl0_248
    | spl0_286 ),
    inference(superposition,[],[f3030,f2435]) ).

fof(f3030,plain,
    ( ~ member(null_class,identity_relation)
    | spl0_286 ),
    inference(avatar_component_clause,[],[f3029]) ).

fof(f27869,plain,
    ( spl0_1099
    | ~ spl0_248
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f23525,f5537,f2433,f27866]) ).

fof(f27866,plain,
    ( spl0_1099
  <=> member(subset_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f5537,plain,
    ( spl0_387
  <=> member(null_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f23525,plain,
    ( member(subset_relation,successor_relation)
    | ~ spl0_248
    | ~ spl0_387 ),
    inference(superposition,[],[f5538,f2435]) ).

fof(f5538,plain,
    ( member(null_class,successor_relation)
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f5537]) ).

fof(f27864,plain,
    ( ~ spl0_1098
    | spl0_219
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2461,f2433,f2119,f27861]) ).

fof(f27861,plain,
    ( spl0_1098
  <=> identity_relation = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f2119,plain,
    ( spl0_219
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f2461,plain,
    ( identity_relation != subset_relation
    | spl0_219
    | ~ spl0_248 ),
    inference(superposition,[],[f2120,f2435]) ).

fof(f2120,plain,
    ( null_class != identity_relation
    | spl0_219 ),
    inference(avatar_component_clause,[],[f2119]) ).

fof(f27847,plain,
    ( spl0_1097
    | ~ spl0_118
    | ~ spl0_248
    | ~ spl0_380
    | ~ spl0_446
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f27818,f22546,f8271,f5446,f2433,f921,f27845]) ).

fof(f27845,plain,
    ( spl0_1097
  <=> ! [X0,X1] :
        ( member(domain_of(subset_relation),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f27818,plain,
    ( ! [X0,X1] :
        ( member(domain_of(subset_relation),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_118
    | ~ spl0_248
    | ~ spl0_380
    | ~ spl0_446
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f27817,f2435]) ).

fof(f27817,plain,
    ( ! [X0,X1] :
        ( member(domain_of(null_class),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_118
    | ~ spl0_380
    | ~ spl0_446
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f27803,f22647]) ).

fof(f22647,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_118
    | ~ spl0_1024 ),
    inference(resolution,[],[f22547,f922]) ).

fof(f27803,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(intersection(null_class,cross_product(universal_class,subset_relation))),X1)
        | ~ subclass(X0,X1) )
    | ~ spl0_380
    | ~ spl0_446 ),
    inference(resolution,[],[f8272,f5447]) ).

fof(f27843,plain,
    ( spl0_1096
    | ~ spl0_118
    | ~ spl0_446
    | ~ spl0_459
    | ~ spl0_849
    | ~ spl0_1024
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27823,f26983,f22546,f19371,f8339,f8271,f921,f27841]) ).

fof(f27841,plain,
    ( spl0_1096
  <=> ! [X0,X1] :
        ( member(universal_class,X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f8339,plain,
    ( spl0_459
  <=> ! [X2,X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X2)
        | ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f27823,plain,
    ( ! [X0,X1] :
        ( member(universal_class,X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_118
    | ~ spl0_446
    | ~ spl0_459
    | ~ spl0_849
    | ~ spl0_1024
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27822,f26985]) ).

fof(f27822,plain,
    ( ! [X0,X1] :
        ( member(complement(null_class),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_118
    | ~ spl0_446
    | ~ spl0_459
    | ~ spl0_849
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f27821,f19373]) ).

fof(f27821,plain,
    ( ! [X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_118
    | ~ spl0_446
    | ~ spl0_459
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f27808,f22647]) ).

fof(f27808,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(subset_relation),universal_class)),universal_class))))),X1)
        | ~ subclass(X0,X1) )
    | ~ spl0_446
    | ~ spl0_459 ),
    inference(resolution,[],[f8272,f8340]) ).

fof(f8340,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,universal_class)
        | ~ subclass(universal_class,X0)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X2)
        | ~ subclass(X0,X2) )
    | ~ spl0_459 ),
    inference(avatar_component_clause,[],[f8339]) ).

fof(f27827,plain,
    ( spl0_1095
    | ~ spl0_37
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f27814,f8271,f339,f27825]) ).

fof(f27825,plain,
    ( spl0_1095
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f27814,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(subset_relation,X0) )
    | ~ spl0_37
    | ~ spl0_446 ),
    inference(resolution,[],[f8272,f340]) ).

fof(f27800,plain,
    ( spl0_446
    | ~ spl0_88
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2445,f2433,f668,f8271]) ).

fof(f2445,plain,
    ( member(subset_relation,universal_class)
    | ~ spl0_88
    | ~ spl0_248 ),
    inference(superposition,[],[f669,f2435]) ).

fof(f27799,plain,
    ( ~ spl0_1094
    | ~ spl0_91
    | ~ spl0_110
    | ~ spl0_248
    | spl0_506
    | ~ spl0_1078 ),
    inference(avatar_split_clause,[],[f27421,f27074,f9927,f2433,f856,f682,f27796]) ).

fof(f27796,plain,
    ( spl0_1094
  <=> subclass(universal_class,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(subset_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f27421,plain,
    ( ~ subclass(universal_class,intersection(element_relation,complement(compose(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))))))
    | ~ spl0_91
    | ~ spl0_110
    | ~ spl0_248
    | spl0_506
    | ~ spl0_1078 ),
    inference(forward_demodulation,[],[f27420,f858]) ).

fof(f27420,plain,
    ( ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))))))
    | ~ spl0_91
    | ~ spl0_248
    | spl0_506
    | ~ spl0_1078 ),
    inference(forward_demodulation,[],[f23537,f27080]) ).

fof(f23537,plain,
    ( ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(subset_relation),domain_of(flip(cross_product(subset_relation,universal_class)))))))
    | ~ spl0_248
    | spl0_506 ),
    inference(superposition,[],[f9929,f2435]) ).

fof(f27794,plain,
    ( ~ spl0_1093
    | ~ spl0_248
    | spl0_1031 ),
    inference(avatar_split_clause,[],[f23608,f22728,f2433,f27791]) ).

fof(f27791,plain,
    ( spl0_1093
  <=> subset_relation = unordered_pair(u,unordered_pair(first(subset_relation),unordered_pair(second(subset_relation),second(subset_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f22728,plain,
    ( spl0_1031
  <=> null_class = unordered_pair(u,unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f23608,plain,
    ( subset_relation != unordered_pair(u,unordered_pair(first(subset_relation),unordered_pair(second(subset_relation),second(subset_relation))))
    | ~ spl0_248
    | spl0_1031 ),
    inference(superposition,[],[f22730,f2435]) ).

fof(f22730,plain,
    ( null_class != unordered_pair(u,unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | spl0_1031 ),
    inference(avatar_component_clause,[],[f22728]) ).

fof(f27714,plain,
    ( spl0_1092
    | ~ spl0_248
    | ~ spl0_386
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f27435,f17102,f5533,f2433,f27711]) ).

fof(f27711,plain,
    ( spl0_1092
  <=> second(subset_relation) = complement(intersection(complement(first(subset_relation)),complement(u))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f5533,plain,
    ( spl0_386
  <=> second(null_class) = complement(intersection(complement(first(null_class)),complement(unordered_pair(first(null_class),first(null_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f27435,plain,
    ( second(subset_relation) = complement(intersection(complement(first(subset_relation)),complement(u)))
    | ~ spl0_248
    | ~ spl0_386
    | ~ spl0_748 ),
    inference(forward_demodulation,[],[f23524,f23583]) ).

fof(f23583,plain,
    ( u = unordered_pair(first(subset_relation),first(subset_relation))
    | ~ spl0_248
    | ~ spl0_748 ),
    inference(superposition,[],[f17104,f2435]) ).

fof(f23524,plain,
    ( second(subset_relation) = complement(intersection(complement(first(subset_relation)),complement(unordered_pair(first(subset_relation),first(subset_relation)))))
    | ~ spl0_248
    | ~ spl0_386 ),
    inference(superposition,[],[f5535,f2435]) ).

fof(f5535,plain,
    ( second(null_class) = complement(intersection(complement(first(null_class)),complement(unordered_pair(first(null_class),first(null_class)))))
    | ~ spl0_386 ),
    inference(avatar_component_clause,[],[f5533]) ).

fof(f27709,plain,
    ( ~ spl0_1091
    | ~ spl0_248
    | spl0_381 ),
    inference(avatar_split_clause,[],[f23522,f5512,f2433,f27706]) ).

fof(f27706,plain,
    ( spl0_1091
  <=> function(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f5512,plain,
    ( spl0_381
  <=> function(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f23522,plain,
    ( ~ function(subset_relation)
    | ~ spl0_248
    | spl0_381 ),
    inference(superposition,[],[f5514,f2435]) ).

fof(f5514,plain,
    ( ~ function(null_class)
    | spl0_381 ),
    inference(avatar_component_clause,[],[f5512]) ).

fof(f27704,plain,
    ( ~ spl0_1090
    | ~ spl0_248
    | spl0_601 ),
    inference(avatar_split_clause,[],[f23557,f12100,f2433,f27701]) ).

fof(f27701,plain,
    ( spl0_1090
  <=> successor_relation = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f12100,plain,
    ( spl0_601
  <=> null_class = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f23557,plain,
    ( successor_relation != subset_relation
    | ~ spl0_248
    | spl0_601 ),
    inference(superposition,[],[f12102,f2435]) ).

fof(f12102,plain,
    ( null_class != successor_relation
    | spl0_601 ),
    inference(avatar_component_clause,[],[f12100]) ).

fof(f27699,plain,
    ( ~ spl0_1089
    | ~ spl0_248
    | spl0_600 ),
    inference(avatar_split_clause,[],[f23556,f12095,f2433,f27696]) ).

fof(f27696,plain,
    ( spl0_1089
  <=> subclass(successor_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f12095,plain,
    ( spl0_600
  <=> subclass(successor_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f23556,plain,
    ( ~ subclass(successor_relation,subset_relation)
    | ~ spl0_248
    | spl0_600 ),
    inference(superposition,[],[f12096,f2435]) ).

fof(f12096,plain,
    ( ~ subclass(successor_relation,null_class)
    | spl0_600 ),
    inference(avatar_component_clause,[],[f12095]) ).

fof(f27637,plain,
    ( spl0_1088
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_189
    | ~ spl0_248
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27375,f26983,f2433,f1761,f856,f728,f27635]) ).

fof(f27635,plain,
    ( spl0_1088
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f27375,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_189
    | ~ spl0_248
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27374,f858]) ).

fof(f27374,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_189
    | ~ spl0_248
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f23199,f26985]) ).

fof(f23199,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_189
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f23105,f2435]) ).

fof(f27633,plain,
    ( spl0_1087
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_188
    | ~ spl0_248
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27373,f26983,f2433,f1757,f856,f728,f27631]) ).

fof(f27631,plain,
    ( spl0_1087
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f27373,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_188
    | ~ spl0_248
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27372,f858]) ).

fof(f27372,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),universal_class)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_188
    | ~ spl0_248
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f23202,f26985]) ).

fof(f23202,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_96
    | ~ spl0_188
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f23106,f2435]) ).

fof(f27261,plain,
    ( spl0_844
    | ~ spl0_25
    | ~ spl0_1051 ),
    inference(avatar_split_clause,[],[f25042,f24987,f280,f19272]) ).

fof(f19272,plain,
    ( spl0_844
  <=> subclass(subset_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f280,plain,
    ( spl0_25
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f25042,plain,
    ( subclass(subset_relation,null_class)
    | ~ spl0_25
    | ~ spl0_1051 ),
    inference(duplicate_literal_removal,[],[f25023]) ).

fof(f25023,plain,
    ( subclass(subset_relation,null_class)
    | subclass(subset_relation,null_class)
    | ~ spl0_25
    | ~ spl0_1051 ),
    inference(resolution,[],[f24988,f281]) ).

fof(f281,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f280]) ).

fof(f27259,plain,
    ( spl0_1086
    | ~ spl0_90
    | ~ spl0_1078 ),
    inference(avatar_split_clause,[],[f27079,f27074,f678,f27256]) ).

fof(f27256,plain,
    ( spl0_1086
  <=> member(omega,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f678,plain,
    ( spl0_90
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f27079,plain,
    ( member(omega,complement(subset_relation))
    | ~ spl0_90
    | ~ spl0_1078 ),
    inference(resolution,[],[f27076,f679]) ).

fof(f679,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f678]) ).

fof(f27254,plain,
    ( spl0_1085
    | ~ spl0_230
    | ~ spl0_1050 ),
    inference(avatar_split_clause,[],[f25018,f24983,f2242,f27251]) ).

fof(f27251,plain,
    ( spl0_1085
  <=> subclass(identity_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f24983,plain,
    ( spl0_1050
  <=> ! [X0] :
        ( subclass(X0,element_relation)
        | ~ member(not_subclass_element(X0,element_relation),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f25018,plain,
    ( subclass(identity_relation,element_relation)
    | ~ spl0_230
    | ~ spl0_1050 ),
    inference(duplicate_literal_removal,[],[f24991]) ).

fof(f24991,plain,
    ( subclass(identity_relation,element_relation)
    | subclass(identity_relation,element_relation)
    | ~ spl0_230
    | ~ spl0_1050 ),
    inference(resolution,[],[f24984,f2243]) ).

fof(f24984,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,element_relation),subset_relation)
        | subclass(X0,element_relation) )
    | ~ spl0_1050 ),
    inference(avatar_component_clause,[],[f24983]) ).

fof(f27249,plain,
    ( spl0_602
    | ~ spl0_1035 ),
    inference(avatar_contradiction_clause,[],[f27210]) ).

fof(f27210,plain,
    ( $false
    | spl0_602
    | ~ spl0_1035 ),
    inference(resolution,[],[f22756,f12107]) ).

fof(f12107,plain,
    ( ~ subclass(null_class,successor_relation)
    | spl0_602 ),
    inference(avatar_component_clause,[],[f12105]) ).

fof(f12105,plain,
    ( spl0_602
  <=> subclass(null_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f22756,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_1035 ),
    inference(avatar_component_clause,[],[f22755]) ).

fof(f22755,plain,
    ( spl0_1035
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f27201,plain,
    ( ~ spl0_88
    | spl0_155
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f19378,f19371,f1336,f668]) ).

fof(f19378,plain,
    ( ~ member(null_class,universal_class)
    | spl0_155
    | ~ spl0_849 ),
    inference(superposition,[],[f1337,f19373]) ).

fof(f1337,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | spl0_155 ),
    inference(avatar_component_clause,[],[f1336]) ).

fof(f27200,plain,
    ( spl0_364
    | ~ spl0_8
    | ~ spl0_110
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f17657,f2400,f856,f206,f4751]) ).

fof(f4751,plain,
    ( spl0_364
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f2400,plain,
    ( spl0_245
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f17657,plain,
    ( member(null_class,element_relation)
    | ~ spl0_8
    | ~ spl0_110
    | ~ spl0_245 ),
    inference(forward_demodulation,[],[f2426,f858]) ).

fof(f2426,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_8
    | ~ spl0_245 ),
    inference(resolution,[],[f2401,f207]) ).

fof(f2401,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f2400]) ).

fof(f27199,plain,
    ( spl0_1084
    | ~ spl0_207
    | ~ spl0_640 ),
    inference(avatar_split_clause,[],[f13186,f13164,f1931,f27196]) ).

fof(f27196,plain,
    ( spl0_1084
  <=> subclass(subset_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f1931,plain,
    ( spl0_207
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f13164,plain,
    ( spl0_640
  <=> subset_relation = intersection(element_relation,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f13186,plain,
    ( subclass(subset_relation,element_relation)
    | ~ spl0_207
    | ~ spl0_640 ),
    inference(superposition,[],[f1932,f13166]) ).

fof(f13166,plain,
    ( subset_relation = intersection(element_relation,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_640 ),
    inference(avatar_component_clause,[],[f13164]) ).

fof(f1932,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f1931]) ).

fof(f27120,plain,
    ( ~ spl0_162
    | ~ spl0_858
    | ~ spl0_1078 ),
    inference(avatar_split_clause,[],[f27078,f27074,f19509,f1372]) ).

fof(f27078,plain,
    ( ~ member(u,subset_relation)
    | ~ spl0_858
    | ~ spl0_1078 ),
    inference(resolution,[],[f27076,f19510]) ).

fof(f27119,plain,
    ( ~ spl0_1083
    | ~ spl0_1076
    | spl0_1082 ),
    inference(avatar_split_clause,[],[f27114,f27110,f26983,f27116]) ).

fof(f27116,plain,
    ( spl0_1083
  <=> member(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f27110,plain,
    ( spl0_1082
  <=> member(complement(null_class),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f27114,plain,
    ( ~ member(universal_class,subset_relation)
    | ~ spl0_1076
    | spl0_1082 ),
    inference(forward_demodulation,[],[f27112,f26985]) ).

fof(f27112,plain,
    ( ~ member(complement(null_class),subset_relation)
    | spl0_1082 ),
    inference(avatar_component_clause,[],[f27110]) ).

fof(f27113,plain,
    ( spl0_1080
    | ~ spl0_1081
    | ~ spl0_1082
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_430
    | ~ spl0_849
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f24336,f22546,f19371,f7313,f921,f856,f754,f27110,f27106,f27103]) ).

fof(f27103,plain,
    ( spl0_1080
  <=> ! [X0] : ~ member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f27106,plain,
    ( spl0_1081
  <=> subclass(universal_class,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f7313,plain,
    ( spl0_430
  <=> ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f24336,plain,
    ( ! [X0] :
        ( ~ member(complement(null_class),subset_relation)
        | ~ subclass(universal_class,complement(element_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_430
    | ~ spl0_849
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f24335,f19373]) ).

fof(f24335,plain,
    ( ! [X0] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),subset_relation)
        | ~ subclass(universal_class,complement(element_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_430
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f24334,f22647]) ).

fof(f24334,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(element_relation))
        | ~ member(X0,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X0),universal_class)),universal_class))))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_430 ),
    inference(forward_demodulation,[],[f7320,f858]) ).

fof(f7320,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(cross_product(universal_class,universal_class)))
        | ~ member(X0,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X0),universal_class)),universal_class))))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_430 ),
    inference(resolution,[],[f7314,f755]) ).

fof(f7314,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class) )
    | ~ spl0_430 ),
    inference(avatar_component_clause,[],[f7313]) ).

fof(f27101,plain,
    ( spl0_1079
    | ~ spl0_20
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1885,f1882,f257,f27099]) ).

fof(f257,plain,
    ( spl0_20
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f1885,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,null_class)
        | ~ member(X0,unordered_pair(u,u)) )
    | ~ spl0_20
    | ~ spl0_199 ),
    inference(resolution,[],[f1883,f258]) ).

fof(f258,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f257]) ).

fof(f27077,plain,
    ( spl0_1078
    | ~ spl0_1077
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f27050,f26983,f25938,f14191,f3299,f921,f27039,f27074]) ).

fof(f3299,plain,
    ( spl0_307
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f27050,plain,
    ( ~ subclass(universal_class,universal_class)
    | subclass(universal_class,complement(subset_relation))
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27049,f26985]) ).

fof(f27049,plain,
    ( ~ subclass(complement(null_class),universal_class)
    | subclass(universal_class,complement(subset_relation))
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27048,f25952]) ).

fof(f27048,plain,
    ( subclass(universal_class,complement(subset_relation))
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f27047,f26985]) ).

fof(f27047,plain,
    ( subclass(complement(null_class),complement(subset_relation))
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_663
    | spl0_1063 ),
    inference(forward_demodulation,[],[f26691,f25952]) ).

fof(f26691,plain,
    ( subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(subset_relation))
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_307
    | ~ spl0_663 ),
    inference(duplicate_literal_removal,[],[f26688]) ).

fof(f26688,plain,
    ( subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(subset_relation))
    | subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(subset_relation))
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_307
    | ~ spl0_663 ),
    inference(resolution,[],[f14192,f3300]) ).

fof(f3300,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_307 ),
    inference(avatar_component_clause,[],[f3299]) ).

fof(f27046,plain,
    ( ~ spl0_6
    | spl0_1077 ),
    inference(avatar_contradiction_clause,[],[f27043]) ).

fof(f27043,plain,
    ( $false
    | ~ spl0_6
    | spl0_1077 ),
    inference(resolution,[],[f27041,f198]) ).

fof(f27041,plain,
    ( ~ subclass(universal_class,universal_class)
    | spl0_1077 ),
    inference(avatar_component_clause,[],[f27039]) ).

fof(f27045,plain,
    ( ~ spl0_8
    | spl0_1077 ),
    inference(avatar_contradiction_clause,[],[f27044]) ).

fof(f27044,plain,
    ( $false
    | ~ spl0_8
    | spl0_1077 ),
    inference(resolution,[],[f27041,f207]) ).

fof(f27042,plain,
    ( spl0_1029
    | ~ spl0_1077
    | ~ spl0_91
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_500
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1066 ),
    inference(avatar_split_clause,[],[f26701,f26206,f25938,f14191,f9870,f3299,f921,f682,f27039,f22621]) ).

fof(f22621,plain,
    ( spl0_1029
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f26701,plain,
    ( ~ subclass(universal_class,universal_class)
    | subclass(universal_class,null_class)
    | ~ spl0_91
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_500
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1066 ),
    inference(forward_demodulation,[],[f26700,f26669]) ).

fof(f26669,plain,
    ( universal_class = complement(null_class)
    | ~ spl0_91
    | ~ spl0_1066 ),
    inference(resolution,[],[f26208,f683]) ).

fof(f26700,plain,
    ( ~ subclass(complement(null_class),universal_class)
    | subclass(universal_class,null_class)
    | ~ spl0_91
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_500
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1066 ),
    inference(forward_demodulation,[],[f26699,f25952]) ).

fof(f26699,plain,
    ( subclass(universal_class,null_class)
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_91
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_500
    | ~ spl0_663
    | spl0_1063
    | ~ spl0_1066 ),
    inference(forward_demodulation,[],[f26698,f26669]) ).

fof(f26698,plain,
    ( subclass(complement(null_class),null_class)
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_118
    | ~ spl0_307
    | ~ spl0_500
    | ~ spl0_663
    | spl0_1063 ),
    inference(forward_demodulation,[],[f26697,f25952]) ).

fof(f26697,plain,
    ( subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),null_class)
    | ~ subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_307
    | ~ spl0_500
    | ~ spl0_663 ),
    inference(forward_demodulation,[],[f26691,f9872]) ).

fof(f9872,plain,
    ( null_class = complement(subset_relation)
    | ~ spl0_500 ),
    inference(avatar_component_clause,[],[f9870]) ).

fof(f26986,plain,
    ( spl0_1076
    | ~ spl0_91
    | ~ spl0_1066 ),
    inference(avatar_split_clause,[],[f26669,f26206,f682,f26983]) ).

fof(f26930,plain,
    ( spl0_1075
    | ~ spl0_110
    | ~ spl0_881 ),
    inference(avatar_split_clause,[],[f24503,f19814,f856,f26928]) ).

fof(f26928,plain,
    ( spl0_1075
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f19814,plain,
    ( spl0_881
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).

fof(f24503,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f24502,f858]) ).

fof(f24502,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f19815,f858]) ).

fof(f19815,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_881 ),
    inference(avatar_component_clause,[],[f19814]) ).

fof(f26925,plain,
    ( spl0_1074
    | ~ spl0_110
    | ~ spl0_883 ),
    inference(avatar_split_clause,[],[f24501,f19840,f856,f26923]) ).

fof(f26923,plain,
    ( spl0_1074
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f19840,plain,
    ( spl0_883
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).

fof(f24501,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f24500,f858]) ).

fof(f24500,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f19841,f858]) ).

fof(f19841,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_883 ),
    inference(avatar_component_clause,[],[f19840]) ).

fof(f26808,plain,
    ( spl0_1073
    | ~ spl0_90
    | ~ spl0_1066 ),
    inference(avatar_split_clause,[],[f26668,f26206,f678,f26805]) ).

fof(f26805,plain,
    ( spl0_1073
  <=> member(omega,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f26668,plain,
    ( member(omega,complement(null_class))
    | ~ spl0_90
    | ~ spl0_1066 ),
    inference(resolution,[],[f26208,f679]) ).

fof(f26802,plain,
    ( spl0_1072
    | ~ spl0_110
    | ~ spl0_847 ),
    inference(avatar_split_clause,[],[f25915,f19335,f856,f26800]) ).

fof(f26800,plain,
    ( spl0_1072
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ subclass(domain_of(X1),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f19335,plain,
    ( spl0_847
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f25915,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ subclass(domain_of(X1),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_847 ),
    inference(forward_demodulation,[],[f25914,f858]) ).

fof(f25914,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_110
    | ~ spl0_847 ),
    inference(forward_demodulation,[],[f19336,f858]) ).

fof(f19336,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class))
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | ~ compatible(X0,X1,X2) )
    | ~ spl0_847 ),
    inference(avatar_component_clause,[],[f19335]) ).

fof(f26790,plain,
    ( spl0_1071
    | ~ spl0_110
    | ~ spl0_791 ),
    inference(avatar_split_clause,[],[f25907,f18365,f856,f26788]) ).

fof(f26788,plain,
    ( spl0_1071
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f18365,plain,
    ( spl0_791
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f25907,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f25906,f858]) ).

fof(f25906,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_110
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f18366,f858]) ).

fof(f18366,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | null_class = X0 )
    | ~ spl0_791 ),
    inference(avatar_component_clause,[],[f18365]) ).

fof(f26725,plain,
    ( spl0_1070
    | ~ spl0_110
    | ~ spl0_742 ),
    inference(avatar_split_clause,[],[f25886,f16962,f856,f26723]) ).

fof(f16962,plain,
    ( spl0_742
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f25886,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | subclass(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_110
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f25885,f858]) ).

fof(f25885,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f25884,f858]) ).

fof(f25884,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16963,f858]) ).

fof(f16963,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) )
    | ~ spl0_742 ),
    inference(avatar_component_clause,[],[f16962]) ).

fof(f26720,plain,
    ( ~ spl0_1069
    | ~ spl0_110
    | spl0_836 ),
    inference(avatar_split_clause,[],[f25913,f19213,f856,f26717]) ).

fof(f26717,plain,
    ( spl0_1069
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f19213,plain,
    ( spl0_836
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f25913,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | spl0_836 ),
    inference(forward_demodulation,[],[f19215,f858]) ).

fof(f19215,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | spl0_836 ),
    inference(avatar_component_clause,[],[f19213]) ).

fof(f26663,plain,
    ( spl0_1044
    | ~ spl0_1067
    | ~ spl0_1068
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f25904,f1443,f856,f754,f26660,f26656,f24830]) ).

fof(f24830,plain,
    ( spl0_1044
  <=> null_class = complement(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f26656,plain,
    ( spl0_1067
  <=> member(complement(element_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f26660,plain,
    ( spl0_1068
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(element_relation),complement(element_relation)),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f25904,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(element_relation),complement(element_relation)),universal_class)),universal_class))))))),subset_relation)
    | ~ member(complement(element_relation),universal_class)
    | null_class = complement(element_relation)
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f25903,f858]) ).

fof(f25903,plain,
    ( ~ member(complement(element_relation),universal_class)
    | null_class = complement(element_relation)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f24531,f858]) ).

fof(f24531,plain,
    ( null_class = complement(element_relation)
    | ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_101
    | ~ spl0_110
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f1449,f858]) ).

fof(f26209,plain,
    ( spl0_1066
    | ~ spl0_260
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f22641,f22546,f2686,f26206]) ).

fof(f2686,plain,
    ( spl0_260
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f22641,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_260
    | ~ spl0_1024 ),
    inference(resolution,[],[f22547,f2687]) ).

fof(f2687,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_260 ),
    inference(avatar_component_clause,[],[f2686]) ).

fof(f25951,plain,
    ( ~ spl0_1065
    | ~ spl0_110
    | spl0_837 ),
    inference(avatar_split_clause,[],[f25912,f19217,f856,f25948]) ).

fof(f25948,plain,
    ( spl0_1065
  <=> member(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f19217,plain,
    ( spl0_837
  <=> member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f25912,plain,
    ( ~ member(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_110
    | spl0_837 ),
    inference(forward_demodulation,[],[f19219,f858]) ).

fof(f19219,plain,
    ( ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | spl0_837 ),
    inference(avatar_component_clause,[],[f19217]) ).

fof(f25946,plain,
    ( ~ spl0_1064
    | ~ spl0_110
    | spl0_708 ),
    inference(avatar_split_clause,[],[f25879,f15884,f856,f25943]) ).

fof(f15884,plain,
    ( spl0_708
  <=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f25879,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | ~ spl0_110
    | spl0_708 ),
    inference(forward_demodulation,[],[f15885,f858]) ).

fof(f15885,plain,
    ( ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | spl0_708 ),
    inference(avatar_component_clause,[],[f15884]) ).

fof(f25941,plain,
    ( ~ spl0_1063
    | ~ spl0_110
    | spl0_707 ),
    inference(avatar_split_clause,[],[f15890,f15880,f856,f25938]) ).

fof(f15880,plain,
    ( spl0_707
  <=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f15890,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),element_relation)
    | ~ spl0_110
    | spl0_707 ),
    inference(forward_demodulation,[],[f15882,f858]) ).

fof(f15882,plain,
    ( ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
    | spl0_707 ),
    inference(avatar_component_clause,[],[f15880]) ).

fof(f25929,plain,
    ( ~ spl0_1062
    | ~ spl0_110
    | spl0_706 ),
    inference(avatar_split_clause,[],[f25880,f15876,f856,f25926]) ).

fof(f25926,plain,
    ( spl0_1062
  <=> null_class = intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f15876,plain,
    ( spl0_706
  <=> null_class = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f25880,plain,
    ( null_class != intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_110
    | spl0_706 ),
    inference(forward_demodulation,[],[f15877,f858]) ).

fof(f15877,plain,
    ( null_class != intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | spl0_706 ),
    inference(avatar_component_clause,[],[f15876]) ).

fof(f25829,plain,
    ( spl0_1044
    | ~ spl0_606
    | ~ spl0_801 ),
    inference(avatar_split_clause,[],[f19688,f18607,f12438,f24830]) ).

fof(f18607,plain,
    ( spl0_801
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f19688,plain,
    ( null_class = complement(element_relation)
    | ~ spl0_606
    | ~ spl0_801 ),
    inference(resolution,[],[f18608,f12440]) ).

fof(f12440,plain,
    ( member(u,element_relation)
    | ~ spl0_606 ),
    inference(avatar_component_clause,[],[f12438]) ).

fof(f18608,plain,
    ( ! [X0] :
        ( ~ member(u,X0)
        | complement(X0) = null_class )
    | ~ spl0_801 ),
    inference(avatar_component_clause,[],[f18607]) ).

fof(f25789,plain,
    ( ~ spl0_1061
    | ~ spl0_110
    | spl0_897 ),
    inference(avatar_split_clause,[],[f24497,f20166,f856,f25786]) ).

fof(f20166,plain,
    ( spl0_897
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f24497,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | spl0_897 ),
    inference(forward_demodulation,[],[f20167,f858]) ).

fof(f20167,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
    | spl0_897 ),
    inference(avatar_component_clause,[],[f20166]) ).

fof(f25782,plain,
    ( ~ spl0_1060
    | ~ spl0_110
    | spl0_896 ),
    inference(avatar_split_clause,[],[f20173,f20162,f856,f25779]) ).

fof(f25779,plain,
    ( spl0_1060
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f20162,plain,
    ( spl0_896
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f20173,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),element_relation)
    | ~ spl0_110
    | spl0_896 ),
    inference(forward_demodulation,[],[f20164,f858]) ).

fof(f20164,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
    | spl0_896 ),
    inference(avatar_component_clause,[],[f20162]) ).

fof(f25541,plain,
    ( spl0_1059
    | ~ spl0_110
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f24280,f9202,f856,f25539]) ).

fof(f25539,plain,
    ( spl0_1059
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,element_relation)),X1)
        | subclass(X0,intersection(X1,element_relation))
        | ~ member(not_subclass_element(X0,intersection(X1,element_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f9202,plain,
    ( spl0_483
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f24280,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,element_relation)),X1)
        | subclass(X0,intersection(X1,element_relation))
        | ~ member(not_subclass_element(X0,intersection(X1,element_relation)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_483 ),
    inference(forward_demodulation,[],[f24279,f858]) ).

fof(f24279,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,element_relation))
        | ~ member(not_subclass_element(X0,intersection(X1,element_relation)),subset_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1) )
    | ~ spl0_110
    | ~ spl0_483 ),
    inference(forward_demodulation,[],[f24278,f858]) ).

fof(f24278,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,element_relation)),subset_relation)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1) )
    | ~ spl0_110
    | ~ spl0_483 ),
    inference(forward_demodulation,[],[f9203,f858]) ).

fof(f9203,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1) )
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f9202]) ).

fof(f25462,plain,
    ( ~ spl0_1058
    | ~ spl0_118
    | spl0_670
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f24315,f22546,f15005,f921,f25459]) ).

fof(f24315,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(null_class),complement(null_class)))),subset_relation)
    | ~ spl0_118
    | spl0_670
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f15007,f22647]) ).

fof(f25441,plain,
    ( ~ spl0_1057
    | ~ spl0_14
    | spl0_335 ),
    inference(avatar_split_clause,[],[f25134,f4138,f232,f25438]) ).

fof(f232,plain,
    ( spl0_14
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f4138,plain,
    ( spl0_335
  <=> member(null_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f25134,plain,
    ( ~ inductive(complement(null_class))
    | ~ spl0_14
    | spl0_335 ),
    inference(resolution,[],[f4139,f233]) ).

fof(f233,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f232]) ).

fof(f4139,plain,
    ( ~ member(null_class,complement(null_class))
    | spl0_335 ),
    inference(avatar_component_clause,[],[f4138]) ).

fof(f25234,plain,
    ( ~ spl0_1056
    | ~ spl0_110
    | spl0_895 ),
    inference(avatar_split_clause,[],[f24496,f20158,f856,f25231]) ).

fof(f25231,plain,
    ( spl0_1056
  <=> member(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f20158,plain,
    ( spl0_895
  <=> member(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f24496,plain,
    ( ~ member(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class)
    | ~ spl0_110
    | spl0_895 ),
    inference(forward_demodulation,[],[f20160,f858]) ).

fof(f20160,plain,
    ( ~ member(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class)
    | spl0_895 ),
    inference(avatar_component_clause,[],[f20158]) ).

fof(f25222,plain,
    ( spl0_1055
    | ~ spl0_118
    | ~ spl0_664
    | spl0_711 ),
    inference(avatar_split_clause,[],[f24260,f15972,f14197,f921,f25220]) ).

fof(f25220,plain,
    ( spl0_1055
  <=> ! [X0] :
        ( subclass(complement(null_class),X0)
        | ~ member(not_subclass_element(complement(null_class),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f14197,plain,
    ( spl0_664
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f24260,plain,
    ( ! [X0] :
        ( subclass(complement(null_class),X0)
        | ~ member(not_subclass_element(complement(null_class),X0),subset_relation) )
    | ~ spl0_118
    | ~ spl0_664
    | spl0_711 ),
    inference(forward_demodulation,[],[f24259,f15981]) ).

fof(f24259,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(null_class),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_118
    | ~ spl0_664
    | spl0_711 ),
    inference(forward_demodulation,[],[f14198,f15981]) ).

fof(f14198,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_664 ),
    inference(avatar_component_clause,[],[f14197]) ).

fof(f25217,plain,
    ( spl0_1054
    | ~ spl0_110
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f24256,f3502,f856,f25215]) ).

fof(f25215,plain,
    ( spl0_1054
  <=> ! [X0] :
        ( subclass(complement(element_relation),X0)
        | ~ member(not_subclass_element(complement(element_relation),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f3502,plain,
    ( spl0_312
  <=> ! [X0] :
        ( subclass(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f24256,plain,
    ( ! [X0] :
        ( subclass(complement(element_relation),X0)
        | ~ member(not_subclass_element(complement(element_relation),X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_312 ),
    inference(forward_demodulation,[],[f24255,f858]) ).

fof(f24255,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(element_relation),X0),subset_relation)
        | subclass(complement(cross_product(universal_class,universal_class)),X0) )
    | ~ spl0_110
    | ~ spl0_312 ),
    inference(forward_demodulation,[],[f3503,f858]) ).

fof(f3503,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation)
        | subclass(complement(cross_product(universal_class,universal_class)),X0) )
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f3502]) ).

fof(f25054,plain,
    ( spl0_1053
    | ~ spl0_118
    | ~ spl0_648
    | spl0_711 ),
    inference(avatar_split_clause,[],[f24252,f15972,f13393,f921,f25052]) ).

fof(f13393,plain,
    ( spl0_648
  <=> ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f24252,plain,
    ( ! [X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_118
    | ~ spl0_648
    | spl0_711 ),
    inference(forward_demodulation,[],[f13394,f15981]) ).

fof(f13394,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_648 ),
    inference(avatar_component_clause,[],[f13393]) ).

fof(f25050,plain,
    ( spl0_1052
    | ~ spl0_110
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f24244,f2749,f856,f25048]) ).

fof(f25048,plain,
    ( spl0_1052
  <=> ! [X0,X1] :
        ( ~ subclass(element_relation,X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f2749,plain,
    ( spl0_262
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f24244,plain,
    ( ! [X0,X1] :
        ( ~ subclass(element_relation,X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_110
    | ~ spl0_262 ),
    inference(forward_demodulation,[],[f2750,f858]) ).

fof(f2750,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f2749]) ).

fof(f24990,plain,
    ( spl0_1051
    | ~ spl0_118
    | ~ spl0_606
    | ~ spl0_661
    | spl0_711
    | ~ spl0_801 ),
    inference(avatar_split_clause,[],[f24705,f18607,f15972,f13976,f12438,f921,f24987]) ).

fof(f24705,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,null_class),subset_relation)
        | subclass(X0,null_class) )
    | ~ spl0_118
    | ~ spl0_606
    | ~ spl0_661
    | spl0_711
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f24704,f15981]) ).

fof(f24704,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,null_class) )
    | ~ spl0_118
    | ~ spl0_606
    | ~ spl0_661
    | spl0_711
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f24703,f19688]) ).

fof(f24703,plain,
    ( ! [X0] :
        ( subclass(X0,null_class)
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) )
    | ~ spl0_118
    | ~ spl0_606
    | ~ spl0_661
    | spl0_711
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f24702,f15981]) ).

fof(f24702,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) )
    | ~ spl0_606
    | ~ spl0_661
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f13977,f19688]) ).

fof(f24989,plain,
    ( spl0_1051
    | ~ spl0_118
    | ~ spl0_662
    | spl0_711 ),
    inference(avatar_split_clause,[],[f24298,f15972,f13982,f921,f24987]) ).

fof(f13982,plain,
    ( spl0_662
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f24298,plain,
    ( ! [X0] :
        ( subclass(X0,null_class)
        | ~ member(not_subclass_element(X0,null_class),subset_relation) )
    | ~ spl0_118
    | ~ spl0_662
    | spl0_711 ),
    inference(forward_demodulation,[],[f24297,f15981]) ).

fof(f24297,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,null_class),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_118
    | ~ spl0_662
    | spl0_711 ),
    inference(forward_demodulation,[],[f13983,f15981]) ).

fof(f13983,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_662 ),
    inference(avatar_component_clause,[],[f13982]) ).

fof(f24985,plain,
    ( spl0_1050
    | ~ spl0_110
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f24277,f2980,f856,f24983]) ).

fof(f2980,plain,
    ( spl0_275
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f24277,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ member(not_subclass_element(X0,element_relation),subset_relation) )
    | ~ spl0_110
    | ~ spl0_275 ),
    inference(forward_demodulation,[],[f24276,f858]) ).

fof(f24276,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,element_relation),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_110
    | ~ spl0_275 ),
    inference(forward_demodulation,[],[f2981,f858]) ).

fof(f2981,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2980]) ).

fof(f24967,plain,
    ( spl0_1049
    | ~ spl0_110
    | ~ spl0_556 ),
    inference(avatar_split_clause,[],[f24258,f10904,f856,f24965]) ).

fof(f24258,plain,
    ( ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_556 ),
    inference(forward_demodulation,[],[f24257,f858]) ).

fof(f24257,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0) )
    | ~ spl0_110
    | ~ spl0_556 ),
    inference(forward_demodulation,[],[f10905,f858]) ).

fof(f24935,plain,
    ( spl0_1048
    | ~ spl0_110
    | ~ spl0_544 ),
    inference(avatar_split_clause,[],[f24296,f10689,f856,f24933]) ).

fof(f24296,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_544 ),
    inference(forward_demodulation,[],[f24295,f858]) ).

fof(f24295,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_544 ),
    inference(forward_demodulation,[],[f10690,f858]) ).

fof(f24851,plain,
    ( ~ spl0_1047
    | ~ spl0_118
    | spl0_638
    | spl0_711 ),
    inference(avatar_split_clause,[],[f24372,f15972,f13150,f921,f24848]) ).

fof(f24848,plain,
    ( spl0_1047
  <=> member(regular(complement(null_class)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f13150,plain,
    ( spl0_638
  <=> member(regular(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f24372,plain,
    ( ~ member(regular(complement(null_class)),subset_relation)
    | ~ spl0_118
    | spl0_638
    | spl0_711 ),
    inference(forward_demodulation,[],[f13152,f15981]) ).

fof(f13152,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | spl0_638 ),
    inference(avatar_component_clause,[],[f13150]) ).

fof(f24845,plain,
    ( ~ spl0_1046
    | ~ spl0_110
    | spl0_296 ),
    inference(avatar_split_clause,[],[f24367,f3251,f856,f24842]) ).

fof(f24842,plain,
    ( spl0_1046
  <=> member(regular(complement(element_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f3251,plain,
    ( spl0_296
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f24367,plain,
    ( ~ member(regular(complement(element_relation)),subset_relation)
    | ~ spl0_110
    | spl0_296 ),
    inference(forward_demodulation,[],[f3253,f858]) ).

fof(f3253,plain,
    ( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | spl0_296 ),
    inference(avatar_component_clause,[],[f3251]) ).

fof(f24840,plain,
    ( spl0_1045
    | ~ spl0_110
    | ~ spl0_425 ),
    inference(avatar_split_clause,[],[f24246,f7287,f856,f24838]) ).

fof(f24838,plain,
    ( spl0_1045
  <=> ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f7287,plain,
    ( spl0_425
  <=> ! [X0,X1] :
        ( ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f24246,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_110
    | ~ spl0_425 ),
    inference(forward_demodulation,[],[f7288,f858]) ).

fof(f7288,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_425 ),
    inference(avatar_component_clause,[],[f7287]) ).

fof(f24836,plain,
    ( spl0_162
    | ~ spl0_8
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f8949,f8407,f206,f1372]) ).

fof(f24833,plain,
    ( ~ spl0_1044
    | ~ spl0_110
    | spl0_297 ),
    inference(avatar_split_clause,[],[f24748,f3255,f856,f24830]) ).

fof(f24748,plain,
    ( null_class != complement(element_relation)
    | ~ spl0_110
    | spl0_297 ),
    inference(forward_demodulation,[],[f3256,f858]) ).

fof(f3256,plain,
    ( null_class != complement(cross_product(universal_class,universal_class))
    | spl0_297 ),
    inference(avatar_component_clause,[],[f3255]) ).

fof(f24828,plain,
    ( ~ spl0_1043
    | ~ spl0_118
    | spl0_710
    | spl0_711 ),
    inference(avatar_split_clause,[],[f24362,f15972,f15967,f921,f24825]) ).

fof(f15967,plain,
    ( spl0_710
  <=> member(regular(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f24362,plain,
    ( ~ member(regular(null_class),subset_relation)
    | ~ spl0_118
    | spl0_710
    | spl0_711 ),
    inference(forward_demodulation,[],[f15969,f15981]) ).

fof(f15969,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | spl0_710 ),
    inference(avatar_component_clause,[],[f15967]) ).

fof(f24821,plain,
    ( ~ spl0_1042
    | ~ spl0_110
    | spl0_550 ),
    inference(avatar_split_clause,[],[f24371,f10819,f856,f24818]) ).

fof(f24371,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation)
    | ~ spl0_110
    | spl0_550 ),
    inference(forward_demodulation,[],[f10821,f858]) ).

fof(f24815,plain,
    ( ~ spl0_1041
    | ~ spl0_118
    | spl0_472
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f24353,f22546,f9147,f921,f24812]) ).

fof(f24812,plain,
    ( spl0_1041
  <=> member(domain_of(null_class),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f9147,plain,
    ( spl0_472
  <=> member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f24353,plain,
    ( ~ member(domain_of(null_class),subset_relation)
    | ~ spl0_118
    | spl0_472
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f9149,f22647]) ).

fof(f9149,plain,
    ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | spl0_472 ),
    inference(avatar_component_clause,[],[f9147]) ).

fof(f24808,plain,
    ( spl0_641
    | ~ spl0_110
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f24243,f1202,f856,f13231]) ).

fof(f24243,plain,
    ( ! [X0] :
        ( member(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_110
    | ~ spl0_140 ),
    inference(forward_demodulation,[],[f1203,f858]) ).

fof(f24749,plain,
    ( spl0_612
    | ~ spl0_101
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f24242,f856,f754,f12597]) ).

fof(f24242,plain,
    ( ! [X0] :
        ( member(X0,element_relation)
        | ~ member(X0,subset_relation) )
    | ~ spl0_101
    | ~ spl0_110 ),
    inference(forward_demodulation,[],[f755,f858]) ).

fof(f24234,plain,
    ( spl0_1040
    | ~ spl0_35
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f22975,f22546,f10306,f9870,f2433,f925,f330,f24231]) ).

fof(f24231,plain,
    ( spl0_1040
  <=> member(subset_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f330,plain,
    ( spl0_35
  <=> member(null_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f10306,plain,
    ( spl0_527
  <=> null_class = complement(complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f22975,plain,
    ( member(subset_relation,null_class)
    | ~ spl0_35
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22974,f22670]) ).

fof(f22670,plain,
    ( ! [X0] : null_class = intersection(X0,null_class)
    | ~ spl0_119
    | ~ spl0_1024 ),
    inference(resolution,[],[f22547,f926]) ).

fof(f22974,plain,
    ( member(subset_relation,intersection(complement(unordered_pair(u,u)),null_class))
    | ~ spl0_35
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22973,f10308]) ).

fof(f10308,plain,
    ( null_class = complement(complement(null_class))
    | ~ spl0_527 ),
    inference(avatar_component_clause,[],[f10306]) ).

fof(f22973,plain,
    ( member(subset_relation,intersection(complement(unordered_pair(u,u)),complement(complement(null_class))))
    | ~ spl0_35
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22972,f22670]) ).

fof(f22972,plain,
    ( member(subset_relation,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),null_class)))))
    | ~ spl0_35
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22971,f10308]) ).

fof(f22971,plain,
    ( member(subset_relation,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(null_class)))))))
    | ~ spl0_35
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22970,f22670]) ).

fof(f22970,plain,
    ( member(subset_relation,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),null_class))))))))
    | ~ spl0_35
    | ~ spl0_248
    | ~ spl0_500 ),
    inference(forward_demodulation,[],[f2443,f9872]) ).

fof(f2443,plain,
    ( member(subset_relation,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(subset_relation)))))))))
    | ~ spl0_35
    | ~ spl0_248 ),
    inference(superposition,[],[f331,f2435]) ).

fof(f331,plain,
    ( member(null_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f24172,plain,
    ( spl0_1039
    | ~ spl0_16
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_119
    | ~ spl0_188
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f23204,f22546,f10306,f9870,f2433,f1757,f925,f856,f728,f240,f24170]) ).

fof(f24170,plain,
    ( spl0_1039
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),subset_relation)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f240,plain,
    ( spl0_16
  <=> null_class = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f23204,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),subset_relation)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_16
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_119
    | ~ spl0_188
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f23203,f858]) ).

fof(f23203,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),subset_relation)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_16
    | ~ spl0_96
    | ~ spl0_119
    | ~ spl0_188
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f23202,f22981]) ).

fof(f22981,plain,
    ( subset_relation = complement(null_class)
    | ~ spl0_16
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22980,f22670]) ).

fof(f22980,plain,
    ( subset_relation = complement(intersection(complement(unordered_pair(u,u)),null_class))
    | ~ spl0_16
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22979,f10308]) ).

fof(f22979,plain,
    ( subset_relation = complement(intersection(complement(unordered_pair(u,u)),complement(complement(null_class))))
    | ~ spl0_16
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22978,f22670]) ).

fof(f22978,plain,
    ( subset_relation = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),null_class)))))
    | ~ spl0_16
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22977,f10308]) ).

fof(f22977,plain,
    ( subset_relation = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(null_class)))))))
    | ~ spl0_16
    | ~ spl0_119
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22976,f22670]) ).

fof(f22976,plain,
    ( subset_relation = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),null_class))))))))
    | ~ spl0_16
    | ~ spl0_248
    | ~ spl0_500 ),
    inference(forward_demodulation,[],[f2442,f9872]) ).

fof(f2442,plain,
    ( subset_relation = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(subset_relation)))))))))
    | ~ spl0_16
    | ~ spl0_248 ),
    inference(superposition,[],[f242,f2435]) ).

fof(f242,plain,
    ( null_class = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f24168,plain,
    ( spl0_1038
    | ~ spl0_16
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_119
    | ~ spl0_189
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f23201,f22546,f10306,f9870,f2433,f1761,f925,f856,f728,f240,f24166]) ).

fof(f24166,plain,
    ( spl0_1038
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),subset_relation)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f23201,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),subset_relation)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_16
    | ~ spl0_96
    | ~ spl0_110
    | ~ spl0_119
    | ~ spl0_189
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f23200,f858]) ).

fof(f23200,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),subset_relation)))))))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_16
    | ~ spl0_96
    | ~ spl0_119
    | ~ spl0_189
    | ~ spl0_248
    | ~ spl0_500
    | ~ spl0_527
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f23199,f22981]) ).

fof(f24080,plain,
    ( ~ spl0_1037
    | ~ spl0_248
    | spl0_372 ),
    inference(avatar_split_clause,[],[f23521,f5409,f2433,f24077]) ).

fof(f24077,plain,
    ( spl0_1037
  <=> single_valued_class(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f5409,plain,
    ( spl0_372
  <=> single_valued_class(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f23521,plain,
    ( ~ single_valued_class(subset_relation)
    | ~ spl0_248
    | spl0_372 ),
    inference(superposition,[],[f5411,f2435]) ).

fof(f5411,plain,
    ( ~ single_valued_class(null_class)
    | spl0_372 ),
    inference(avatar_component_clause,[],[f5409]) ).

fof(f23736,plain,
    ( spl0_1036
    | spl0_162
    | ~ spl0_426
    | ~ spl0_444 ),
    inference(avatar_split_clause,[],[f8201,f8198,f7296,f1372,f23734]) ).

fof(f23734,plain,
    ( spl0_1036
  <=> ! [X2,X0,X1] :
        ( subset_relation = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f7296,plain,
    ( spl0_426
  <=> ! [X0] :
        ( member(u,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f8198,plain,
    ( spl0_444
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f8201,plain,
    ( ! [X2,X0,X1] :
        ( subset_relation = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
    | spl0_162
    | ~ spl0_426
    | ~ spl0_444 ),
    inference(forward_demodulation,[],[f8199,f7505]) ).

fof(f7505,plain,
    ( null_class = subset_relation
    | spl0_162
    | ~ spl0_426 ),
    inference(resolution,[],[f7297,f1374]) ).

fof(f1374,plain,
    ( ~ member(u,subset_relation)
    | spl0_162 ),
    inference(avatar_component_clause,[],[f1372]) ).

fof(f7297,plain,
    ( ! [X0] :
        ( member(u,X0)
        | null_class = X0 )
    | ~ spl0_426 ),
    inference(avatar_component_clause,[],[f7296]) ).

fof(f8199,plain,
    ( ! [X2,X0,X1] :
        ( regular(intersection(unordered_pair(X0,X1),X2)) = X1
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | null_class = intersection(unordered_pair(X0,X1),X2) )
    | ~ spl0_444 ),
    inference(avatar_component_clause,[],[f8198]) ).

fof(f22785,plain,
    ( spl0_1029
    | ~ spl0_260
    | ~ spl0_996
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f22700,f22546,f22063,f2686,f22621]) ).

fof(f22063,plain,
    ( spl0_996
  <=> null_class = complement(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f22700,plain,
    ( subclass(universal_class,null_class)
    | ~ spl0_260
    | ~ spl0_996
    | ~ spl0_1024 ),
    inference(forward_demodulation,[],[f22641,f22065]) ).

fof(f22065,plain,
    ( null_class = complement(null_class)
    | ~ spl0_996 ),
    inference(avatar_component_clause,[],[f22063]) ).

fof(f22759,plain,
    ( spl0_200
    | ~ spl0_92
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3246,f3029,f686,f1896]) ).

fof(f1896,plain,
    ( spl0_200
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f686,plain,
    ( spl0_92
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f3246,plain,
    ( member(null_class,subset_relation)
    | ~ spl0_92
    | ~ spl0_286 ),
    inference(resolution,[],[f3031,f687]) ).

fof(f687,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f686]) ).

fof(f3031,plain,
    ( member(null_class,identity_relation)
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f3029]) ).

fof(f22758,plain,
    ( ~ spl0_1029
    | ~ spl0_6
    | ~ spl0_11
    | ~ spl0_238
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2494,f2429,f2275,f218,f197,f22621]) ).

fof(f218,plain,
    ( spl0_11
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f2275,plain,
    ( spl0_238
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2494,plain,
    ( ~ subclass(universal_class,null_class)
    | ~ spl0_6
    | ~ spl0_11
    | ~ spl0_238
    | ~ spl0_247 ),
    inference(forward_demodulation,[],[f2474,f2294]) ).

fof(f2294,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_6
    | ~ spl0_238 ),
    inference(resolution,[],[f2276,f198]) ).

fof(f2276,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f2275]) ).

fof(f2474,plain,
    ( ~ subclass(universal_class,complement(universal_class))
    | ~ spl0_11
    | ~ spl0_247 ),
    inference(resolution,[],[f2430,f219]) ).

fof(f219,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f218]) ).

fof(f22757,plain,
    ( spl0_1035
    | ~ spl0_6
    | ~ spl0_238
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f2300,f2283,f2275,f197,f22755]) ).

fof(f2283,plain,
    ( spl0_240
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f2300,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_6
    | ~ spl0_238
    | ~ spl0_240 ),
    inference(forward_demodulation,[],[f2297,f2294]) ).

fof(f2297,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_6
    | ~ spl0_240 ),
    inference(resolution,[],[f2284,f198]) ).

fof(f2284,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_240 ),
    inference(avatar_component_clause,[],[f2283]) ).

fof(f22753,plain,
    ( spl0_1034
    | ~ spl0_40
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1960,f1940,f351,f22750]) ).

fof(f22750,plain,
    ( spl0_1034
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f351,plain,
    ( spl0_40
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f1940,plain,
    ( spl0_209
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f1960,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_40
    | ~ spl0_209 ),
    inference(superposition,[],[f1941,f353]) ).

fof(f353,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f1941,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f1940]) ).

fof(f22742,plain,
    ( spl0_1033
    | ~ spl0_996
    | ~ spl0_1032 ),
    inference(avatar_split_clause,[],[f22737,f22733,f22063,f22739]) ).

fof(f22739,plain,
    ( spl0_1033
  <=> member(regular(subset_relation),complement(compose(null_class,domain_of(flip(cross_product(null_class,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f22733,plain,
    ( spl0_1032
  <=> member(regular(subset_relation),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f22737,plain,
    ( member(regular(subset_relation),complement(compose(null_class,domain_of(flip(cross_product(null_class,universal_class))))))
    | ~ spl0_996
    | ~ spl0_1032 ),
    inference(forward_demodulation,[],[f22735,f22065]) ).

fof(f22735,plain,
    ( member(regular(subset_relation),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))
    | ~ spl0_1032 ),
    inference(avatar_component_clause,[],[f22733]) ).

fof(f22736,plain,
    ( spl0_1032
    | ~ spl0_30
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f6491,f6485,f300,f22733]) ).

fof(f300,plain,
    ( spl0_30
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f6491,plain,
    ( member(regular(subset_relation),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))
    | ~ spl0_30
    | ~ spl0_400 ),
    inference(resolution,[],[f6487,f301]) ).

fof(f301,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f22731,plain,
    ( ~ spl0_1031
    | spl0_152
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f22714,f17102,f1291,f22728]) ).

fof(f1291,plain,
    ( spl0_152
  <=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f22714,plain,
    ( null_class != unordered_pair(u,unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | spl0_152
    | ~ spl0_748 ),
    inference(forward_demodulation,[],[f1292,f17104]) ).

fof(f1292,plain,
    ( null_class != unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | spl0_152 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f22699,plain,
    ( ~ spl0_421
    | ~ spl0_1024 ),
    inference(avatar_contradiction_clause,[],[f22637]) ).

fof(f22637,plain,
    ( $false
    | ~ spl0_421
    | ~ spl0_1024 ),
    inference(resolution,[],[f22547,f6798]) ).

fof(f6798,plain,
    ( member(unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))),null_class)
    | ~ spl0_421 ),
    inference(avatar_component_clause,[],[f6796]) ).

fof(f6796,plain,
    ( spl0_421
  <=> member(unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f22636,plain,
    ( ~ spl0_1030
    | ~ spl0_5
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f2408,f2369,f192,f22633]) ).

fof(f22633,plain,
    ( spl0_1030
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f192,plain,
    ( spl0_5
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f2369,plain,
    ( spl0_242
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f2408,plain,
    ( ~ inductive(choice)
    | ~ spl0_5
    | ~ spl0_242 ),
    inference(resolution,[],[f2370,f194]) ).

fof(f194,plain,
    ( function(choice)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f192]) ).

fof(f2370,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f2369]) ).

fof(f22624,plain,
    ( spl0_1028
    | spl0_1029
    | ~ spl0_260
    | ~ spl0_500
    | ~ spl0_612 ),
    inference(avatar_split_clause,[],[f12683,f12597,f9870,f2686,f22621,f22617]) ).

fof(f22617,plain,
    ( spl0_1028
  <=> member(not_subclass_element(universal_class,null_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f12683,plain,
    ( subclass(universal_class,null_class)
    | member(not_subclass_element(universal_class,null_class),element_relation)
    | ~ spl0_260
    | ~ spl0_500
    | ~ spl0_612 ),
    inference(forward_demodulation,[],[f12682,f9872]) ).

fof(f12682,plain,
    ( member(not_subclass_element(universal_class,null_class),element_relation)
    | subclass(universal_class,complement(subset_relation))
    | ~ spl0_260
    | ~ spl0_500
    | ~ spl0_612 ),
    inference(forward_demodulation,[],[f12637,f9872]) ).

fof(f12637,plain,
    ( member(not_subclass_element(universal_class,complement(subset_relation)),element_relation)
    | subclass(universal_class,complement(subset_relation))
    | ~ spl0_260
    | ~ spl0_612 ),
    inference(resolution,[],[f12598,f2687]) ).

fof(f22614,plain,
    ( spl0_1027
    | ~ spl0_37
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f8262,f1224,f339,f22612]) ).

fof(f22612,plain,
    ( spl0_1027
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f1224,plain,
    ( spl0_144
  <=> member(u,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f8262,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(u,X0) )
    | ~ spl0_37
    | ~ spl0_144 ),
    inference(resolution,[],[f1226,f340]) ).

fof(f1226,plain,
    ( member(u,cross_product(universal_class,universal_class))
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1224]) ).

fof(f22609,plain,
    ( spl0_1026
    | ~ spl0_77
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1629,f1600,f595,f22607]) ).

fof(f22607,plain,
    ( spl0_1026
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f595,plain,
    ( spl0_77
  <=> ! [X9,X11,X10] :
        ( ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1600,plain,
    ( spl0_179
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1629,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_77
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f596]) ).

fof(f596,plain,
    ( ! [X10,X11,X9] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | ~ operation(X10) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f1601,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f1600]) ).

fof(f22604,plain,
    ( spl0_1025
    | ~ spl0_77
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1604,f1596,f595,f22602]) ).

fof(f22602,plain,
    ( spl0_1025
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f1596,plain,
    ( spl0_178
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f1604,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_77
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f596]) ).

fof(f1597,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f1596]) ).

fof(f22548,plain,
    ( spl0_1024
    | ~ spl0_20
    | ~ spl0_996 ),
    inference(avatar_split_clause,[],[f22241,f22063,f257,f22546]) ).

fof(f22241,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_20
    | ~ spl0_996 ),
    inference(duplicate_literal_removal,[],[f22196]) ).

fof(f22196,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,null_class) )
    | ~ spl0_20
    | ~ spl0_996 ),
    inference(superposition,[],[f258,f22065]) ).

fof(f22544,plain,
    ( spl0_1023
    | ~ spl0_110
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f12325,f1863,f856,f22542]) ).

fof(f22542,plain,
    ( spl0_1023
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f1863,plain,
    ( spl0_197
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f12325,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_110
    | ~ spl0_197 ),
    inference(superposition,[],[f1864,f858]) ).

fof(f1864,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f1863]) ).

fof(f22540,plain,
    ( spl0_1022
    | ~ spl0_101
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1867,f1863,f754,f22538]) ).

fof(f22538,plain,
    ( spl0_1022
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f1867,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_197 ),
    inference(resolution,[],[f1864,f755]) ).

fof(f22513,plain,
    ( spl0_1021
    | ~ spl0_110
    | ~ spl0_1020 ),
    inference(avatar_split_clause,[],[f22509,f22506,f856,f22511]) ).

fof(f22511,plain,
    ( spl0_1021
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f22506,plain,
    ( spl0_1020
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f22509,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_110
    | ~ spl0_1020 ),
    inference(forward_demodulation,[],[f22507,f858]) ).

fof(f22507,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_1020 ),
    inference(avatar_component_clause,[],[f22506]) ).

fof(f22508,plain,
    ( spl0_1020
    | ~ spl0_172
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1777,f1757,f1505,f22506]) ).

fof(f1505,plain,
    ( spl0_172
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1777,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_172
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f1506]) ).

fof(f1506,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1505]) ).

fof(f22476,plain,
    ( spl0_1019
    | ~ spl0_68
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1866,f1863,f538,f22474]) ).

fof(f22474,plain,
    ( spl0_1019
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f538,plain,
    ( spl0_68
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,X0)
        | ~ member(X3,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f1866,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_197 ),
    inference(resolution,[],[f1864,f539]) ).

fof(f539,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | ~ member(X3,X1)
        | ~ member(X2,X0) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f538]) ).

fof(f22455,plain,
    ( spl0_1018
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_1017 ),
    inference(avatar_split_clause,[],[f22451,f22443,f19371,f856,f22453]) ).

fof(f22453,plain,
    ( spl0_1018
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),element_relation)
        | ~ operation(X3)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f22443,plain,
    ( spl0_1017
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f22451,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),element_relation)
        | ~ operation(X3)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_1017 ),
    inference(forward_demodulation,[],[f22450,f19373]) ).

fof(f22450,plain,
    ( ! [X2,X3,X0,X1] :
        ( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),element_relation)
        | ~ operation(X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_1017 ),
    inference(forward_demodulation,[],[f22449,f19373]) ).

fof(f22449,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),element_relation)
        | ~ operation(X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_1017 ),
    inference(forward_demodulation,[],[f22448,f19373]) ).

fof(f22448,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),element_relation)
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_1017 ),
    inference(forward_demodulation,[],[f22447,f19373]) ).

fof(f22447,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_1017 ),
    inference(forward_demodulation,[],[f22446,f19373]) ).

fof(f22446,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_1017 ),
    inference(forward_demodulation,[],[f22444,f858]) ).

fof(f22444,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_1017 ),
    inference(avatar_component_clause,[],[f22443]) ).

fof(f22445,plain,
    ( spl0_1017
    | ~ spl0_39
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1870,f1863,f347,f22443]) ).

fof(f347,plain,
    ( spl0_39
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1870,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_197 ),
    inference(superposition,[],[f1864,f348]) ).

fof(f348,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f22441,plain,
    ( spl0_218
    | ~ spl0_8
    | ~ spl0_741
    | ~ spl0_996 ),
    inference(avatar_split_clause,[],[f22370,f22063,f16949,f206,f2110]) ).

fof(f2110,plain,
    ( spl0_218
  <=> member(null_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f16949,plain,
    ( spl0_741
  <=> ! [X0] :
        ( ~ subclass(complement(null_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f22370,plain,
    ( member(null_class,null_class)
    | ~ spl0_8
    | ~ spl0_741
    | ~ spl0_996 ),
    inference(forward_demodulation,[],[f17189,f22065]) ).

fof(f17189,plain,
    ( member(null_class,complement(null_class))
    | ~ spl0_8
    | ~ spl0_741 ),
    inference(resolution,[],[f16950,f207]) ).

fof(f16950,plain,
    ( ! [X0] :
        ( ~ subclass(complement(null_class),X0)
        | member(null_class,X0) )
    | ~ spl0_741 ),
    inference(avatar_component_clause,[],[f16949]) ).

fof(f22427,plain,
    ( spl0_1016
    | ~ spl0_84
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1552,f1545,f643,f22425]) ).

fof(f22425,plain,
    ( spl0_1016
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(X3))
        | ~ operation(X2)
        | ~ homomorphism(X4,X3,X5)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f643,plain,
    ( spl0_84
  <=> ! [X10,X11,X0,X9,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
        | ~ homomorphism(X9,X10,X11)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f1545,plain,
    ( spl0_175
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1552,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(X3))
        | ~ operation(X2)
        | ~ homomorphism(X4,X3,X5)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) )
    | ~ spl0_84
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f644]) ).

fof(f644,plain,
    ( ! [X10,X0,X11,X1,X9] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
        | ~ homomorphism(X9,X10,X11)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f643]) ).

fof(f1546,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | ~ operation(X0) )
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f1545]) ).

fof(f22414,plain,
    ( spl0_1015
    | ~ spl0_173
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1857,f1851,f1512,f22412]) ).

fof(f22412,plain,
    ( spl0_1015
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f1512,plain,
    ( spl0_173
  <=> ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1851,plain,
    ( spl0_195
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f1857,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(regular(cross_product(X0,X1)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173
    | ~ spl0_195 ),
    inference(superposition,[],[f1852,f1513]) ).

fof(f1513,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f1512]) ).

fof(f1852,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f1851]) ).

fof(f22395,plain,
    ( spl0_1014
    | ~ spl0_84
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1531,f1512,f643,f22393]) ).

fof(f22393,plain,
    ( spl0_1014
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
        | ~ homomorphism(X3,X2,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f1531,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
        | ~ homomorphism(X3,X2,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_84
    | ~ spl0_173 ),
    inference(superposition,[],[f644,f1513]) ).

fof(f22390,plain,
    ( spl0_1013
    | ~ spl0_170
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1641,f1600,f1461,f22388]) ).

fof(f22388,plain,
    ( spl0_1013
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f1641,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) )
    | ~ spl0_170
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1462]) ).

fof(f22385,plain,
    ( spl0_1012
    | ~ spl0_171
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1634,f1600,f1465,f22383]) ).

fof(f22383,plain,
    ( spl0_1012
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f1634,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) )
    | ~ spl0_171
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1466]) ).

fof(f22380,plain,
    ( spl0_1011
    | ~ spl0_170
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1616,f1596,f1461,f22378]) ).

fof(f22378,plain,
    ( spl0_1011
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f1616,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) )
    | ~ spl0_170
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1462]) ).

fof(f22375,plain,
    ( spl0_1010
    | ~ spl0_171
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1609,f1596,f1465,f22373]) ).

fof(f22373,plain,
    ( spl0_1010
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f1609,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) )
    | ~ spl0_171
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1466]) ).

fof(f22369,plain,
    ( spl0_218
    | ~ spl0_335
    | ~ spl0_996 ),
    inference(avatar_split_clause,[],[f22168,f22063,f4138,f2110]) ).

fof(f22168,plain,
    ( member(null_class,null_class)
    | ~ spl0_335
    | ~ spl0_996 ),
    inference(superposition,[],[f4140,f22065]) ).

fof(f4140,plain,
    ( member(null_class,complement(null_class))
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f4138]) ).

fof(f22336,plain,
    ( spl0_1009
    | ~ spl0_110
    | ~ spl0_1008 ),
    inference(avatar_split_clause,[],[f22332,f22329,f856,f22334]) ).

fof(f22334,plain,
    ( spl0_1009
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),element_relation)
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f22329,plain,
    ( spl0_1008
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f22332,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),element_relation)
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1)) )
    | ~ spl0_110
    | ~ spl0_1008 ),
    inference(forward_demodulation,[],[f22330,f858]) ).

fof(f22330,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_1008 ),
    inference(avatar_component_clause,[],[f22329]) ).

fof(f22331,plain,
    ( spl0_1008
    | ~ spl0_78
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1495,f1465,f600,f22329]) ).

fof(f600,plain,
    ( spl0_78
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1495,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f601]) ).

fof(f601,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f600]) ).

fof(f22295,plain,
    ( spl0_1007
    | ~ spl0_110
    | ~ spl0_1006 ),
    inference(avatar_split_clause,[],[f22291,f22288,f856,f22293]) ).

fof(f22293,plain,
    ( spl0_1007
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),element_relation)
        | null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f22288,plain,
    ( spl0_1006
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f22291,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),element_relation)
        | null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2)) )
    | ~ spl0_110
    | ~ spl0_1006 ),
    inference(forward_demodulation,[],[f22289,f858]) ).

fof(f22289,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_1006 ),
    inference(avatar_component_clause,[],[f22288]) ).

fof(f22290,plain,
    ( spl0_1006
    | ~ spl0_78
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1477,f1461,f600,f22288]) ).

fof(f1477,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f601]) ).

fof(f22286,plain,
    ( spl0_1005
    | ~ spl0_11
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1854,f1851,f218,f22284]) ).

fof(f22284,plain,
    ( spl0_1005
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f1854,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) )
    | ~ spl0_11
    | ~ spl0_195 ),
    inference(resolution,[],[f1852,f219]) ).

fof(f22266,plain,
    ( spl0_1004
    | ~ spl0_46
    | ~ spl0_84
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f919,f878,f643,f404,f22264]) ).

fof(f22264,plain,
    ( spl0_1004
  <=> ! [X0,X3,X2,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f404,plain,
    ( spl0_46
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f878,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f919,plain,
    ( ! [X2,X3,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
    | ~ spl0_46
    | ~ spl0_84
    | ~ spl0_115 ),
    inference(forward_demodulation,[],[f917,f405]) ).

fof(f405,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f917,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
    | ~ spl0_84
    | ~ spl0_115 ),
    inference(resolution,[],[f879,f644]) ).

fof(f879,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f878]) ).

fof(f22145,plain,
    ( spl0_1003
    | ~ spl0_74
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1633,f1600,f575,f22143]) ).

fof(f22143,plain,
    ( spl0_1003
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f1633,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_74
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f576]) ).

fof(f22140,plain,
    ( spl0_1002
    | ~ spl0_74
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1608,f1596,f575,f22138]) ).

fof(f22138,plain,
    ( spl0_1002
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f1608,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_74
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f576]) ).

fof(f22086,plain,
    ( spl0_1001
    | ~ spl0_110
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f12324,f1838,f856,f22084]) ).

fof(f22084,plain,
    ( spl0_1001
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f1838,plain,
    ( spl0_194
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f12324,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_110
    | ~ spl0_194 ),
    inference(superposition,[],[f1839,f858]) ).

fof(f1839,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f1838]) ).

fof(f22082,plain,
    ( spl0_1000
    | ~ spl0_101
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1842,f1838,f754,f22080]) ).

fof(f22080,plain,
    ( spl0_1000
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f1842,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_194 ),
    inference(resolution,[],[f1839,f755]) ).

fof(f22078,plain,
    ( spl0_999
    | ~ spl0_84
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f774,f746,f643,f22076]) ).

fof(f22076,plain,
    ( spl0_999
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(X0))
        | ~ homomorphism(X1,X0,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f774,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(X0))
        | ~ homomorphism(X1,X0,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) )
    | ~ spl0_84
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f644]) ).

fof(f22074,plain,
    ( ~ spl0_997
    | spl0_998
    | ~ spl0_39
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1873,f1863,f347,f22072,f22068]) ).

fof(f22068,plain,
    ( spl0_997
  <=> operation(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f22072,plain,
    ( spl0_998
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ operation(X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f1873,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ operation(X3)
        | ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(null_class,universal_class))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_39
    | ~ spl0_197 ),
    inference(superposition,[],[f1864,f348]) ).

fof(f22066,plain,
    ( ~ spl0_162
    | spl0_996
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_297
    | spl0_711
    | ~ spl0_801 ),
    inference(avatar_split_clause,[],[f19705,f18607,f15972,f3255,f1202,f921,f856,f22063,f1372]) ).

fof(f19705,plain,
    ( null_class = complement(null_class)
    | ~ member(u,subset_relation)
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_140
    | ~ spl0_297
    | spl0_711
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f19704,f15981]) ).

fof(f19704,plain,
    ( null_class = complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(u,subset_relation)
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_297
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f19703,f858]) ).

fof(f19703,plain,
    ( null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(u,subset_relation)
    | ~ spl0_110
    | ~ spl0_140
    | ~ spl0_297
    | ~ spl0_801 ),
    inference(forward_demodulation,[],[f19691,f12338]) ).

fof(f12338,plain,
    ( null_class = complement(element_relation)
    | ~ spl0_110
    | ~ spl0_297 ),
    inference(superposition,[],[f3257,f858]) ).

fof(f3257,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f3255]) ).

fof(f19691,plain,
    ( null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(u,subset_relation)
    | ~ spl0_140
    | ~ spl0_801 ),
    inference(resolution,[],[f18608,f1203]) ).

fof(f22044,plain,
    ( spl0_995
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_994 ),
    inference(avatar_split_clause,[],[f22040,f22033,f19371,f856,f22042]) ).

fof(f22042,plain,
    ( spl0_995
  <=> ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f22033,plain,
    ( spl0_994
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f22040,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_994 ),
    inference(forward_demodulation,[],[f22039,f19373]) ).

fof(f22039,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_994 ),
    inference(forward_demodulation,[],[f22038,f19373]) ).

fof(f22038,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_994 ),
    inference(forward_demodulation,[],[f22037,f19373]) ).

fof(f22037,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_994 ),
    inference(forward_demodulation,[],[f22036,f19373]) ).

fof(f22036,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_994 ),
    inference(forward_demodulation,[],[f22034,f858]) ).

fof(f22034,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_994 ),
    inference(avatar_component_clause,[],[f22033]) ).

fof(f22035,plain,
    ( spl0_994
    | ~ spl0_39
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1845,f1838,f347,f22033]) ).

fof(f1845,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_194 ),
    inference(superposition,[],[f1839,f348]) ).

fof(f22004,plain,
    ( spl0_993
    | ~ spl0_68
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1841,f1838,f538,f22002]) ).

fof(f22002,plain,
    ( spl0_993
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f1841,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_194 ),
    inference(resolution,[],[f1839,f539]) ).

fof(f21989,plain,
    ( spl0_992
    | ~ spl0_71
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1488,f1465,f558,f21987]) ).

fof(f21987,plain,
    ( spl0_992
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f558,plain,
    ( spl0_71
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f1488,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) )
    | ~ spl0_71
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f559]) ).

fof(f559,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f558]) ).

fof(f21985,plain,
    ( spl0_991
    | ~ spl0_71
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1470,f1461,f558,f21983]) ).

fof(f21983,plain,
    ( spl0_991
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f1470,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) )
    | ~ spl0_71
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f559]) ).

fof(f21944,plain,
    ( spl0_990
    | ~ spl0_426
    | ~ spl0_801 ),
    inference(avatar_split_clause,[],[f19680,f18607,f7296,f21942]) ).

fof(f21942,plain,
    ( spl0_990
  <=> ! [X0] :
        ( complement(X0) = null_class
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f19680,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | null_class = X0 )
    | ~ spl0_426
    | ~ spl0_801 ),
    inference(resolution,[],[f18608,f7297]) ).

fof(f21940,plain,
    ( spl0_989
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_988 ),
    inference(avatar_split_clause,[],[f21936,f21931,f19371,f856,f21938]) ).

fof(f21938,plain,
    ( spl0_989
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),element_relation)
        | ~ member(X2,null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f21931,plain,
    ( spl0_988
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f21936,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),element_relation)
        | ~ member(X2,null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_988 ),
    inference(forward_demodulation,[],[f21935,f858]) ).

fof(f21935,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_988 ),
    inference(forward_demodulation,[],[f21934,f19373]) ).

fof(f21934,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_988 ),
    inference(forward_demodulation,[],[f21932,f858]) ).

fof(f21932,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_988 ),
    inference(avatar_component_clause,[],[f21931]) ).

fof(f21933,plain,
    ( spl0_988
    | ~ spl0_183
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1797,f1761,f1679,f21931]) ).

fof(f1679,plain,
    ( spl0_183
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f1797,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_183
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f1680]) ).

fof(f1680,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1679]) ).

fof(f21909,plain,
    ( spl0_987
    | ~ spl0_110
    | ~ spl0_986 ),
    inference(avatar_split_clause,[],[f21905,f21902,f856,f21907]) ).

fof(f21907,plain,
    ( spl0_987
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f21902,plain,
    ( spl0_986
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f21905,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
    | ~ spl0_110
    | ~ spl0_986 ),
    inference(forward_demodulation,[],[f21903,f858]) ).

fof(f21903,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
    | ~ spl0_986 ),
    inference(avatar_component_clause,[],[f21902]) ).

fof(f21904,plain,
    ( spl0_986
    | ~ spl0_63
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1793,f1761,f500,f21902]) ).

fof(f500,plain,
    ( spl0_63
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,domain_of(X0))
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1793,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
    | ~ spl0_63
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f501]) ).

fof(f501,plain,
    ( ! [X0,X4] :
        ( member(X4,domain_of(X0))
        | ~ member(X4,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f500]) ).

fof(f21863,plain,
    ( spl0_985
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f21859,f21854,f19371,f856,f21861]) ).

fof(f21861,plain,
    ( spl0_985
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f21859,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_984 ),
    inference(forward_demodulation,[],[f21858,f858]) ).

fof(f21858,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_984 ),
    inference(forward_demodulation,[],[f21857,f19373]) ).

fof(f21857,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_984 ),
    inference(forward_demodulation,[],[f21855,f858]) ).

fof(f21856,plain,
    ( spl0_984
    | ~ spl0_183
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1779,f1757,f1679,f21854]) ).

fof(f1779,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_183
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f1680]) ).

fof(f21835,plain,
    ( spl0_983
    | ~ spl0_110
    | ~ spl0_982 ),
    inference(avatar_split_clause,[],[f21830,f21827,f856,f21833]) ).

fof(f21833,plain,
    ( spl0_983
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).

fof(f21827,plain,
    ( spl0_982
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f21830,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
    | ~ spl0_110
    | ~ spl0_982 ),
    inference(forward_demodulation,[],[f21828,f858]) ).

fof(f21828,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
    | ~ spl0_982 ),
    inference(avatar_component_clause,[],[f21827]) ).

fof(f21829,plain,
    ( spl0_982
    | ~ spl0_63
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1775,f1757,f500,f21827]) ).

fof(f1775,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
    | ~ spl0_63
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f501]) ).

fof(f21809,plain,
    ( spl0_981
    | ~ spl0_110
    | ~ spl0_980 ),
    inference(avatar_split_clause,[],[f21805,f21802,f856,f21807]) ).

fof(f21807,plain,
    ( spl0_981
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),element_relation)
        | ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f21802,plain,
    ( spl0_980
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f21805,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),element_relation)
        | ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_110
    | ~ spl0_980 ),
    inference(forward_demodulation,[],[f21803,f858]) ).

fof(f21803,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_980 ),
    inference(avatar_component_clause,[],[f21802]) ).

fof(f21804,plain,
    ( spl0_980
    | ~ spl0_173
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1799,f1761,f1512,f21802]) ).

fof(f1799,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173
    | ~ spl0_189 ),
    inference(superposition,[],[f1762,f1513]) ).

fof(f21770,plain,
    ( spl0_979
    | ~ spl0_110
    | ~ spl0_978 ),
    inference(avatar_split_clause,[],[f21766,f21763,f856,f21768]) ).

fof(f21768,plain,
    ( spl0_979
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f21763,plain,
    ( spl0_978
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f21766,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_110
    | ~ spl0_978 ),
    inference(forward_demodulation,[],[f21764,f858]) ).

fof(f21764,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_978 ),
    inference(avatar_component_clause,[],[f21763]) ).

fof(f21765,plain,
    ( spl0_978
    | ~ spl0_172
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1800,f1761,f1505,f21763]) ).

fof(f1800,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_172
    | ~ spl0_189 ),
    inference(duplicate_literal_removal,[],[f1795]) ).

fof(f1795,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_172
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f1506]) ).

fof(f21748,plain,
    ( spl0_977
    | ~ spl0_110
    | ~ spl0_976 ),
    inference(avatar_split_clause,[],[f21744,f21741,f856,f21746]) ).

fof(f21746,plain,
    ( spl0_977
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f21741,plain,
    ( spl0_976
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f21744,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_110
    | ~ spl0_976 ),
    inference(forward_demodulation,[],[f21742,f858]) ).

fof(f21742,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_976 ),
    inference(avatar_component_clause,[],[f21741]) ).

fof(f21743,plain,
    ( spl0_976
    | ~ spl0_175
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1647,f1600,f1545,f21741]) ).

fof(f1647,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_175
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1546]) ).

fof(f21739,plain,
    ( spl0_952
    | ~ spl0_975
    | ~ spl0_108
    | spl0_953 ),
    inference(avatar_split_clause,[],[f21617,f21372,f848,f21736,f21368]) ).

fof(f21368,plain,
    ( spl0_952
  <=> null_class = omega ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f21736,plain,
    ( spl0_975
  <=> subclass(omega,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f848,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f21372,plain,
    ( spl0_953
  <=> member(regular(omega),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f21617,plain,
    ( ~ subclass(omega,null_class)
    | null_class = omega
    | ~ spl0_108
    | spl0_953 ),
    inference(resolution,[],[f21374,f849]) ).

fof(f849,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f848]) ).

fof(f21374,plain,
    ( ~ member(regular(omega),null_class)
    | spl0_953 ),
    inference(avatar_component_clause,[],[f21372]) ).

fof(f21721,plain,
    ( spl0_974
    | ~ spl0_110
    | ~ spl0_973 ),
    inference(avatar_split_clause,[],[f21717,f21714,f856,f21719]) ).

fof(f21719,plain,
    ( spl0_974
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f21714,plain,
    ( spl0_973
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f21717,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_110
    | ~ spl0_973 ),
    inference(forward_demodulation,[],[f21715,f858]) ).

fof(f21715,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_973 ),
    inference(avatar_component_clause,[],[f21714]) ).

fof(f21716,plain,
    ( spl0_973
    | ~ spl0_175
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1622,f1596,f1545,f21714]) ).

fof(f1622,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_175
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1546]) ).

fof(f21699,plain,
    ( spl0_972
    | ~ spl0_110
    | ~ spl0_971 ),
    inference(avatar_split_clause,[],[f21695,f21692,f856,f21697]) ).

fof(f21697,plain,
    ( spl0_972
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),element_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).

fof(f21692,plain,
    ( spl0_971
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f21695,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),element_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4)) )
    | ~ spl0_110
    | ~ spl0_971 ),
    inference(forward_demodulation,[],[f21693,f858]) ).

fof(f21693,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class))
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
        | ~ compatible(X0,X1,X2) )
    | ~ spl0_971 ),
    inference(avatar_component_clause,[],[f21692]) ).

fof(f21694,plain,
    ( spl0_971
    | ~ spl0_78
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1564,f1545,f600,f21692]) ).

fof(f1564,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f601]) ).

fof(f21659,plain,
    ( spl0_970
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_969 ),
    inference(avatar_split_clause,[],[f21655,f21650,f19371,f856,f21657]) ).

fof(f21657,plain,
    ( spl0_970
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),element_relation)
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f21655,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),element_relation)
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_969 ),
    inference(forward_demodulation,[],[f21654,f858]) ).

fof(f21654,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_969 ),
    inference(forward_demodulation,[],[f21653,f19373]) ).

fof(f21653,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_969 ),
    inference(forward_demodulation,[],[f21651,f858]) ).

fof(f21652,plain,
    ( spl0_969
    | ~ spl0_180
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1796,f1761,f1654,f21650]) ).

fof(f1654,plain,
    ( spl0_180
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f1796,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_180
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f1655]) ).

fof(f1655,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_180 ),
    inference(avatar_component_clause,[],[f1654]) ).

fof(f21615,plain,
    ( spl0_968
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_967 ),
    inference(avatar_split_clause,[],[f21611,f21606,f19371,f856,f21613]) ).

fof(f21613,plain,
    ( spl0_968
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).

fof(f21611,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_967 ),
    inference(forward_demodulation,[],[f21610,f858]) ).

fof(f21610,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_967 ),
    inference(forward_demodulation,[],[f21609,f19373]) ).

fof(f21609,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_967 ),
    inference(forward_demodulation,[],[f21607,f858]) ).

fof(f21608,plain,
    ( spl0_967
    | ~ spl0_180
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1778,f1757,f1654,f21606]) ).

fof(f1778,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_180
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f1655]) ).

fof(f21571,plain,
    ( spl0_966
    | ~ spl0_110
    | ~ spl0_965 ),
    inference(avatar_split_clause,[],[f21567,f21564,f856,f21569]) ).

fof(f21569,plain,
    ( spl0_966
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f21564,plain,
    ( spl0_965
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f21567,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
    | ~ spl0_110
    | ~ spl0_965 ),
    inference(forward_demodulation,[],[f21565,f858]) ).

fof(f21565,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
    | ~ spl0_965 ),
    inference(avatar_component_clause,[],[f21564]) ).

fof(f21566,plain,
    ( spl0_965
    | ~ spl0_125
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1637,f1600,f999,f21564]) ).

fof(f1637,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
    | ~ spl0_125
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1000]) ).

fof(f21529,plain,
    ( spl0_964
    | ~ spl0_110
    | ~ spl0_963 ),
    inference(avatar_split_clause,[],[f21525,f21522,f856,f21527]) ).

fof(f21527,plain,
    ( spl0_964
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f21522,plain,
    ( spl0_963
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f21525,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
    | ~ spl0_110
    | ~ spl0_963 ),
    inference(forward_demodulation,[],[f21523,f858]) ).

fof(f21523,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
    | ~ spl0_963 ),
    inference(avatar_component_clause,[],[f21522]) ).

fof(f21524,plain,
    ( spl0_963
    | ~ spl0_124
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1631,f1600,f995,f21522]) ).

fof(f1631,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
    | ~ spl0_124
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f996]) ).

fof(f21487,plain,
    ( spl0_962
    | ~ spl0_110
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f21483,f21480,f856,f21485]) ).

fof(f21485,plain,
    ( spl0_962
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f21480,plain,
    ( spl0_961
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f21483,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
    | ~ spl0_110
    | ~ spl0_961 ),
    inference(forward_demodulation,[],[f21481,f858]) ).

fof(f21481,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
    | ~ spl0_961 ),
    inference(avatar_component_clause,[],[f21480]) ).

fof(f21482,plain,
    ( spl0_961
    | ~ spl0_125
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1612,f1596,f999,f21480]) ).

fof(f1612,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
    | ~ spl0_125
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1000]) ).

fof(f21445,plain,
    ( spl0_960
    | ~ spl0_110
    | ~ spl0_959 ),
    inference(avatar_split_clause,[],[f21441,f21438,f856,f21443]) ).

fof(f21443,plain,
    ( spl0_960
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f21438,plain,
    ( spl0_959
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f21441,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
    | ~ spl0_110
    | ~ spl0_959 ),
    inference(forward_demodulation,[],[f21439,f858]) ).

fof(f21439,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
    | ~ spl0_959 ),
    inference(avatar_component_clause,[],[f21438]) ).

fof(f21440,plain,
    ( spl0_959
    | ~ spl0_124
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1606,f1596,f995,f21438]) ).

fof(f1606,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
    | ~ spl0_124
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f996]) ).

fof(f21435,plain,
    ( spl0_958
    | ~ spl0_78
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1032,f999,f600,f21433]) ).

fof(f21433,plain,
    ( spl0_958
  <=> ! [X4,X0,X3,X2,X1] :
        ( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f1032,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f601]) ).

fof(f21430,plain,
    ( spl0_957
    | ~ spl0_78
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1015,f995,f600,f21428]) ).

fof(f21428,plain,
    ( spl0_957
  <=> ! [X4,X0,X3,X2,X1] :
        ( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f1015,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f601]) ).

fof(f21425,plain,
    ( spl0_956
    | ~ spl0_83
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1530,f1512,f637,f21423]) ).

fof(f21423,plain,
    ( spl0_956
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f637,plain,
    ( spl0_83
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f1530,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_83
    | ~ spl0_173 ),
    inference(superposition,[],[f638,f1513]) ).

fof(f638,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f637]) ).

fof(f21384,plain,
    ( spl0_955
    | ~ spl0_110
    | ~ spl0_954 ),
    inference(avatar_split_clause,[],[f21380,f21377,f856,f21382]) ).

fof(f21382,plain,
    ( spl0_955
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f21377,plain,
    ( spl0_954
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f21380,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_110
    | ~ spl0_954 ),
    inference(forward_demodulation,[],[f21378,f858]) ).

fof(f21378,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_954 ),
    inference(avatar_component_clause,[],[f21377]) ).

fof(f21379,plain,
    ( spl0_954
    | ~ spl0_119
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1643,f1600,f925,f21377]) ).

fof(f1643,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_119
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f926]) ).

fof(f21375,plain,
    ( spl0_952
    | ~ spl0_953
    | ~ spl0_23
    | ~ spl0_700 ),
    inference(avatar_split_clause,[],[f15907,f15817,f269,f21372,f21368]) ).

fof(f269,plain,
    ( spl0_23
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f15817,plain,
    ( spl0_700
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,omega) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f15907,plain,
    ( ~ member(regular(omega),null_class)
    | null_class = omega
    | ~ spl0_23
    | ~ spl0_700 ),
    inference(resolution,[],[f15818,f270]) ).

fof(f270,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f15818,plain,
    ( ! [X0] :
        ( ~ member(X0,omega)
        | ~ member(X0,null_class) )
    | ~ spl0_700 ),
    inference(avatar_component_clause,[],[f15817]) ).

fof(f21329,plain,
    ( spl0_951
    | ~ spl0_110
    | ~ spl0_950 ),
    inference(avatar_split_clause,[],[f21325,f21322,f856,f21327]) ).

fof(f21327,plain,
    ( spl0_951
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f21322,plain,
    ( spl0_950
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f21325,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_110
    | ~ spl0_950 ),
    inference(forward_demodulation,[],[f21323,f858]) ).

fof(f21323,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_950 ),
    inference(avatar_component_clause,[],[f21322]) ).

fof(f21324,plain,
    ( spl0_950
    | ~ spl0_118
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1636,f1600,f921,f21322]) ).

fof(f1636,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_118
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f922]) ).

fof(f21283,plain,
    ( spl0_949
    | ~ spl0_110
    | ~ spl0_948 ),
    inference(avatar_split_clause,[],[f21279,f21276,f856,f21281]) ).

fof(f21281,plain,
    ( spl0_949
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f21276,plain,
    ( spl0_948
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f21279,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_110
    | ~ spl0_948 ),
    inference(forward_demodulation,[],[f21277,f858]) ).

fof(f21277,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_948 ),
    inference(avatar_component_clause,[],[f21276]) ).

fof(f21278,plain,
    ( spl0_948
    | ~ spl0_119
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1618,f1596,f925,f21276]) ).

fof(f1618,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_119
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f926]) ).

fof(f21237,plain,
    ( spl0_947
    | ~ spl0_110
    | ~ spl0_946 ),
    inference(avatar_split_clause,[],[f21233,f21230,f856,f21235]) ).

fof(f21235,plain,
    ( spl0_947
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f21230,plain,
    ( spl0_946
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f21233,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_110
    | ~ spl0_946 ),
    inference(forward_demodulation,[],[f21231,f858]) ).

fof(f21231,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_946 ),
    inference(avatar_component_clause,[],[f21230]) ).

fof(f21232,plain,
    ( spl0_946
    | ~ spl0_118
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1611,f1596,f921,f21230]) ).

fof(f1611,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_118
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f922]) ).

fof(f21227,plain,
    ( spl0_945
    | ~ spl0_78
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f967,f925,f600,f21225]) ).

fof(f21225,plain,
    ( spl0_945
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f967,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f601]) ).

fof(f21161,plain,
    ( spl0_944
    | ~ spl0_78
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f948,f921,f600,f21159]) ).

fof(f21159,plain,
    ( spl0_944
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f948,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f601]) ).

fof(f21156,plain,
    ( spl0_943
    | ~ spl0_25
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1630,f1600,f280,f21154]) ).

fof(f21154,plain,
    ( spl0_943
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f1630,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_25
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f281]) ).

fof(f21151,plain,
    ( spl0_942
    | ~ spl0_25
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1605,f1596,f280,f21149]) ).

fof(f21149,plain,
    ( spl0_942
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f1605,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_25
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f281]) ).

fof(f21094,plain,
    ( spl0_941
    | ~ spl0_110
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f12323,f1821,f856,f21092]) ).

fof(f21092,plain,
    ( spl0_941
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f1821,plain,
    ( spl0_192
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f12323,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_110
    | ~ spl0_192 ),
    inference(superposition,[],[f1822,f858]) ).

fof(f1822,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_192 ),
    inference(avatar_component_clause,[],[f1821]) ).

fof(f21090,plain,
    ( spl0_940
    | ~ spl0_101
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1825,f1821,f754,f21088]) ).

fof(f21088,plain,
    ( spl0_940
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f1825,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_192 ),
    inference(resolution,[],[f1822,f755]) ).

fof(f21085,plain,
    ( spl0_939
    | ~ spl0_23
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1635,f1600,f269,f21083]) ).

fof(f21083,plain,
    ( spl0_939
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f1635,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f270]) ).

fof(f21080,plain,
    ( spl0_938
    | ~ spl0_23
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1610,f1596,f269,f21078]) ).

fof(f21078,plain,
    ( spl0_938
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f1610,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f270]) ).

fof(f21017,plain,
    ( spl0_937
    | ~ spl0_110
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f12322,f1803,f856,f21015]) ).

fof(f21015,plain,
    ( spl0_937
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f1803,plain,
    ( spl0_190
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f12322,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_110
    | ~ spl0_190 ),
    inference(superposition,[],[f1804,f858]) ).

fof(f1804,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_190 ),
    inference(avatar_component_clause,[],[f1803]) ).

fof(f21013,plain,
    ( spl0_936
    | ~ spl0_101
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1807,f1803,f754,f21011]) ).

fof(f21011,plain,
    ( spl0_936
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f1807,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_190 ),
    inference(resolution,[],[f1804,f755]) ).

fof(f20997,plain,
    ( spl0_935
    | ~ spl0_161
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1492,f1465,f1368,f20995]) ).

fof(f20995,plain,
    ( spl0_935
  <=> ! [X0] :
        ( null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
        | ~ member(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f1368,plain,
    ( spl0_161
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f1492,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
        | ~ member(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_161
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f1369]) ).

fof(f1369,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1368]) ).

fof(f20981,plain,
    ( spl0_934
    | ~ spl0_161
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1474,f1461,f1368,f20979]) ).

fof(f20979,plain,
    ( spl0_934
  <=> ! [X0] :
        ( null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f1474,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_161
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f1369]) ).

fof(f20976,plain,
    ( spl0_933
    | ~ spl0_82
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1529,f1512,f633,f20974]) ).

fof(f20974,plain,
    ( spl0_933
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f633,plain,
    ( spl0_82
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f1529,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_82
    | ~ spl0_173 ),
    inference(superposition,[],[f634,f1513]) ).

fof(f634,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f633]) ).

fof(f20872,plain,
    ( spl0_932
    | ~ spl0_110
    | ~ spl0_931 ),
    inference(avatar_split_clause,[],[f20868,f20865,f856,f20870]) ).

fof(f20870,plain,
    ( spl0_932
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f20865,plain,
    ( spl0_931
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f20868,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_110
    | ~ spl0_931 ),
    inference(forward_demodulation,[],[f20866,f858]) ).

fof(f20866,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_931 ),
    inference(avatar_component_clause,[],[f20865]) ).

fof(f20867,plain,
    ( spl0_931
    | ~ spl0_45
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1789,f1761,f400,f20865]) ).

fof(f400,plain,
    ( spl0_45
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1789,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_45
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f401]) ).

fof(f401,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f400]) ).

fof(f20781,plain,
    ( spl0_930
    | ~ spl0_110
    | ~ spl0_929 ),
    inference(avatar_split_clause,[],[f20777,f20774,f856,f20779]) ).

fof(f20779,plain,
    ( spl0_930
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f20774,plain,
    ( spl0_929
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f20777,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
    | ~ spl0_110
    | ~ spl0_929 ),
    inference(forward_demodulation,[],[f20775,f858]) ).

fof(f20775,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
    | ~ spl0_929 ),
    inference(avatar_component_clause,[],[f20774]) ).

fof(f20776,plain,
    ( spl0_929
    | ~ spl0_45
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1771,f1757,f400,f20774]) ).

fof(f1771,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
    | ~ spl0_45
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f401]) ).

fof(f20731,plain,
    ( spl0_928
    | ~ spl0_110
    | ~ spl0_927 ),
    inference(avatar_split_clause,[],[f20727,f20724,f856,f20729]) ).

fof(f20729,plain,
    ( spl0_928
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f20724,plain,
    ( spl0_927
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f20727,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_110
    | ~ spl0_927 ),
    inference(forward_demodulation,[],[f20725,f858]) ).

fof(f20725,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3))) )
    | ~ spl0_927 ),
    inference(avatar_component_clause,[],[f20724]) ).

fof(f20726,plain,
    ( spl0_927
    | ~ spl0_41
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1792,f1761,f379,f20724]) ).

fof(f379,plain,
    ( spl0_41
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1792,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_41
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f380]) ).

fof(f380,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f20705,plain,
    ( spl0_926
    | ~ spl0_110
    | ~ spl0_925 ),
    inference(avatar_split_clause,[],[f20701,f20698,f856,f20703]) ).

fof(f20703,plain,
    ( spl0_926
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f20698,plain,
    ( spl0_925
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f20701,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_110
    | ~ spl0_925 ),
    inference(forward_demodulation,[],[f20699,f858]) ).

fof(f20699,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3))) )
    | ~ spl0_925 ),
    inference(avatar_component_clause,[],[f20698]) ).

fof(f20700,plain,
    ( spl0_925
    | ~ spl0_41
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1774,f1757,f379,f20698]) ).

fof(f1774,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_41
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f380]) ).

fof(f20696,plain,
    ( spl0_924
    | ~ spl0_71
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1430,f1425,f558,f20694]) ).

fof(f20694,plain,
    ( spl0_924
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f1425,plain,
    ( spl0_168
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1430,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) )
    | ~ spl0_71
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f559]) ).

fof(f1426,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1425]) ).

fof(f20539,plain,
    ( spl0_923
    | ~ spl0_110
    | ~ spl0_922 ),
    inference(avatar_split_clause,[],[f20535,f20532,f856,f20537]) ).

fof(f20537,plain,
    ( spl0_923
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f20532,plain,
    ( spl0_922
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f20535,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_110
    | ~ spl0_922 ),
    inference(forward_demodulation,[],[f20533,f858]) ).

fof(f20533,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_922 ),
    inference(avatar_component_clause,[],[f20532]) ).

fof(f20534,plain,
    ( spl0_922
    | ~ spl0_28
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1785,f1761,f292,f20532]) ).

fof(f292,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1785,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_28
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f293]) ).

fof(f293,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f292]) ).

fof(f20502,plain,
    ( spl0_921
    | ~ spl0_110
    | ~ spl0_920 ),
    inference(avatar_split_clause,[],[f20498,f20495,f856,f20500]) ).

fof(f20500,plain,
    ( spl0_921
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f20495,plain,
    ( spl0_920
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f20498,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_110
    | ~ spl0_920 ),
    inference(forward_demodulation,[],[f20496,f858]) ).

fof(f20496,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_920 ),
    inference(avatar_component_clause,[],[f20495]) ).

fof(f20497,plain,
    ( spl0_920
    | ~ spl0_27
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1784,f1761,f288,f20495]) ).

fof(f1784,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_27
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f289]) ).

fof(f20480,plain,
    ( spl0_919
    | ~ spl0_110
    | ~ spl0_917 ),
    inference(avatar_split_clause,[],[f20471,f20468,f856,f20478]) ).

fof(f20478,plain,
    ( spl0_919
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),element_relation)
        | ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f20468,plain,
    ( spl0_917
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f20471,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),element_relation)
        | ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_110
    | ~ spl0_917 ),
    inference(forward_demodulation,[],[f20469,f858]) ).

fof(f20469,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_917 ),
    inference(avatar_component_clause,[],[f20468]) ).

fof(f20476,plain,
    ( ~ spl0_918
    | ~ spl0_3
    | ~ spl0_894 ),
    inference(avatar_split_clause,[],[f20212,f20139,f182,f20473]) ).

fof(f20473,plain,
    ( spl0_918
  <=> member(w,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f182,plain,
    ( spl0_3
  <=> member(w,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f20212,plain,
    ( ~ member(w,null_class)
    | ~ spl0_3
    | ~ spl0_894 ),
    inference(resolution,[],[f20140,f184]) ).

fof(f184,plain,
    ( member(w,x)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f20470,plain,
    ( spl0_917
    | ~ spl0_173
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1781,f1757,f1512,f20468]) ).

fof(f1781,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173
    | ~ spl0_188 ),
    inference(superposition,[],[f1758,f1513]) ).

fof(f20438,plain,
    ( spl0_916
    | ~ spl0_110
    | ~ spl0_915 ),
    inference(avatar_split_clause,[],[f20434,f20431,f856,f20436]) ).

fof(f20436,plain,
    ( spl0_916
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f20431,plain,
    ( spl0_915
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f20434,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_110
    | ~ spl0_915 ),
    inference(forward_demodulation,[],[f20432,f858]) ).

fof(f20432,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_915 ),
    inference(avatar_component_clause,[],[f20431]) ).

fof(f20433,plain,
    ( spl0_915
    | ~ spl0_28
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1767,f1757,f292,f20431]) ).

fof(f1767,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_28
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f293]) ).

fof(f20401,plain,
    ( spl0_914
    | ~ spl0_110
    | ~ spl0_913 ),
    inference(avatar_split_clause,[],[f20397,f20394,f856,f20399]) ).

fof(f20399,plain,
    ( spl0_914
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f20394,plain,
    ( spl0_913
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f20397,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_110
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f20395,f858]) ).

fof(f20395,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_913 ),
    inference(avatar_component_clause,[],[f20394]) ).

fof(f20396,plain,
    ( spl0_913
    | ~ spl0_27
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1766,f1757,f288,f20394]) ).

fof(f1766,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_27
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f289]) ).

fof(f20392,plain,
    ( spl0_912
    | ~ spl0_137
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1566,f1545,f1145,f20390]) ).

fof(f20390,plain,
    ( spl0_912
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
        | ~ operation(X2)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f1145,plain,
    ( spl0_137
  <=> ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1566,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
        | ~ operation(X2)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) )
    | ~ spl0_137
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f1146]) ).

fof(f1146,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1145]) ).

fof(f20388,plain,
    ( spl0_911
    | ~ spl0_81
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1528,f1512,f629,f20386]) ).

fof(f20386,plain,
    ( spl0_911
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f629,plain,
    ( spl0_81
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1528,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_81
    | ~ spl0_173 ),
    inference(superposition,[],[f630,f1513]) ).

fof(f630,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f629]) ).

fof(f20367,plain,
    ( ~ spl0_910
    | ~ spl0_2
    | ~ spl0_894 ),
    inference(avatar_split_clause,[],[f20211,f20139,f177,f20364]) ).

fof(f20364,plain,
    ( spl0_910
  <=> member(v,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f177,plain,
    ( spl0_2
  <=> member(v,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f20211,plain,
    ( ~ member(v,null_class)
    | ~ spl0_2
    | ~ spl0_894 ),
    inference(resolution,[],[f20140,f179]) ).

fof(f179,plain,
    ( member(v,x)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f177]) ).

fof(f20362,plain,
    ( spl0_909
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(avatar_split_clause,[],[f20358,f20352,f19371,f856,f20360]) ).

fof(f20360,plain,
    ( spl0_909
  <=> ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),element_relation)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f20358,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),element_relation)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f20357,f19373]) ).

fof(f20357,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),element_relation)
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f20356,f19373]) ).

fof(f20356,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f20355,f19373]) ).

fof(f20355,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_908 ),
    inference(forward_demodulation,[],[f20353,f858]) ).

fof(f20354,plain,
    ( spl0_908
    | ~ spl0_39
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1828,f1821,f347,f20352]) ).

fof(f1828,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_192 ),
    inference(superposition,[],[f1822,f348]) ).

fof(f20334,plain,
    ( spl0_907
    | ~ spl0_110
    | ~ spl0_906 ),
    inference(avatar_split_clause,[],[f20330,f20327,f856,f20332]) ).

fof(f20332,plain,
    ( spl0_907
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f20327,plain,
    ( spl0_906
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).

fof(f20330,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_110
    | ~ spl0_906 ),
    inference(forward_demodulation,[],[f20328,f858]) ).

fof(f20328,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_906 ),
    inference(avatar_component_clause,[],[f20327]) ).

fof(f20329,plain,
    ( spl0_906
    | ~ spl0_168
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1640,f1600,f1425,f20327]) ).

fof(f1640,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_168
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1426]) ).

fof(f20309,plain,
    ( spl0_905
    | ~ spl0_110
    | ~ spl0_904 ),
    inference(avatar_split_clause,[],[f20305,f20302,f856,f20307]) ).

fof(f20307,plain,
    ( spl0_905
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f20302,plain,
    ( spl0_904
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f20305,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_110
    | ~ spl0_904 ),
    inference(forward_demodulation,[],[f20303,f858]) ).

fof(f20303,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_904 ),
    inference(avatar_component_clause,[],[f20302]) ).

fof(f20304,plain,
    ( spl0_904
    | ~ spl0_168
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1615,f1596,f1425,f20302]) ).

fof(f1615,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_168
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1426]) ).

fof(f20284,plain,
    ( spl0_903
    | ~ spl0_110
    | ~ spl0_902 ),
    inference(avatar_split_clause,[],[f20209,f20206,f856,f20282]) ).

fof(f20282,plain,
    ( spl0_903
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),element_relation)
        | null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f20206,plain,
    ( spl0_902
  <=> ! [X0,X3,X2,X1] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f20209,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),element_relation)
        | null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2)) )
    | ~ spl0_110
    | ~ spl0_902 ),
    inference(forward_demodulation,[],[f20207,f858]) ).

fof(f20207,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | null_class = X0 )
    | ~ spl0_902 ),
    inference(avatar_component_clause,[],[f20206]) ).

fof(f20208,plain,
    ( spl0_902
    | ~ spl0_78
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1437,f1425,f600,f20206]) ).

fof(f1437,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f601]) ).

fof(f20204,plain,
    ( spl0_900
    | spl0_367
    | ~ spl0_901
    | ~ spl0_110
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f12391,f1834,f856,f20201,f4776,f20197]) ).

fof(f20197,plain,
    ( spl0_900
  <=> domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class))))))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f20201,plain,
    ( spl0_901
  <=> member(element_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f1834,plain,
    ( spl0_193
  <=> ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f12391,plain,
    ( ~ member(element_relation,universal_class)
    | element_relation = null_class
    | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(element_relation,element_relation),universal_class)),universal_class)))))))))))
    | ~ spl0_110
    | ~ spl0_193 ),
    inference(superposition,[],[f1835,f858]) ).

fof(f1835,plain,
    ( ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f1834]) ).

fof(f20188,plain,
    ( ~ spl0_899
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_896 ),
    inference(avatar_split_clause,[],[f20175,f20162,f15972,f3255,f921,f856,f20185]) ).

fof(f20185,plain,
    ( spl0_899
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(null_class,null_class),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f20175,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(null_class,null_class),universal_class)),universal_class))))))),element_relation)
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_896 ),
    inference(forward_demodulation,[],[f20174,f15981]) ).

fof(f20174,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),element_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_896 ),
    inference(forward_demodulation,[],[f20173,f12338]) ).

fof(f20183,plain,
    ( ~ spl0_898
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_897 ),
    inference(avatar_split_clause,[],[f20172,f20166,f15972,f3255,f921,f856,f20180]) ).

fof(f20172,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(null_class,null_class),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_897 ),
    inference(forward_demodulation,[],[f20171,f15981]) ).

fof(f20171,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_897 ),
    inference(forward_demodulation,[],[f20170,f858]) ).

fof(f20170,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_897 ),
    inference(forward_demodulation,[],[f20167,f12338]) ).

fof(f20169,plain,
    ( spl0_706
    | ~ spl0_895
    | ~ spl0_896
    | spl0_897
    | ~ spl0_74
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1381,f1368,f575,f20166,f20162,f20158,f15876]) ).

fof(f1381,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
    | ~ member(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class)
    | null_class = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_74
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f576]) ).

fof(f20141,plain,
    ( spl0_894
    | ~ spl0_20
    | ~ spl0_880 ),
    inference(avatar_split_clause,[],[f19884,f19809,f257,f20139]) ).

fof(f19809,plain,
    ( spl0_880
  <=> null_class = complement(x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).

fof(f19884,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,x) )
    | ~ spl0_20
    | ~ spl0_880 ),
    inference(superposition,[],[f258,f19811]) ).

fof(f19811,plain,
    ( null_class = complement(x)
    | ~ spl0_880 ),
    inference(avatar_component_clause,[],[f19809]) ).

fof(f20137,plain,
    ( spl0_893
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(avatar_split_clause,[],[f20133,f20127,f19371,f856,f20135]) ).

fof(f20135,plain,
    ( spl0_893
  <=> ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),element_relation)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f20133,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),element_relation)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f20132,f19373]) ).

fof(f20132,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),element_relation)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f20131,f19373]) ).

fof(f20131,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_849
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f20130,f19373]) ).

fof(f20130,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_892 ),
    inference(forward_demodulation,[],[f20128,f858]) ).

fof(f20129,plain,
    ( spl0_892
    | ~ spl0_39
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1810,f1803,f347,f20127]) ).

fof(f1810,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_190 ),
    inference(superposition,[],[f1804,f348]) ).

fof(f20068,plain,
    ( spl0_891
    | ~ spl0_83
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12305,f856,f637,f20066]) ).

fof(f20066,plain,
    ( spl0_891
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(element_relation,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f12305,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(element_relation,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_83
    | ~ spl0_110 ),
    inference(superposition,[],[f638,f858]) ).

fof(f20064,plain,
    ( spl0_890
    | ~ spl0_82
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12304,f856,f633,f20062]) ).

fof(f20062,plain,
    ( spl0_890
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(element_relation,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).

fof(f12304,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(element_relation,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
    | ~ spl0_82
    | ~ spl0_110 ),
    inference(superposition,[],[f634,f858]) ).

fof(f20060,plain,
    ( spl0_889
    | ~ spl0_68
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1824,f1821,f538,f20058]) ).

fof(f20058,plain,
    ( spl0_889
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f1824,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_192 ),
    inference(resolution,[],[f1822,f539]) ).

fof(f19883,plain,
    ( spl0_888
    | ~ spl0_68
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1806,f1803,f538,f19881]) ).

fof(f19881,plain,
    ( spl0_888
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f1806,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_190 ),
    inference(resolution,[],[f1804,f539]) ).

fof(f19879,plain,
    ( spl0_887
    | ~ spl0_80
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1527,f1512,f622,f19877]) ).

fof(f19877,plain,
    ( spl0_887
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f622,plain,
    ( spl0_80
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f1527,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_80
    | ~ spl0_173 ),
    inference(superposition,[],[f623,f1513]) ).

fof(f623,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f622]) ).

fof(f19875,plain,
    ( ~ spl0_885
    | spl0_886
    | ~ spl0_77
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1082,f1056,f595,f19873,f19869]) ).

fof(f19869,plain,
    ( spl0_885
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f19873,plain,
    ( spl0_886
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
        | homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | ~ operation(X1)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f1056,plain,
    ( spl0_129
  <=> ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f1082,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation)
        | ~ operation(X1)
        | ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | ~ operation(flip(cross_product(subset_relation,universal_class))) )
    | ~ spl0_77
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f596]) ).

fof(f1057,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1056]) ).

fof(f19850,plain,
    ( spl0_884
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_883 ),
    inference(avatar_split_clause,[],[f19846,f19840,f15972,f3255,f921,f856,f19848]) ).

fof(f19848,plain,
    ( spl0_884
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(null_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f19846,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(null_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f19845,f858]) ).

fof(f19845,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(null_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f19844,f15981]) ).

fof(f19844,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f19843,f858]) ).

fof(f19843,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f19841,f12338]) ).

fof(f19842,plain,
    ( spl0_883
    | ~ spl0_140
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1791,f1761,f1202,f19840]) ).

fof(f1791,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_140
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f1203]) ).

fof(f19824,plain,
    ( spl0_882
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_881 ),
    inference(avatar_split_clause,[],[f19820,f19814,f15972,f3255,f921,f856,f19822]) ).

fof(f19822,plain,
    ( spl0_882
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(null_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).

fof(f19820,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(null_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f19819,f858]) ).

fof(f19819,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(null_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f19818,f15981]) ).

fof(f19818,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f19817,f858]) ).

fof(f19817,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f19815,f12338]) ).

fof(f19816,plain,
    ( spl0_881
    | ~ spl0_140
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1773,f1757,f1202,f19814]) ).

fof(f1773,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_140
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f1203]) ).

fof(f19812,plain,
    ( spl0_880
    | ~ spl0_1
    | ~ spl0_801 ),
    inference(avatar_split_clause,[],[f19702,f18607,f172,f19809]) ).

fof(f19702,plain,
    ( null_class = complement(x)
    | ~ spl0_1
    | ~ spl0_801 ),
    inference(resolution,[],[f18608,f174]) ).

fof(f19785,plain,
    ( spl0_879
    | ~ spl0_110
    | ~ spl0_878 ),
    inference(avatar_split_clause,[],[f19781,f19778,f856,f19783]) ).

fof(f19783,plain,
    ( spl0_879
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f19778,plain,
    ( spl0_878
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f19781,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_110
    | ~ spl0_878 ),
    inference(forward_demodulation,[],[f19779,f858]) ).

fof(f19779,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_878 ),
    inference(avatar_component_clause,[],[f19778]) ).

fof(f19780,plain,
    ( spl0_878
    | ~ spl0_150
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1638,f1600,f1284,f19778]) ).

fof(f1284,plain,
    ( spl0_150
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1638,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_150
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1285]) ).

fof(f1285,plain,
    ( ! [X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1284]) ).

fof(f19754,plain,
    ( spl0_877
    | ~ spl0_110
    | ~ spl0_876 ),
    inference(avatar_split_clause,[],[f19750,f19747,f856,f19752]) ).

fof(f19752,plain,
    ( spl0_877
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f19747,plain,
    ( spl0_876
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f19750,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_110
    | ~ spl0_876 ),
    inference(forward_demodulation,[],[f19748,f858]) ).

fof(f19748,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_876 ),
    inference(avatar_component_clause,[],[f19747]) ).

fof(f19749,plain,
    ( spl0_876
    | ~ spl0_150
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1613,f1596,f1284,f19747]) ).

fof(f1613,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_150
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1285]) ).

fof(f19723,plain,
    ( spl0_875
    | ~ spl0_110
    | ~ spl0_874 ),
    inference(avatar_split_clause,[],[f19719,f19716,f856,f19721]) ).

fof(f19721,plain,
    ( spl0_875
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),element_relation)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f19716,plain,
    ( spl0_874
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f19719,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),element_relation)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1)) )
    | ~ spl0_110
    | ~ spl0_874 ),
    inference(forward_demodulation,[],[f19717,f858]) ).

fof(f19717,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))) )
    | ~ spl0_874 ),
    inference(avatar_component_clause,[],[f19716]) ).

fof(f19718,plain,
    ( spl0_874
    | ~ spl0_78
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1324,f1284,f600,f19716]) ).

fof(f1324,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f601]) ).

fof(f19710,plain,
    ( spl0_873
    | ~ spl0_39
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1831,f1821,f347,f19708]) ).

fof(f19708,plain,
    ( spl0_873
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f1831,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_39
    | ~ spl0_192 ),
    inference(superposition,[],[f1822,f348]) ).

fof(f19669,plain,
    ( spl0_872
    | ~ spl0_110
    | ~ spl0_871 ),
    inference(avatar_split_clause,[],[f19665,f19662,f856,f19667]) ).

fof(f19667,plain,
    ( spl0_872
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(domain_of(X1),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f19662,plain,
    ( spl0_871
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).

fof(f19665,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(domain_of(X1),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2) )
    | ~ spl0_110
    | ~ spl0_871 ),
    inference(forward_demodulation,[],[f19663,f858]) ).

fof(f19663,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2) )
    | ~ spl0_871 ),
    inference(avatar_component_clause,[],[f19662]) ).

fof(f19664,plain,
    ( spl0_871
    | ~ spl0_175
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f1675,f1669,f1545,f19662]) ).

fof(f1669,plain,
    ( spl0_182
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1675,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2) )
    | ~ spl0_175
    | ~ spl0_182 ),
    inference(resolution,[],[f1670,f1546]) ).

fof(f1670,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f1669]) ).

fof(f19643,plain,
    ( spl0_870
    | ~ spl0_110
    | ~ spl0_869 ),
    inference(avatar_split_clause,[],[f19639,f19636,f856,f19641]) ).

fof(f19641,plain,
    ( spl0_870
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f19639,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 )
    | ~ spl0_110
    | ~ spl0_869 ),
    inference(forward_demodulation,[],[f19637,f858]) ).

fof(f19637,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | null_class = X3 )
    | ~ spl0_869 ),
    inference(avatar_component_clause,[],[f19636]) ).

fof(f19638,plain,
    ( spl0_869
    | ~ spl0_114
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1798,f1761,f874,f19636]) ).

fof(f1798,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 )
    | ~ spl0_114
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f875]) ).

fof(f19617,plain,
    ( spl0_868
    | ~ spl0_110
    | ~ spl0_867 ),
    inference(avatar_split_clause,[],[f19613,f19610,f856,f19615]) ).

fof(f19615,plain,
    ( spl0_868
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f19610,plain,
    ( spl0_867
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f19613,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
    | ~ spl0_110
    | ~ spl0_867 ),
    inference(forward_demodulation,[],[f19611,f858]) ).

fof(f19611,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class))))) )
    | ~ spl0_867 ),
    inference(avatar_component_clause,[],[f19610]) ).

fof(f19612,plain,
    ( spl0_867
    | ~ spl0_115
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1794,f1761,f878,f19610]) ).

fof(f1794,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
    | ~ spl0_115
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f879]) ).

fof(f19594,plain,
    ( spl0_866
    | ~ spl0_44
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f17453,f17102,f396,f19592]) ).

fof(f19592,plain,
    ( spl0_866
  <=> ! [X0] :
        ( ~ member(X0,u)
        | first(null_class) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f396,plain,
    ( spl0_44
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f17453,plain,
    ( ! [X0] :
        ( ~ member(X0,u)
        | first(null_class) = X0 )
    | ~ spl0_44
    | ~ spl0_748 ),
    inference(duplicate_literal_removal,[],[f17290]) ).

fof(f17290,plain,
    ( ! [X0] :
        ( ~ member(X0,u)
        | first(null_class) = X0
        | first(null_class) = X0 )
    | ~ spl0_44
    | ~ spl0_748 ),
    inference(superposition,[],[f397,f17104]) ).

fof(f397,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f396]) ).

fof(f19590,plain,
    ( spl0_865
    | ~ spl0_110
    | ~ spl0_864 ),
    inference(avatar_split_clause,[],[f19586,f19583,f856,f19588]) ).

fof(f19588,plain,
    ( spl0_865
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f19586,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 )
    | ~ spl0_110
    | ~ spl0_864 ),
    inference(forward_demodulation,[],[f19584,f858]) ).

fof(f19584,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | null_class = X3 )
    | ~ spl0_864 ),
    inference(avatar_component_clause,[],[f19583]) ).

fof(f19585,plain,
    ( spl0_864
    | ~ spl0_114
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1780,f1757,f874,f19583]) ).

fof(f1780,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 )
    | ~ spl0_114
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f875]) ).

fof(f19567,plain,
    ( spl0_863
    | ~ spl0_110
    | ~ spl0_862 ),
    inference(avatar_split_clause,[],[f19563,f19560,f856,f19565]) ).

fof(f19565,plain,
    ( spl0_863
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f19560,plain,
    ( spl0_862
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f19563,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
    | ~ spl0_110
    | ~ spl0_862 ),
    inference(forward_demodulation,[],[f19561,f858]) ).

fof(f19561,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class))))) )
    | ~ spl0_862 ),
    inference(avatar_component_clause,[],[f19560]) ).

fof(f19562,plain,
    ( spl0_862
    | ~ spl0_115
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1776,f1757,f878,f19560]) ).

fof(f1776,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
    | ~ spl0_115
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f879]) ).

fof(f19541,plain,
    ( spl0_861
    | ~ spl0_110
    | ~ spl0_860 ),
    inference(avatar_split_clause,[],[f19537,f19534,f856,f19539]) ).

fof(f19539,plain,
    ( spl0_861
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f19534,plain,
    ( spl0_860
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f19537,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_110
    | ~ spl0_860 ),
    inference(forward_demodulation,[],[f19535,f858]) ).

fof(f19535,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_860 ),
    inference(avatar_component_clause,[],[f19534]) ).

fof(f19536,plain,
    ( spl0_860
    | ~ spl0_149
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1646,f1600,f1280,f19534]) ).

fof(f1280,plain,
    ( spl0_149
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1646,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_149
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1281]) ).

fof(f1281,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1280]) ).

fof(f19515,plain,
    ( spl0_859
    | ~ spl0_110
    | ~ spl0_857 ),
    inference(avatar_split_clause,[],[f19507,f19504,f856,f19513]) ).

fof(f19513,plain,
    ( spl0_859
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f19504,plain,
    ( spl0_857
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f19507,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_110
    | ~ spl0_857 ),
    inference(forward_demodulation,[],[f19505,f858]) ).

fof(f19505,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_857 ),
    inference(avatar_component_clause,[],[f19504]) ).

fof(f19511,plain,
    ( spl0_858
    | ~ spl0_247
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f17298,f17102,f2429,f19509]) ).

fof(f17298,plain,
    ( ! [X0] :
        ( ~ member(u,X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_247
    | ~ spl0_748 ),
    inference(superposition,[],[f2430,f17104]) ).

fof(f19506,plain,
    ( spl0_857
    | ~ spl0_149
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1621,f1596,f1280,f19504]) ).

fof(f1621,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_149
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1281]) ).

fof(f19485,plain,
    ( spl0_856
    | ~ spl0_110
    | ~ spl0_855 ),
    inference(avatar_split_clause,[],[f19481,f19478,f856,f19483]) ).

fof(f19483,plain,
    ( spl0_856
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),element_relation)
        | ~ function(X0)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f19478,plain,
    ( spl0_855
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f19481,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),element_relation)
        | ~ function(X0)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2)) )
    | ~ spl0_110
    | ~ spl0_855 ),
    inference(forward_demodulation,[],[f19479,f858]) ).

fof(f19479,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
        | ~ function(X0) )
    | ~ spl0_855 ),
    inference(avatar_component_clause,[],[f19478]) ).

fof(f19480,plain,
    ( spl0_855
    | ~ spl0_78
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1307,f1280,f600,f19478]) ).

fof(f1307,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f601]) ).

fof(f19459,plain,
    ( spl0_854
    | ~ spl0_110
    | ~ spl0_853 ),
    inference(avatar_split_clause,[],[f19455,f19451,f856,f19457]) ).

fof(f19457,plain,
    ( spl0_854
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f19451,plain,
    ( spl0_853
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f19455,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_853 ),
    inference(forward_demodulation,[],[f19454,f858]) ).

fof(f19454,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_853 ),
    inference(forward_demodulation,[],[f19452,f858]) ).

fof(f19452,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_853 ),
    inference(avatar_component_clause,[],[f19451]) ).

fof(f19453,plain,
    ( spl0_853
    | ~ spl0_101
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1787,f1761,f754,f19451]) ).

fof(f1787,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f755]) ).

fof(f19435,plain,
    ( spl0_852
    | ~ spl0_110
    | ~ spl0_851 ),
    inference(avatar_split_clause,[],[f19431,f19427,f856,f19433]) ).

fof(f19433,plain,
    ( spl0_852
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f19427,plain,
    ( spl0_851
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f19431,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_851 ),
    inference(forward_demodulation,[],[f19430,f858]) ).

fof(f19430,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_851 ),
    inference(forward_demodulation,[],[f19428,f858]) ).

fof(f19428,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_851 ),
    inference(avatar_component_clause,[],[f19427]) ).

fof(f19429,plain,
    ( spl0_851
    | ~ spl0_101
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1769,f1757,f754,f19427]) ).

fof(f1769,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f755]) ).

fof(f19377,plain,
    ( spl0_849
    | spl0_850
    | ~ spl0_39
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1813,f1803,f347,f19375,f19371]) ).

fof(f19375,plain,
    ( spl0_850
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f1813,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_39
    | ~ spl0_190 ),
    inference(superposition,[],[f1804,f348]) ).

fof(f19352,plain,
    ( spl0_848
    | ~ spl0_137
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1439,f1425,f1145,f19350]) ).

fof(f19350,plain,
    ( spl0_848
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f1439,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) )
    | ~ spl0_137
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f1146]) ).

fof(f19337,plain,
    ( spl0_847
    | ~ spl0_161
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1561,f1545,f1368,f19335]) ).

fof(f1561,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_161
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f1369]) ).

fof(f19333,plain,
    ( spl0_846
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1459,f1443,f500,f404,f19331]) ).

fof(f19331,plain,
    ( spl0_846
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f1459,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f1454,f405]) ).

fof(f1454,plain,
    ( ! [X0] :
        ( null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class),X0) )
    | ~ spl0_63
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f501]) ).

fof(f19279,plain,
    ( spl0_845
    | ~ spl0_129
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1496,f1465,f1056,f19277]) ).

fof(f19277,plain,
    ( spl0_845
  <=> ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f1496,plain,
    ( ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_129
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f1057]) ).

fof(f19275,plain,
    ( spl0_248
    | ~ spl0_844
    | ~ spl0_108
    | spl0_828 ),
    inference(avatar_split_clause,[],[f19211,f19096,f848,f19272,f2433]) ).

fof(f19211,plain,
    ( ~ subclass(subset_relation,null_class)
    | null_class = subset_relation
    | ~ spl0_108
    | spl0_828 ),
    inference(resolution,[],[f19098,f849]) ).

fof(f19098,plain,
    ( ~ member(regular(subset_relation),null_class)
    | spl0_828 ),
    inference(avatar_component_clause,[],[f19096]) ).

fof(f19270,plain,
    ( spl0_843
    | ~ spl0_129
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1478,f1461,f1056,f19268]) ).

fof(f19268,plain,
    ( spl0_843
  <=> ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f1478,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_129
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f1057]) ).

fof(f19254,plain,
    ( spl0_842
    | ~ spl0_110
    | ~ spl0_841 ),
    inference(avatar_split_clause,[],[f19250,f19247,f856,f19252]) ).

fof(f19252,plain,
    ( spl0_842
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f19250,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_110
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f19248,f858]) ).

fof(f19249,plain,
    ( spl0_841
    | ~ spl0_173
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f1684,f1679,f1512,f19247]) ).

fof(f1684,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173
    | ~ spl0_183 ),
    inference(superposition,[],[f1680,f1513]) ).

fof(f19244,plain,
    ( spl0_840
    | ~ spl0_153
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1770,f1757,f1296,f19242]) ).

fof(f19242,plain,
    ( spl0_840
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f1296,plain,
    ( spl0_153
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f1770,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_153
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f1297]) ).

fof(f1297,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1296]) ).

fof(f19236,plain,
    ( ~ spl0_839
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_836 ),
    inference(avatar_split_clause,[],[f19226,f19213,f15972,f3255,f921,f856,f19233]) ).

fof(f19226,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(null_class),complement(null_class)),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_836 ),
    inference(forward_demodulation,[],[f19225,f15981]) ).

fof(f19225,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_836 ),
    inference(forward_demodulation,[],[f19224,f858]) ).

fof(f19224,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_836 ),
    inference(forward_demodulation,[],[f19215,f12338]) ).

fof(f19231,plain,
    ( ~ spl0_838
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_837 ),
    inference(avatar_split_clause,[],[f19223,f19217,f15972,f3255,f921,f856,f19228]) ).

fof(f19228,plain,
    ( spl0_838
  <=> member(complement(null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f19223,plain,
    ( ~ member(complement(null_class),universal_class)
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | spl0_837 ),
    inference(forward_demodulation,[],[f19222,f15981]) ).

fof(f19222,plain,
    ( ~ member(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_837 ),
    inference(forward_demodulation,[],[f19221,f858]) ).

fof(f19221,plain,
    ( ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_837 ),
    inference(forward_demodulation,[],[f19219,f12338]) ).

fof(f19220,plain,
    ( ~ spl0_836
    | ~ spl0_837
    | spl0_547
    | ~ spl0_140
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1452,f1443,f1202,f10802,f19217,f19213]) ).

fof(f10802,plain,
    ( spl0_547
  <=> null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f1452,plain,
    ( null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_140
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f1203]) ).

fof(f19208,plain,
    ( spl0_835
    | ~ spl0_153
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1801,f1761,f1296,f19206]) ).

fof(f19206,plain,
    ( spl0_835
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f1801,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_153
    | ~ spl0_189 ),
    inference(duplicate_literal_removal,[],[f1788]) ).

fof(f1788,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_153
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f1297]) ).

fof(f19189,plain,
    ( spl0_834
    | ~ spl0_110
    | ~ spl0_833 ),
    inference(avatar_split_clause,[],[f19185,f19182,f856,f19187]) ).

fof(f19187,plain,
    ( spl0_834
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f19185,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_110
    | ~ spl0_833 ),
    inference(forward_demodulation,[],[f19183,f858]) ).

fof(f19184,plain,
    ( spl0_833
    | ~ spl0_76
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f1682,f1679,f591,f19182]) ).

fof(f591,plain,
    ( spl0_76
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1682,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_76
    | ~ spl0_183 ),
    inference(resolution,[],[f1680,f592]) ).

fof(f592,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f591]) ).

fof(f19117,plain,
    ( spl0_832
    | ~ spl0_173
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f1676,f1669,f1512,f19115]) ).

fof(f19115,plain,
    ( spl0_832
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),compose(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f1676,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),compose(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173
    | ~ spl0_182 ),
    inference(superposition,[],[f1670,f1513]) ).

fof(f19112,plain,
    ( spl0_831
    | ~ spl0_133
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1639,f1600,f1109,f19110]) ).

fof(f19110,plain,
    ( spl0_831
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f1109,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1639,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_133
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f1110]) ).

fof(f1110,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1109]) ).

fof(f19107,plain,
    ( spl0_830
    | ~ spl0_133
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1614,f1596,f1109,f19105]) ).

fof(f19105,plain,
    ( spl0_830
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f1614,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_133
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f1110]) ).

fof(f19103,plain,
    ( spl0_829
    | ~ spl0_128
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1568,f1545,f1052,f19101]) ).

fof(f19101,plain,
    ( spl0_829
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),regular(X3))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f1052,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1568,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),regular(X3))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
        | null_class = X3 )
    | ~ spl0_128
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f1053]) ).

fof(f1053,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,null_class)
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1052]) ).

fof(f19099,plain,
    ( spl0_248
    | ~ spl0_828
    | ~ spl0_23
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f13887,f11626,f269,f19096,f2433]) ).

fof(f11626,plain,
    ( spl0_590
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f13887,plain,
    ( ~ member(regular(subset_relation),null_class)
    | null_class = subset_relation
    | ~ spl0_23
    | ~ spl0_590 ),
    inference(resolution,[],[f11627,f270]) ).

fof(f11627,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | ~ member(X0,null_class) )
    | ~ spl0_590 ),
    inference(avatar_component_clause,[],[f11626]) ).

fof(f19094,plain,
    ( spl0_827
    | ~ spl0_129
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1565,f1545,f1056,f19092]) ).

fof(f19092,plain,
    ( spl0_827
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f1565,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
    | ~ spl0_129
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f1057]) ).

fof(f19079,plain,
    ( spl0_826
    | ~ spl0_110
    | ~ spl0_825 ),
    inference(avatar_split_clause,[],[f19075,f19072,f856,f19077]) ).

fof(f19077,plain,
    ( spl0_826
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),element_relation)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f19072,plain,
    ( spl0_825
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f19075,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),element_relation)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1)) )
    | ~ spl0_110
    | ~ spl0_825 ),
    inference(forward_demodulation,[],[f19073,f858]) ).

fof(f19073,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))) )
    | ~ spl0_825 ),
    inference(avatar_component_clause,[],[f19072]) ).

fof(f19074,plain,
    ( spl0_825
    | ~ spl0_78
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1128,f1109,f600,f19072]) ).

fof(f1128,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f601]) ).

fof(f19051,plain,
    ( spl0_824
    | ~ spl0_110
    | ~ spl0_823 ),
    inference(avatar_split_clause,[],[f19047,f19044,f856,f19049]) ).

fof(f19049,plain,
    ( spl0_824
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f19047,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_110
    | ~ spl0_823 ),
    inference(forward_demodulation,[],[f19045,f858]) ).

fof(f19046,plain,
    ( spl0_823
    | ~ spl0_173
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1659,f1654,f1512,f19044]) ).

fof(f1659,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_173
    | ~ spl0_180 ),
    inference(superposition,[],[f1655,f1513]) ).

fof(f19042,plain,
    ( spl0_822
    | ~ spl0_44
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1556,f1545,f396,f19040]) ).

fof(f19040,plain,
    ( spl0_822
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),unordered_pair(X3,X4))
        | ~ operation(X2)
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f1556,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),unordered_pair(X3,X4))
        | ~ operation(X2)
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 )
    | ~ spl0_44
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f397]) ).

fof(f19038,plain,
    ( spl0_601
    | ~ spl0_600
    | ~ spl0_108
    | spl0_808 ),
    inference(avatar_split_clause,[],[f18940,f18804,f848,f12095,f12100]) ).

fof(f18804,plain,
    ( spl0_808
  <=> member(regular(successor_relation),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f18940,plain,
    ( ~ subclass(successor_relation,null_class)
    | null_class = successor_relation
    | ~ spl0_108
    | spl0_808 ),
    inference(resolution,[],[f18806,f849]) ).

fof(f18806,plain,
    ( ~ member(regular(successor_relation),null_class)
    | spl0_808 ),
    inference(avatar_component_clause,[],[f18804]) ).

fof(f18988,plain,
    ( spl0_821
    | ~ spl0_110
    | ~ spl0_820 ),
    inference(avatar_split_clause,[],[f18984,f18981,f856,f18986]) ).

fof(f18986,plain,
    ( spl0_821
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f18981,plain,
    ( spl0_820
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f18984,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_110
    | ~ spl0_820 ),
    inference(forward_demodulation,[],[f18982,f858]) ).

fof(f18982,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_820 ),
    inference(avatar_component_clause,[],[f18981]) ).

fof(f18983,plain,
    ( spl0_820
    | ~ spl0_68
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1786,f1761,f538,f18981]) ).

fof(f1786,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_68
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f539]) ).

fof(f18957,plain,
    ( spl0_819
    | ~ spl0_110
    | ~ spl0_818 ),
    inference(avatar_split_clause,[],[f18953,f18950,f856,f18955]) ).

fof(f18955,plain,
    ( spl0_819
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f18950,plain,
    ( spl0_818
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f18953,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
    | ~ spl0_110
    | ~ spl0_818 ),
    inference(forward_demodulation,[],[f18951,f858]) ).

fof(f18951,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
    | ~ spl0_818 ),
    inference(avatar_component_clause,[],[f18950]) ).

fof(f18952,plain,
    ( spl0_818
    | ~ spl0_68
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1768,f1757,f538,f18950]) ).

fof(f1768,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
    | ~ spl0_68
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f539]) ).

fof(f18948,plain,
    ( spl0_817
    | ~ spl0_44
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1487,f1465,f396,f18946]) ).

fof(f18946,plain,
    ( spl0_817
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f1487,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_44
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f397]) ).

fof(f18944,plain,
    ( spl0_816
    | ~ spl0_44
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1469,f1461,f396,f18942]) ).

fof(f18942,plain,
    ( spl0_816
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f1469,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 )
    | ~ spl0_44
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f397]) ).

fof(f18931,plain,
    ( spl0_451
    | ~ spl0_813
    | spl0_814
    | ~ spl0_815
    | ~ spl0_74
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1086,f1056,f575,f18928,f18924,f18920,f8293]) ).

fof(f8293,plain,
    ( spl0_451
  <=> null_class = domain_of(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f18920,plain,
    ( spl0_813
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f18924,plain,
    ( spl0_814
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f18928,plain,
    ( spl0_815
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f1086,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
    | ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_74
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f576]) ).

fof(f18904,plain,
    ( spl0_812
    | ~ spl0_110
    | ~ spl0_811 ),
    inference(avatar_split_clause,[],[f18900,f18897,f856,f18902]) ).

fof(f18902,plain,
    ( spl0_812
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f18900,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_110
    | ~ spl0_811 ),
    inference(forward_demodulation,[],[f18898,f858]) ).

fof(f18899,plain,
    ( spl0_811
    | ~ spl0_37
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f1683,f1679,f339,f18897]) ).

fof(f1683,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_37
    | ~ spl0_183 ),
    inference(resolution,[],[f1680,f340]) ).

fof(f18893,plain,
    ( spl0_810
    | ~ spl0_135
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1578,f1570,f1137,f18891]) ).

fof(f18891,plain,
    ( spl0_810
  <=> ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f1137,plain,
    ( spl0_135
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1570,plain,
    ( spl0_176
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f1578,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_135
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f1138]) ).

fof(f1138,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1137]) ).

fof(f1571,plain,
    ( ! [X2,X0,X1] :
        ( subclass(cross_product(X0,X1),X2)
        | not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))))) )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f1570]) ).

fof(f18887,plain,
    ( spl0_809
    | ~ spl0_134
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1577,f1570,f1133,f18885]) ).

fof(f18885,plain,
    ( spl0_809
  <=> ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f1133,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1577,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_134
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f1134]) ).

fof(f1134,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1133]) ).

fof(f18807,plain,
    ( spl0_601
    | ~ spl0_808
    | ~ spl0_23
    | ~ spl0_576 ),
    inference(avatar_split_clause,[],[f11717,f11230,f269,f18804,f12100]) ).

fof(f11230,plain,
    ( spl0_576
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f11717,plain,
    ( ~ member(regular(successor_relation),null_class)
    | null_class = successor_relation
    | ~ spl0_23
    | ~ spl0_576 ),
    inference(resolution,[],[f11231,f270]) ).

fof(f11231,plain,
    ( ! [X0] :
        ( ~ member(X0,successor_relation)
        | ~ member(X0,null_class) )
    | ~ spl0_576 ),
    inference(avatar_component_clause,[],[f11230]) ).

fof(f18658,plain,
    ( spl0_807
    | ~ spl0_110
    | ~ spl0_804 ),
    inference(avatar_split_clause,[],[f18628,f18619,f856,f18656]) ).

fof(f18656,plain,
    ( spl0_807
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f18628,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_110
    | ~ spl0_804 ),
    inference(forward_demodulation,[],[f18620,f858]) ).

fof(f18633,plain,
    ( spl0_806
    | ~ spl0_110
    | ~ spl0_800 ),
    inference(avatar_split_clause,[],[f18629,f18530,f856,f18631]) ).

fof(f18631,plain,
    ( spl0_806
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f18629,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) )
    | ~ spl0_110
    | ~ spl0_800 ),
    inference(forward_demodulation,[],[f18531,f858]) ).

fof(f18627,plain,
    ( spl0_805
    | ~ spl0_110
    | ~ spl0_799
    | ~ spl0_804 ),
    inference(avatar_split_clause,[],[f18623,f18619,f18526,f856,f18625]) ).

fof(f18625,plain,
    ( spl0_805
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f18526,plain,
    ( spl0_799
  <=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f18623,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_110
    | ~ spl0_799
    | ~ spl0_804 ),
    inference(forward_demodulation,[],[f18622,f858]) ).

fof(f18622,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_799
    | ~ spl0_804 ),
    inference(forward_demodulation,[],[f18620,f18528]) ).

fof(f18528,plain,
    ( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_799 ),
    inference(avatar_component_clause,[],[f18526]) ).

fof(f18621,plain,
    ( spl0_804
    | ~ spl0_76
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1657,f1654,f591,f18619]) ).

fof(f1657,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_76
    | ~ spl0_180 ),
    inference(resolution,[],[f1655,f592]) ).

fof(f18617,plain,
    ( spl0_803
    | ~ spl0_128
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1498,f1465,f1052,f18615]) ).

fof(f18615,plain,
    ( spl0_803
  <=> ! [X0,X1] :
        ( null_class = intersection(regular(X0),X1)
        | ~ member(intersection(regular(X0),X1),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f1498,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(regular(X0),X1)
        | ~ member(intersection(regular(X0),X1),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = X0 )
    | ~ spl0_128
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f1053]) ).

fof(f18613,plain,
    ( spl0_802
    | ~ spl0_128
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1480,f1461,f1052,f18611]) ).

fof(f18611,plain,
    ( spl0_802
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,regular(X1))
        | ~ member(intersection(X0,regular(X1)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f1480,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,regular(X1))
        | ~ member(intersection(X0,regular(X1)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_128
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f1053]) ).

fof(f18609,plain,
    ( spl0_801
    | ~ spl0_20
    | ~ spl0_426 ),
    inference(avatar_split_clause,[],[f7519,f7296,f257,f18607]) ).

fof(f7519,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(u,X0) )
    | ~ spl0_20
    | ~ spl0_426 ),
    inference(resolution,[],[f7297,f258]) ).

fof(f18532,plain,
    ( spl0_799
    | spl0_800
    | ~ spl0_39
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f1686,f1679,f347,f18530,f18526]) ).

fof(f1686,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_183 ),
    inference(superposition,[],[f1680,f348]) ).

fof(f18500,plain,
    ( spl0_798
    | ~ spl0_110
    | ~ spl0_797 ),
    inference(avatar_split_clause,[],[f18496,f18493,f856,f18498]) ).

fof(f18498,plain,
    ( spl0_798
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f18496,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_110
    | ~ spl0_797 ),
    inference(forward_demodulation,[],[f18494,f858]) ).

fof(f18495,plain,
    ( spl0_797
    | ~ spl0_39
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1626,f1596,f347,f18493]) ).

fof(f1626,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_39
    | ~ spl0_178 ),
    inference(superposition,[],[f1597,f348]) ).

fof(f18478,plain,
    ( spl0_795
    | ~ spl0_796
    | ~ spl0_39
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1593,f1586,f347,f18475,f18472]) ).

fof(f18472,plain,
    ( spl0_795
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f18475,plain,
    ( spl0_796
  <=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f1586,plain,
    ( spl0_177
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f1593,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_39
    | ~ spl0_177 ),
    inference(superposition,[],[f1587,f348]) ).

fof(f1587,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2)) )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f1586]) ).

fof(f18470,plain,
    ( spl0_794
    | ~ spl0_137
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1326,f1284,f1145,f18468]) ).

fof(f18468,plain,
    ( spl0_794
  <=> ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f1326,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) )
    | ~ spl0_137
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f1146]) ).

fof(f18411,plain,
    ( spl0_793
    | ~ spl0_45
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1450,f1443,f400,f18409]) ).

fof(f18409,plain,
    ( spl0_793
  <=> ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(complement(intersection(X0,X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f1450,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(complement(intersection(X0,X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) )
    | ~ spl0_45
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f401]) ).

fof(f18375,plain,
    ( spl0_792
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_791 ),
    inference(avatar_split_clause,[],[f18371,f18365,f15972,f3255,f921,f856,f18373]) ).

fof(f18373,plain,
    ( spl0_792
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | ~ subclass(X0,null_class)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f18371,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | ~ subclass(X0,null_class)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f18370,f858]) ).

fof(f18370,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f18369,f15981]) ).

fof(f18369,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f18368,f858]) ).

fof(f18368,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f18366,f12338]) ).

fof(f18367,plain,
    ( spl0_791
    | ~ spl0_161
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1434,f1425,f1368,f18365]) ).

fof(f1434,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_161
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f1369]) ).

fof(f18362,plain,
    ( spl0_790
    | ~ spl0_120
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1645,f1600,f929,f18360]) ).

fof(f18360,plain,
    ( spl0_790
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f929,plain,
    ( spl0_120
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1645,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | subclass(X1,X2) )
    | ~ spl0_120
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f930]) ).

fof(f930,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_120 ),
    inference(avatar_component_clause,[],[f929]) ).

fof(f18357,plain,
    ( spl0_789
    | ~ spl0_120
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1620,f1596,f929,f18355]) ).

fof(f18355,plain,
    ( spl0_789
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f1620,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X1,X2) )
    | ~ spl0_120
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f930]) ).

fof(f18352,plain,
    ( spl0_788
    | ~ spl0_106
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1582,f1570,f821,f18350]) ).

fof(f18350,plain,
    ( spl0_788
  <=> ! [X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
        | function(cross_product(X0,X1))
        | ~ single_valued_class(cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f821,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1582,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
        | function(cross_product(X0,X1))
        | ~ single_valued_class(cross_product(X0,X1)) )
    | ~ spl0_106
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f822]) ).

fof(f822,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f821]) ).

fof(f18322,plain,
    ( spl0_787
    | ~ spl0_110
    | ~ spl0_786 ),
    inference(avatar_split_clause,[],[f18318,f18315,f856,f18320]) ).

fof(f18320,plain,
    ( spl0_787
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),element_relation)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f18315,plain,
    ( spl0_786
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f18318,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),element_relation)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2)) )
    | ~ spl0_110
    | ~ spl0_786 ),
    inference(forward_demodulation,[],[f18316,f858]) ).

fof(f18316,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_786 ),
    inference(avatar_component_clause,[],[f18315]) ).

fof(f18317,plain,
    ( spl0_786
    | ~ spl0_78
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f984,f929,f600,f18315]) ).

fof(f984,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f601]) ).

fof(f18120,plain,
    ( spl0_785
    | ~ spl0_110
    | ~ spl0_784 ),
    inference(avatar_split_clause,[],[f18116,f18112,f856,f18118]) ).

fof(f18118,plain,
    ( spl0_785
  <=> ! [X0,X1] :
        ( element_relation = compose(X0,X1)
        | not_subclass_element(element_relation,compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,compose(X0,X1))),first(not_subclass_element(element_relation,compose(X0,X1)))),unordered_pair(first(not_subclass_element(element_relation,compose(X0,X1))),unordered_pair(second(not_subclass_element(element_relation,compose(X0,X1))),second(not_subclass_element(element_relation,compose(X0,X1)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f18112,plain,
    ( spl0_784
  <=> ! [X0,X1] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
        | cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f18116,plain,
    ( ! [X0,X1] :
        ( element_relation = compose(X0,X1)
        | not_subclass_element(element_relation,compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,compose(X0,X1))),first(not_subclass_element(element_relation,compose(X0,X1)))),unordered_pair(first(not_subclass_element(element_relation,compose(X0,X1))),unordered_pair(second(not_subclass_element(element_relation,compose(X0,X1))),second(not_subclass_element(element_relation,compose(X0,X1)))))) )
    | ~ spl0_110
    | ~ spl0_784 ),
    inference(forward_demodulation,[],[f18115,f858]) ).

fof(f18115,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(element_relation,compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,compose(X0,X1))),first(not_subclass_element(element_relation,compose(X0,X1)))),unordered_pair(first(not_subclass_element(element_relation,compose(X0,X1))),unordered_pair(second(not_subclass_element(element_relation,compose(X0,X1))),second(not_subclass_element(element_relation,compose(X0,X1))))))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_110
    | ~ spl0_784 ),
    inference(forward_demodulation,[],[f18113,f858]) ).

fof(f18113,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_784 ),
    inference(avatar_component_clause,[],[f18112]) ).

fof(f18114,plain,
    ( spl0_784
    | ~ spl0_131
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1576,f1570,f1098,f18112]) ).

fof(f1098,plain,
    ( spl0_131
  <=> ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f1576,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_131
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f1099]) ).

fof(f1099,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1098]) ).

fof(f18110,plain,
    ( spl0_783
    | ~ spl0_71
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1026,f999,f558,f18108]) ).

fof(f18108,plain,
    ( spl0_783
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,cross_product(X1,X2)),X3)
        | not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f1026,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,cross_product(X1,X2)),X3)
        | not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) )
    | ~ spl0_71
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f559]) ).

fof(f18106,plain,
    ( spl0_782
    | ~ spl0_71
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1009,f995,f558,f18104]) ).

fof(f18104,plain,
    ( spl0_782
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(cross_product(X0,X1),X2),X3)
        | not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f1009,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(cross_product(X0,X1),X2),X3)
        | not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) )
    | ~ spl0_71
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f559]) ).

fof(f18036,plain,
    ( spl0_781
    | ~ spl0_110
    | ~ spl0_780 ),
    inference(avatar_split_clause,[],[f18032,f18029,f856,f18034]) ).

fof(f18034,plain,
    ( spl0_781
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f18032,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),element_relation)
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
    | ~ spl0_110
    | ~ spl0_780 ),
    inference(forward_demodulation,[],[f18030,f858]) ).

fof(f18031,plain,
    ( spl0_780
    | ~ spl0_37
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1658,f1654,f339,f18029]) ).

fof(f1658,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
    | ~ spl0_37
    | ~ spl0_180 ),
    inference(resolution,[],[f1655,f340]) ).

fof(f18027,plain,
    ( spl0_778
    | ~ spl0_779
    | ~ spl0_116
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f17452,f17102,f882,f18024,f18020]) ).

fof(f18020,plain,
    ( spl0_778
  <=> null_class = first(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f18024,plain,
    ( spl0_779
  <=> inductive(u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f882,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f17452,plain,
    ( ~ inductive(u)
    | null_class = first(null_class)
    | ~ spl0_116
    | ~ spl0_748 ),
    inference(duplicate_literal_removal,[],[f17292]) ).

fof(f17292,plain,
    ( ~ inductive(u)
    | null_class = first(null_class)
    | null_class = first(null_class)
    | ~ spl0_116
    | ~ spl0_748 ),
    inference(superposition,[],[f883,f17104]) ).

fof(f883,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | null_class = X1
        | null_class = X0 )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f882]) ).

fof(f17847,plain,
    ( spl0_777
    | ~ spl0_99
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1644,f1600,f746,f17845]) ).

fof(f17845,plain,
    ( spl0_777
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f1644,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_99
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f747]) ).

fof(f17824,plain,
    ( spl0_776
    | ~ spl0_110
    | ~ spl0_775 ),
    inference(avatar_split_clause,[],[f17820,f17817,f856,f17822]) ).

fof(f17822,plain,
    ( spl0_776
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f17817,plain,
    ( spl0_775
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f17820,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_110
    | ~ spl0_775 ),
    inference(forward_demodulation,[],[f17818,f858]) ).

fof(f17818,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_775 ),
    inference(avatar_component_clause,[],[f17817]) ).

fof(f17819,plain,
    ( spl0_775
    | ~ spl0_63
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1628,f1600,f500,f17817]) ).

fof(f1628,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_63
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f501]) ).

fof(f17814,plain,
    ( spl0_774
    | ~ spl0_99
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1619,f1596,f746,f17812]) ).

fof(f17812,plain,
    ( spl0_774
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f1619,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_99
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f747]) ).

fof(f17808,plain,
    ( ~ spl0_773
    | ~ spl0_110
    | spl0_253 ),
    inference(avatar_split_clause,[],[f17803,f2635,f856,f17805]) ).

fof(f17805,plain,
    ( spl0_773
  <=> member(null_class,cross_product(element_relation,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f2635,plain,
    ( spl0_253
  <=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f17803,plain,
    ( ~ member(null_class,cross_product(element_relation,universal_class))
    | ~ spl0_110
    | spl0_253 ),
    inference(forward_demodulation,[],[f2636,f858]) ).

fof(f2636,plain,
    ( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_253 ),
    inference(avatar_component_clause,[],[f2635]) ).

fof(f17798,plain,
    ( spl0_329
    | ~ spl0_71
    | ~ spl0_253
    | ~ spl0_417
    | ~ spl0_421
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f17656,f17102,f6796,f6780,f2635,f558,f3612]) ).

fof(f3612,plain,
    ( spl0_329
  <=> null_class = unordered_pair(u,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f6780,plain,
    ( spl0_417
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | u = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f17656,plain,
    ( null_class = unordered_pair(u,u)
    | ~ spl0_71
    | ~ spl0_253
    | ~ spl0_417
    | ~ spl0_421
    | ~ spl0_748 ),
    inference(forward_demodulation,[],[f17655,f17104]) ).

fof(f17655,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),u)
    | ~ spl0_71
    | ~ spl0_253
    | ~ spl0_417
    | ~ spl0_421 ),
    inference(forward_demodulation,[],[f2665,f6979]) ).

fof(f6979,plain,
    ( u = unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))
    | ~ spl0_417
    | ~ spl0_421 ),
    inference(resolution,[],[f6781,f6798]) ).

fof(f6781,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | u = X0 )
    | ~ spl0_417 ),
    inference(avatar_component_clause,[],[f6780]) ).

fof(f2665,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | ~ spl0_71
    | ~ spl0_253 ),
    inference(resolution,[],[f2637,f559]) ).

fof(f2637,plain,
    ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_253 ),
    inference(avatar_component_clause,[],[f2635]) ).

fof(f17778,plain,
    ( spl0_772
    | ~ spl0_110
    | ~ spl0_771 ),
    inference(avatar_split_clause,[],[f17774,f17771,f856,f17776]) ).

fof(f17776,plain,
    ( spl0_772
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f17771,plain,
    ( spl0_771
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f17774,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_110
    | ~ spl0_771 ),
    inference(forward_demodulation,[],[f17772,f858]) ).

fof(f17772,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_771 ),
    inference(avatar_component_clause,[],[f17771]) ).

fof(f17773,plain,
    ( spl0_771
    | ~ spl0_63
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1603,f1596,f500,f17771]) ).

fof(f1603,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_63
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f501]) ).

fof(f17769,plain,
    ( spl0_770
    | ~ spl0_160
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1579,f1570,f1361,f17767]) ).

fof(f17767,plain,
    ( spl0_770
  <=> ! [X4,X0,X3,X2,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ member(X3,X0)
        | ~ member(X4,X1)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f1361,plain,
    ( spl0_160
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f1579,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ member(X3,X0)
        | ~ member(X4,X1)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) )
    | ~ spl0_160
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f1362]) ).

fof(f1362,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(cross_product(X3,X1),X4)
        | ~ member(X2,X3)
        | ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1361]) ).

fof(f17735,plain,
    ( spl0_769
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(avatar_split_clause,[],[f17622,f17611,f15972,f3255,f921,f856,f17733]) ).

fof(f17733,plain,
    ( spl0_769
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | ~ member(not_subclass_element(intersection(X0,null_class),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f17611,plain,
    ( spl0_768
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f17622,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | ~ member(not_subclass_element(intersection(X0,null_class),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17621,f15981]) ).

fof(f17621,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,null_class),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17620,f858]) ).

fof(f17620,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,null_class),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17619,f12338]) ).

fof(f17619,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,null_class),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation)
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17618,f15981]) ).

fof(f17618,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation)
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17617,f12338]) ).

fof(f17617,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,null_class),X1),subset_relation)
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17616,f858]) ).

fof(f17616,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,null_class),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17615,f15981]) ).

fof(f17615,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17614,f858]) ).

fof(f17614,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_768 ),
    inference(forward_demodulation,[],[f17612,f12338]) ).

fof(f17612,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_768 ),
    inference(avatar_component_clause,[],[f17611]) ).

fof(f17725,plain,
    ( ~ spl0_364
    | ~ spl0_110
    | spl0_158 ),
    inference(avatar_split_clause,[],[f17722,f1350,f856,f4751]) ).

fof(f1350,plain,
    ( spl0_158
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f17722,plain,
    ( ~ member(null_class,element_relation)
    | ~ spl0_110
    | spl0_158 ),
    inference(forward_demodulation,[],[f1352,f858]) ).

fof(f1352,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_158 ),
    inference(avatar_component_clause,[],[f1350]) ).

fof(f17623,plain,
    ( spl0_361
    | ~ spl0_370
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f17285,f17102,f4795,f4702]) ).

fof(f4795,plain,
    ( spl0_370
  <=> member(unordered_pair(first(null_class),first(null_class)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f17285,plain,
    ( member(u,null_class)
    | ~ spl0_370
    | ~ spl0_748 ),
    inference(superposition,[],[f4797,f17104]) ).

fof(f4797,plain,
    ( member(unordered_pair(first(null_class),first(null_class)),null_class)
    | ~ spl0_370 ),
    inference(avatar_component_clause,[],[f4795]) ).

fof(f17613,plain,
    ( spl0_768
    | ~ spl0_125
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1384,f1368,f999,f17611]) ).

fof(f1384,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X1) )
    | ~ spl0_125
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f1000]) ).

fof(f17584,plain,
    ( spl0_767
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(avatar_split_clause,[],[f17580,f17569,f15972,f3255,f921,f856,f17582]) ).

fof(f17582,plain,
    ( spl0_767
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | ~ member(not_subclass_element(intersection(null_class,X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f17569,plain,
    ( spl0_766
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f17580,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | ~ member(not_subclass_element(intersection(null_class,X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17579,f15981]) ).

fof(f17579,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1)
        | ~ member(not_subclass_element(intersection(null_class,X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17578,f858]) ).

fof(f17578,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1)
        | ~ member(not_subclass_element(intersection(null_class,X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17577,f12338]) ).

fof(f17577,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(null_class,X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation)
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17576,f15981]) ).

fof(f17576,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation)
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17575,f12338]) ).

fof(f17575,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(null_class,X0),X1),subset_relation)
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17574,f858]) ).

fof(f17574,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(null_class,X0),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17573,f15981]) ).

fof(f17573,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17572,f858]) ).

fof(f17572,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_766 ),
    inference(forward_demodulation,[],[f17570,f12338]) ).

fof(f17570,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_766 ),
    inference(avatar_component_clause,[],[f17569]) ).

fof(f17571,plain,
    ( spl0_766
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1379,f1368,f995,f17569]) ).

fof(f1379,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),subset_relation)
        | ~ member(not_subclass_element(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),X1) )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f996]) ).

fof(f17567,plain,
    ( spl0_765
    | ~ spl0_137
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1309,f1280,f1145,f17565]) ).

fof(f17565,plain,
    ( spl0_765
  <=> ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
        | ~ member(X1,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f1309,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
        | ~ member(X1,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
    | ~ spl0_137
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f1146]) ).

fof(f17552,plain,
    ( spl0_764
    | ~ spl0_110
    | ~ spl0_763 ),
    inference(avatar_split_clause,[],[f17548,f17545,f856,f17550]) ).

fof(f17550,plain,
    ( spl0_764
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),element_relation)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f17545,plain,
    ( spl0_763
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f17548,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),element_relation)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1)) )
    | ~ spl0_110
    | ~ spl0_763 ),
    inference(forward_demodulation,[],[f17546,f858]) ).

fof(f17546,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_763 ),
    inference(avatar_component_clause,[],[f17545]) ).

fof(f17547,plain,
    ( spl0_763
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f789,f746,f600,f17545]) ).

fof(f789,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f601]) ).

fof(f17282,plain,
    ( spl0_762
    | ~ spl0_108
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1642,f1600,f848,f17280]) ).

fof(f17280,plain,
    ( spl0_762
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f1642,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | null_class = X1 )
    | ~ spl0_108
    | ~ spl0_179 ),
    inference(resolution,[],[f1601,f849]) ).

fof(f17277,plain,
    ( spl0_761
    | ~ spl0_108
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1617,f1596,f848,f17275]) ).

fof(f17275,plain,
    ( spl0_761
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f1617,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | null_class = X1 )
    | ~ spl0_108
    | ~ spl0_178 ),
    inference(resolution,[],[f1597,f849]) ).

fof(f17273,plain,
    ( spl0_760
    | ~ spl0_41
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1453,f1443,f379,f17271]) ).

fof(f17271,plain,
    ( spl0_760
  <=> ! [X0] :
        ( null_class = complement(complement(X0))
        | ~ member(complement(complement(X0)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f1453,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | ~ member(complement(complement(X0)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_41
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f380]) ).

fof(f17269,plain,
    ( spl0_759
    | ~ spl0_141
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1422,f1419,f1212,f17267]) ).

fof(f17267,plain,
    ( spl0_759
  <=> ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f1212,plain,
    ( spl0_141
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1419,plain,
    ( spl0_167
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1422,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 )
    | ~ spl0_141
    | ~ spl0_167 ),
    inference(resolution,[],[f1420,f1213]) ).

fof(f1213,plain,
    ( ! [X2,X0,X1] :
        ( subclass(unordered_pair(X0,X1),X2)
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0 )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1212]) ).

fof(f1420,plain,
    ( ! [X0] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | ~ inductive(X0)
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1419]) ).

fof(f17242,plain,
    ( spl0_758
    | ~ spl0_110
    | ~ spl0_757 ),
    inference(avatar_split_clause,[],[f17238,f17235,f856,f17240]) ).

fof(f17240,plain,
    ( spl0_758
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),element_relation)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f17235,plain,
    ( spl0_757
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f17238,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),element_relation)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2)) )
    | ~ spl0_110
    | ~ spl0_757 ),
    inference(forward_demodulation,[],[f17236,f858]) ).

fof(f17236,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_757 ),
    inference(avatar_component_clause,[],[f17235]) ).

fof(f17237,plain,
    ( spl0_757
    | ~ spl0_78
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f907,f848,f600,f17235]) ).

fof(f907,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f601]) ).

fof(f17197,plain,
    ( spl0_756
    | ~ spl0_110
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f12320,f1669,f856,f17195]) ).

fof(f17195,plain,
    ( spl0_756
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f12320,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_110
    | ~ spl0_182 ),
    inference(superposition,[],[f1670,f858]) ).

fof(f17171,plain,
    ( spl0_755
    | ~ spl0_110
    | ~ spl0_754 ),
    inference(avatar_split_clause,[],[f17167,f17164,f856,f17169]) ).

fof(f17169,plain,
    ( spl0_755
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ subclass(universal_class,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f17164,plain,
    ( spl0_754
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f17167,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ subclass(universal_class,X3) )
    | ~ spl0_110
    | ~ spl0_754 ),
    inference(forward_demodulation,[],[f17165,f858]) ).

fof(f17165,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_754 ),
    inference(avatar_component_clause,[],[f17164]) ).

fof(f17166,plain,
    ( spl0_754
    | ~ spl0_99
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1782,f1761,f746,f17164]) ).

fof(f1782,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_99
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f747]) ).

fof(f17145,plain,
    ( spl0_753
    | ~ spl0_110
    | ~ spl0_752 ),
    inference(avatar_split_clause,[],[f17141,f17138,f856,f17143]) ).

fof(f17143,plain,
    ( spl0_753
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ subclass(universal_class,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f17138,plain,
    ( spl0_752
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f17141,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ subclass(universal_class,X3) )
    | ~ spl0_110
    | ~ spl0_752 ),
    inference(forward_demodulation,[],[f17139,f858]) ).

fof(f17139,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_752 ),
    inference(avatar_component_clause,[],[f17138]) ).

fof(f17140,plain,
    ( spl0_752
    | ~ spl0_99
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1764,f1757,f746,f17138]) ).

fof(f1764,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_99
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f747]) ).

fof(f17136,plain,
    ( spl0_751
    | ~ spl0_101
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f1673,f1669,f754,f17134]) ).

fof(f17134,plain,
    ( spl0_751
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f1673,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_182 ),
    inference(resolution,[],[f1670,f755]) ).

fof(f17114,plain,
    ( spl0_750
    | ~ spl0_110
    | ~ spl0_749 ),
    inference(avatar_split_clause,[],[f17110,f17107,f856,f17112]) ).

fof(f17112,plain,
    ( spl0_750
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f17110,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_749 ),
    inference(forward_demodulation,[],[f17108,f858]) ).

fof(f17109,plain,
    ( spl0_749
    | ~ spl0_39
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1649,f1600,f347,f17107]) ).

fof(f1649,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_179 ),
    inference(superposition,[],[f1601,f348]) ).

fof(f17105,plain,
    ( spl0_748
    | ~ spl0_370
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f6978,f6780,f4795,f17102]) ).

fof(f6978,plain,
    ( u = unordered_pair(first(null_class),first(null_class))
    | ~ spl0_370
    | ~ spl0_417 ),
    inference(resolution,[],[f6781,f4797]) ).

fof(f17072,plain,
    ( spl0_747
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(avatar_split_clause,[],[f17068,f17057,f15972,f3255,f921,f856,f17070]) ).

fof(f17070,plain,
    ( spl0_747
  <=> ! [X0] :
        ( null_class = intersection(X0,null_class)
        | ~ member(regular(intersection(X0,null_class)),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f17057,plain,
    ( spl0_746
  <=> ! [X0] :
        ( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f17068,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,null_class)
        | ~ member(regular(intersection(X0,null_class)),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17067,f15981]) ).

fof(f17067,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(intersection(X0,null_class)),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17066,f858]) ).

fof(f17066,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(intersection(X0,null_class)),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17065,f12338]) ).

fof(f17065,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,null_class)),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation)
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17064,f15981]) ).

fof(f17064,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation)
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17063,f12338]) ).

fof(f17063,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),element_relation)
        | member(regular(intersection(X0,null_class)),subset_relation)
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17062,f858]) ).

fof(f17062,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,null_class)),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17061,f15981]) ).

fof(f17061,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17060,f858]) ).

fof(f17060,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_746 ),
    inference(forward_demodulation,[],[f17058,f12338]) ).

fof(f17058,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_746 ),
    inference(avatar_component_clause,[],[f17057]) ).

fof(f17059,plain,
    ( spl0_746
    | ~ spl0_119
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1388,f1368,f925,f17057]) ).

fof(f1388,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_119
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f926]) ).

fof(f17032,plain,
    ( spl0_745
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(avatar_split_clause,[],[f17028,f17017,f15972,f3255,f921,f856,f17030]) ).

fof(f17030,plain,
    ( spl0_745
  <=> ! [X0] :
        ( null_class = intersection(null_class,X0)
        | ~ member(regular(intersection(null_class,X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f17017,plain,
    ( spl0_744
  <=> ! [X0] :
        ( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f17028,plain,
    ( ! [X0] :
        ( null_class = intersection(null_class,X0)
        | ~ member(regular(intersection(null_class,X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17027,f15981]) ).

fof(f17027,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
        | ~ member(regular(intersection(null_class,X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17026,f858]) ).

fof(f17026,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
        | ~ member(regular(intersection(null_class,X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17025,f12338]) ).

fof(f17025,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(null_class,X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation)
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17024,f15981]) ).

fof(f17024,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation)
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17023,f12338]) ).

fof(f17023,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),element_relation)
        | member(regular(intersection(null_class,X0)),subset_relation)
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17022,f858]) ).

fof(f17022,plain,
    ( ! [X0] :
        ( member(regular(intersection(null_class,X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17021,f15981]) ).

fof(f17021,plain,
    ( ! [X0] :
        ( member(regular(intersection(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17020,f858]) ).

fof(f17020,plain,
    ( ! [X0] :
        ( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_744 ),
    inference(forward_demodulation,[],[f17018,f12338]) ).

fof(f17018,plain,
    ( ! [X0] :
        ( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_744 ),
    inference(avatar_component_clause,[],[f17017]) ).

fof(f17019,plain,
    ( spl0_744
    | ~ spl0_118
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1383,f1368,f921,f17017]) ).

fof(f1383,plain,
    ( ! [X0] :
        ( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_118
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f922]) ).

fof(f16977,plain,
    ( spl0_743
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(avatar_split_clause,[],[f16973,f16962,f15972,f3255,f921,f856,f16975]) ).

fof(f16973,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,null_class)),subset_relation)
        | subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16972,f15981]) ).

fof(f16972,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16971,f858]) ).

fof(f16971,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16970,f12338]) ).

fof(f16970,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,null_class))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16969,f15981]) ).

fof(f16969,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16968,f858]) ).

fof(f16968,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16967,f12338]) ).

fof(f16967,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,null_class)),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_118
    | ~ spl0_297
    | spl0_711
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16966,f15981]) ).

fof(f16966,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16965,f858]) ).

fof(f16965,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_742 ),
    inference(forward_demodulation,[],[f16963,f12338]) ).

fof(f16964,plain,
    ( spl0_742
    | ~ spl0_140
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1249,f1216,f1202,f16962]) ).

fof(f1216,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1249,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_140
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f1203]) ).

fof(f1217,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1216]) ).

fof(f16951,plain,
    ( spl0_741
    | ~ spl0_37
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f4182,f4138,f339,f16949]) ).

fof(f4182,plain,
    ( ! [X0] :
        ( ~ subclass(complement(null_class),X0)
        | member(null_class,X0) )
    | ~ spl0_37
    | ~ spl0_335 ),
    inference(resolution,[],[f4140,f340]) ).

fof(f16947,plain,
    ( spl0_740
    | ~ spl0_110
    | ~ spl0_739 ),
    inference(avatar_split_clause,[],[f16943,f16940,f856,f16945]) ).

fof(f16945,plain,
    ( spl0_740
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),element_relation)
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f16943,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),element_relation)
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_110
    | ~ spl0_739 ),
    inference(forward_demodulation,[],[f16941,f858]) ).

fof(f16942,plain,
    ( spl0_739
    | ~ spl0_39
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1590,f1586,f347,f16940]) ).

fof(f1590,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_177 ),
    inference(superposition,[],[f1587,f348]) ).

fof(f16936,plain,
    ( spl0_738
    | spl0_546
    | ~ spl0_71
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1122,f1109,f558,f10730,f16934]) ).

fof(f16934,plain,
    ( spl0_738
  <=> ! [X2] :
        ( ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f10730,plain,
    ( spl0_546
  <=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f1122,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) )
    | ~ spl0_71
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f559]) ).

fof(f16640,plain,
    ( ~ spl0_158
    | ~ spl0_736
    | spl0_737
    | ~ spl0_152
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f4726,f1679,f1291,f16638,f16634,f1350]) ).

fof(f16634,plain,
    ( spl0_736
  <=> member(second(null_class),domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f16638,plain,
    ( spl0_737
  <=> ! [X0] :
        ( member(null_class,compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X0),universal_class)))),universal_class)),X0))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X0),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f4726,plain,
    ( ! [X0] :
        ( member(null_class,compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X0),universal_class)))),universal_class)),X0))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(null_class,cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X0),universal_class)))),universal_class) )
    | ~ spl0_152
    | ~ spl0_183 ),
    inference(superposition,[],[f1680,f1293]) ).

fof(f1293,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f16590,plain,
    ( spl0_735
    | ~ spl0_75
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1550,f1545,f585,f16588]) ).

fof(f16588,plain,
    ( spl0_735
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f585,plain,
    ( spl0_75
  <=> ! [X0,X1] :
        ( ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f1550,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_75
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f586]) ).

fof(f586,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f585]) ).

fof(f16586,plain,
    ( spl0_734
    | ~ spl0_141
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1543,f1512,f1212,f16584]) ).

fof(f16584,plain,
    ( spl0_734
  <=> ! [X2,X0,X1] :
        ( subclass(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f1543,plain,
    ( ! [X2,X0,X1] :
        ( subclass(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_141
    | ~ spl0_173 ),
    inference(superposition,[],[f1213,f1513]) ).

fof(f16582,plain,
    ( spl0_733
    | ~ spl0_74
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1071,f1052,f575,f16580]) ).

fof(f16580,plain,
    ( spl0_733
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
        | null_class = X0
        | ~ member(regular(X0),universal_class)
        | null_class = regular(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f1071,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
        | null_class = X0
        | ~ member(regular(X0),universal_class)
        | null_class = regular(X0) )
    | ~ spl0_74
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f576]) ).

fof(f16578,plain,
    ( spl0_732
    | ~ spl0_71
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f961,f925,f558,f16576]) ).

fof(f16576,plain,
    ( spl0_732
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f961,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) )
    | ~ spl0_71
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f559]) ).

fof(f16574,plain,
    ( spl0_731
    | ~ spl0_71
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f942,f921,f558,f16572]) ).

fof(f16572,plain,
    ( spl0_731
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f942,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) )
    | ~ spl0_71
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f559]) ).

fof(f16555,plain,
    ( spl0_730
    | ~ spl0_110
    | ~ spl0_729 ),
    inference(avatar_split_clause,[],[f16551,f16548,f856,f16553]) ).

fof(f16553,plain,
    ( spl0_730
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f16548,plain,
    ( spl0_729
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f16551,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class) )
    | ~ spl0_110
    | ~ spl0_729 ),
    inference(forward_demodulation,[],[f16549,f858]) ).

fof(f16549,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_729 ),
    inference(avatar_component_clause,[],[f16548]) ).

fof(f16550,plain,
    ( spl0_729
    | ~ spl0_11
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1783,f1761,f218,f16548]) ).

fof(f1783,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f219]) ).

fof(f16531,plain,
    ( spl0_728
    | ~ spl0_110
    | ~ spl0_726 ),
    inference(avatar_split_clause,[],[f16522,f16519,f856,f16529]) ).

fof(f16529,plain,
    ( spl0_728
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f16519,plain,
    ( spl0_726
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f16522,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class) )
    | ~ spl0_110
    | ~ spl0_726 ),
    inference(forward_demodulation,[],[f16520,f858]) ).

fof(f16520,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_726 ),
    inference(avatar_component_clause,[],[f16519]) ).

fof(f16527,plain,
    ( spl0_727
    | ~ spl0_251
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9220,f9161,f2509,f16524]) ).

fof(f16524,plain,
    ( spl0_727
  <=> null_class = complement(complement(unordered_pair(u,u))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f2509,plain,
    ( spl0_251
  <=> member(null_class,complement(unordered_pair(u,u))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f9161,plain,
    ( spl0_475
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f9220,plain,
    ( null_class = complement(complement(unordered_pair(u,u)))
    | ~ spl0_251
    | ~ spl0_475 ),
    inference(resolution,[],[f9162,f2511]) ).

fof(f2511,plain,
    ( member(null_class,complement(unordered_pair(u,u)))
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f2509]) ).

fof(f9162,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | complement(X0) = null_class )
    | ~ spl0_475 ),
    inference(avatar_component_clause,[],[f9161]) ).

fof(f16521,plain,
    ( spl0_726
    | ~ spl0_11
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1765,f1757,f218,f16519]) ).

fof(f1765,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f219]) ).

fof(f16218,plain,
    ( spl0_725
    | ~ spl0_11
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1664,f1661,f218,f16216]) ).

fof(f16216,plain,
    ( spl0_725
  <=> ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f1661,plain,
    ( spl0_181
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1664,plain,
    ( ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_11
    | ~ spl0_181 ),
    inference(resolution,[],[f1662,f219]) ).

fof(f1662,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f1661]) ).

fof(f16214,plain,
    ( spl0_724
    | ~ spl0_138
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1541,f1512,f1167,f16212]) ).

fof(f16212,plain,
    ( spl0_724
  <=> ! [X0,X1] :
        ( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
        | null_class = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f1167,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1541,plain,
    ( ! [X0,X1] :
        ( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
        | null_class = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_138
    | ~ spl0_173 ),
    inference(superposition,[],[f1168,f1513]) ).

fof(f1168,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1167]) ).

fof(f16210,plain,
    ( spl0_723
    | ~ spl0_128
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1441,f1425,f1052,f16208]) ).

fof(f16208,plain,
    ( spl0_723
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f1441,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_128
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f1053]) ).

fof(f16206,plain,
    ( spl0_722
    | ~ spl0_129
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1438,f1425,f1056,f16204]) ).

fof(f16204,plain,
    ( spl0_722
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f1438,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_129
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f1057]) ).

fof(f16193,plain,
    ( spl0_721
    | ~ spl0_25
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1378,f1368,f280,f16191]) ).

fof(f16191,plain,
    ( spl0_721
  <=> ! [X0] :
        ( member(not_subclass_element(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),subset_relation)
        | ~ member(not_subclass_element(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),cross_product(universal_class,universal_class))
        | subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f1378,plain,
    ( ! [X0] :
        ( member(not_subclass_element(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),subset_relation)
        | ~ member(not_subclass_element(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),cross_product(universal_class,universal_class))
        | subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_25
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f281]) ).

fof(f16113,plain,
    ( spl0_720
    | ~ spl0_79
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12303,f856,f616,f16111]) ).

fof(f16111,plain,
    ( spl0_720
  <=> ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f616,plain,
    ( spl0_79
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f12303,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_79
    | ~ spl0_110 ),
    inference(superposition,[],[f617,f858]) ).

fof(f617,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f616]) ).

fof(f16109,plain,
    ( spl0_719
    | ~ spl0_38
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1581,f1570,f343,f16107]) ).

fof(f16107,plain,
    ( spl0_719
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ subclass(X2,cross_product(X0,X1))
        | cross_product(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f343,plain,
    ( spl0_38
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1581,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ subclass(X2,cross_product(X0,X1))
        | cross_product(X0,X1) = X2 )
    | ~ spl0_38
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f344]) ).

fof(f344,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f16105,plain,
    ( spl0_718
    | ~ spl0_76
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1554,f1545,f591,f16103]) ).

fof(f16103,plain,
    ( spl0_718
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f1554,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_76
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f592]) ).

fof(f16101,plain,
    ( spl0_717
    | ~ spl0_79
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f801,f754,f616,f16099]) ).

fof(f16099,plain,
    ( spl0_717
  <=> ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f801,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_79
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f617]) ).

fof(f16080,plain,
    ( spl0_219
    | ~ spl0_716
    | ~ spl0_108
    | spl0_669 ),
    inference(avatar_split_clause,[],[f15699,f14920,f848,f16077,f2119]) ).

fof(f14920,plain,
    ( spl0_669
  <=> member(regular(identity_relation),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f15699,plain,
    ( ~ subclass(identity_relation,null_class)
    | null_class = identity_relation
    | ~ spl0_108
    | spl0_669 ),
    inference(resolution,[],[f14922,f849]) ).

fof(f14922,plain,
    ( ~ member(regular(identity_relation),null_class)
    | spl0_669 ),
    inference(avatar_component_clause,[],[f14920]) ).

fof(f16002,plain,
    ( spl0_715
    | ~ spl0_110
    | ~ spl0_714 ),
    inference(avatar_split_clause,[],[f15998,f15995,f856,f16000]) ).

fof(f16000,plain,
    ( spl0_715
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),element_relation)
        | ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f15995,plain,
    ( spl0_714
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f15998,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),element_relation)
        | ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0)) )
    | ~ spl0_110
    | ~ spl0_714 ),
    inference(forward_demodulation,[],[f15996,f858]) ).

fof(f15996,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_714 ),
    inference(avatar_component_clause,[],[f15995]) ).

fof(f15997,plain,
    ( spl0_714
    | ~ spl0_46
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1625,f1596,f404,f15995]) ).

fof(f1625,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_46
    | ~ spl0_178 ),
    inference(superposition,[],[f1597,f405]) ).

fof(f15993,plain,
    ( spl0_713
    | ~ spl0_122
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1540,f1512,f937,f15991]) ).

fof(f15991,plain,
    ( spl0_713
  <=> ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f937,plain,
    ( spl0_122
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1540,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_122
    | ~ spl0_173 ),
    inference(superposition,[],[f938,f1513]) ).

fof(f938,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f937]) ).

fof(f15989,plain,
    ( spl0_712
    | ~ spl0_44
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1429,f1425,f396,f15987]) ).

fof(f15987,plain,
    ( spl0_712
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f1429,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 )
    | ~ spl0_44
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f397]) ).

fof(f15975,plain,
    ( ~ spl0_711
    | ~ spl0_110
    | ~ spl0_297
    | spl0_707 ),
    inference(avatar_split_clause,[],[f15891,f15880,f3255,f856,f15972]) ).

fof(f15891,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),element_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_707 ),
    inference(forward_demodulation,[],[f15890,f12338]) ).

fof(f15970,plain,
    ( ~ spl0_710
    | ~ spl0_110
    | ~ spl0_297
    | spl0_708 ),
    inference(avatar_split_clause,[],[f15889,f15884,f3255,f856,f15967]) ).

fof(f15889,plain,
    ( ~ member(regular(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_708 ),
    inference(forward_demodulation,[],[f15888,f858]) ).

fof(f15888,plain,
    ( ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_708 ),
    inference(forward_demodulation,[],[f15885,f12338]) ).

fof(f15898,plain,
    ( ~ spl0_709
    | ~ spl0_110
    | ~ spl0_297
    | spl0_706 ),
    inference(avatar_split_clause,[],[f15893,f15876,f3255,f856,f15895]) ).

fof(f15895,plain,
    ( spl0_709
  <=> null_class = intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f15893,plain,
    ( null_class != intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_110
    | ~ spl0_297
    | spl0_706 ),
    inference(forward_demodulation,[],[f15892,f858]) ).

fof(f15892,plain,
    ( null_class != intersection(cross_product(universal_class,universal_class),complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_110
    | ~ spl0_297
    | spl0_706 ),
    inference(forward_demodulation,[],[f15877,f12338]) ).

fof(f15887,plain,
    ( spl0_706
    | ~ spl0_707
    | spl0_708
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1382,f1368,f269,f15884,f15880,f15876]) ).

fof(f1382,plain,
    ( member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
    | null_class = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f270]) ).

fof(f15849,plain,
    ( spl0_705
    | ~ spl0_110
    | ~ spl0_704 ),
    inference(avatar_split_clause,[],[f15845,f15842,f856,f15847]) ).

fof(f15847,plain,
    ( spl0_705
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),element_relation)
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f15842,plain,
    ( spl0_704
  <=> ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f15845,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),element_relation)
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_110
    | ~ spl0_704 ),
    inference(forward_demodulation,[],[f15843,f858]) ).

fof(f15843,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_704 ),
    inference(avatar_component_clause,[],[f15842]) ).

fof(f15844,plain,
    ( spl0_704
    | ~ spl0_46
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1592,f1586,f404,f15842]) ).

fof(f1592,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_46
    | ~ spl0_177 ),
    inference(superposition,[],[f1587,f405]) ).

fof(f15832,plain,
    ( spl0_703
    | ~ spl0_110
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f15828,f15825,f856,f15830]) ).

fof(f15830,plain,
    ( spl0_703
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),element_relation)
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f15825,plain,
    ( spl0_702
  <=> ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f15828,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),element_relation)
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_110
    | ~ spl0_702 ),
    inference(forward_demodulation,[],[f15826,f858]) ).

fof(f15826,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_702 ),
    inference(avatar_component_clause,[],[f15825]) ).

fof(f15827,plain,
    ( spl0_702
    | ~ spl0_46
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1589,f1586,f404,f15825]) ).

fof(f1589,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_46
    | ~ spl0_177 ),
    inference(superposition,[],[f1587,f405]) ).

fof(f15823,plain,
    ( spl0_701
    | ~ spl0_76
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1526,f1512,f591,f15821]) ).

fof(f15821,plain,
    ( spl0_701
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f1526,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_76
    | ~ spl0_173 ),
    inference(superposition,[],[f592,f1513]) ).

fof(f15819,plain,
    ( spl0_700
    | ~ spl0_20
    | ~ spl0_560 ),
    inference(avatar_split_clause,[],[f11092,f11029,f257,f15817]) ).

fof(f11029,plain,
    ( spl0_560
  <=> null_class = complement(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f11092,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,omega) )
    | ~ spl0_20
    | ~ spl0_560 ),
    inference(superposition,[],[f258,f11031]) ).

fof(f11031,plain,
    ( null_class = complement(omega)
    | ~ spl0_560 ),
    inference(avatar_component_clause,[],[f11029]) ).

fof(f15815,plain,
    ( ~ spl0_504
    | spl0_699
    | ~ spl0_150
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1385,f1368,f1284,f15813,f9918]) ).

fof(f9918,plain,
    ( spl0_504
  <=> subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f15813,plain,
    ( spl0_699
  <=> ! [X0] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),subset_relation)
        | ~ member(X0,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f1385,plain,
    ( ! [X0] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),subset_relation)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class) )
    | ~ spl0_150
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f1285]) ).

fof(f15796,plain,
    ( spl0_698
    | ~ spl0_68
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f1677,f1669,f538,f15794]) ).

fof(f15794,plain,
    ( spl0_698
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f1677,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_182 ),
    inference(duplicate_literal_removal,[],[f1672]) ).

fof(f1672,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_182 ),
    inference(resolution,[],[f1670,f539]) ).

fof(f15790,plain,
    ( spl0_697
    | ~ spl0_110
    | ~ spl0_696 ),
    inference(avatar_split_clause,[],[f15786,f15782,f856,f15788]) ).

fof(f15788,plain,
    ( spl0_697
  <=> ! [X0] :
        ( element_relation = X0
        | not_subclass_element(element_relation,X0) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,X0)),first(not_subclass_element(element_relation,X0))),unordered_pair(first(not_subclass_element(element_relation,X0)),unordered_pair(second(not_subclass_element(element_relation,X0)),second(not_subclass_element(element_relation,X0)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f15782,plain,
    ( spl0_696
  <=> ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f15786,plain,
    ( ! [X0] :
        ( element_relation = X0
        | not_subclass_element(element_relation,X0) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,X0)),first(not_subclass_element(element_relation,X0))),unordered_pair(first(not_subclass_element(element_relation,X0)),unordered_pair(second(not_subclass_element(element_relation,X0)),second(not_subclass_element(element_relation,X0)))))
        | ~ function(X0) )
    | ~ spl0_110
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f15785,f858]) ).

fof(f15785,plain,
    ( ! [X0] :
        ( not_subclass_element(element_relation,X0) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,X0)),first(not_subclass_element(element_relation,X0))),unordered_pair(first(not_subclass_element(element_relation,X0)),unordered_pair(second(not_subclass_element(element_relation,X0)),second(not_subclass_element(element_relation,X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_110
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f15783,f858]) ).

fof(f15783,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_696 ),
    inference(avatar_component_clause,[],[f15782]) ).

fof(f15784,plain,
    ( spl0_696
    | ~ spl0_126
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1573,f1570,f1003,f15782]) ).

fof(f1003,plain,
    ( spl0_126
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1573,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_126
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f1004]) ).

fof(f1004,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f1003]) ).

fof(f15769,plain,
    ( ~ spl0_694
    | spl0_695
    | ~ spl0_158
    | ~ spl0_152
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f4725,f1669,f1291,f1350,f15767,f15763]) ).

fof(f15767,plain,
    ( spl0_695
  <=> ! [X0,X1] :
        ( member(null_class,compose(X0,X1))
        | null_class = intersection(cross_product(unordered_pair(second(null_class),second(null_class)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X1),universal_class)))),universal_class),X0),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f4725,plain,
    ( ! [X0,X1] :
        ( ~ member(null_class,cross_product(universal_class,universal_class))
        | member(null_class,compose(X0,X1))
        | ~ member(second(null_class),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(null_class),second(null_class)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X1),universal_class)))),universal_class),X0),universal_class)))) )
    | ~ spl0_152
    | ~ spl0_182 ),
    inference(superposition,[],[f1670,f1293]) ).

fof(f15761,plain,
    ( spl0_693
    | ~ spl0_28
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1535,f1512,f292,f15759]) ).

fof(f15759,plain,
    ( spl0_693
  <=> ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f1535,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_28
    | ~ spl0_173 ),
    inference(superposition,[],[f293,f1513]) ).

fof(f15757,plain,
    ( ~ spl0_504
    | spl0_692
    | ~ spl0_149
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1391,f1368,f1280,f15755,f9918]) ).

fof(f15755,plain,
    ( spl0_692
  <=> ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),subset_relation)
        | ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f1391,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),subset_relation)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),cross_product(universal_class,universal_class))
        | ~ function(X1)
        | ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class) )
    | ~ spl0_149
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f1281]) ).

fof(f15750,plain,
    ( spl0_691
    | ~ spl0_37
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1555,f1545,f339,f15748]) ).

fof(f15748,plain,
    ( spl0_691
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),X3)
        | ~ operation(X2)
        | ~ subclass(X3,X4)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f1555,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),X3)
        | ~ operation(X2)
        | ~ subclass(X3,X4)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
    | ~ spl0_37
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f340]) ).

fof(f15743,plain,
    ( ~ spl0_689
    | ~ spl0_690
    | spl0_373
    | ~ spl0_115
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1455,f1443,f878,f5414,f15740,f15736]) ).

fof(f15736,plain,
    ( spl0_689
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f15740,plain,
    ( spl0_690
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f5414,plain,
    ( spl0_373
  <=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f1455,plain,
    ( null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
    | ~ spl0_115
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f879]) ).

fof(f15703,plain,
    ( spl0_688
    | ~ spl0_370
    | ~ spl0_417
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f15691,f15688,f6780,f4795,f15701]) ).

fof(f15691,plain,
    ( ! [X0] :
        ( member(null_class,compose(X0,regular(cross_product(u,universal_class))))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_370
    | ~ spl0_417
    | ~ spl0_686 ),
    inference(forward_demodulation,[],[f15689,f6978]) ).

fof(f15697,plain,
    ( ~ spl0_687
    | ~ spl0_370
    | ~ spl0_417
    | spl0_685 ),
    inference(avatar_split_clause,[],[f15692,f15684,f6780,f4795,f15694]) ).

fof(f15694,plain,
    ( spl0_687
  <=> null_class = cross_product(u,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f15684,plain,
    ( spl0_685
  <=> null_class = cross_product(unordered_pair(first(null_class),first(null_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f15692,plain,
    ( null_class != cross_product(u,universal_class)
    | ~ spl0_370
    | ~ spl0_417
    | spl0_685 ),
    inference(forward_demodulation,[],[f15685,f6978]) ).

fof(f15685,plain,
    ( null_class != cross_product(unordered_pair(first(null_class),first(null_class)),universal_class)
    | spl0_685 ),
    inference(avatar_component_clause,[],[f15684]) ).

fof(f15690,plain,
    ( spl0_685
    | ~ spl0_158
    | spl0_686
    | ~ spl0_152
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f4724,f1654,f1291,f15688,f1350,f15684]) ).

fof(f4724,plain,
    ( ! [X0] :
        ( member(null_class,compose(X0,regular(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class))))
        | ~ member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X0),universal_class)))))
        | ~ member(null_class,cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(null_class),first(null_class)),universal_class) )
    | ~ spl0_152
    | ~ spl0_180 ),
    inference(superposition,[],[f1655,f1293]) ).

fof(f15682,plain,
    ( spl0_684
    | ~ spl0_29
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1559,f1545,f296,f15680]) ).

fof(f15680,plain,
    ( spl0_684
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f296,plain,
    ( spl0_29
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f1559,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
    | ~ spl0_29
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f297]) ).

fof(f297,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f15678,plain,
    ( spl0_683
    | ~ spl0_30
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1558,f1545,f300,f15676]) ).

fof(f15676,plain,
    ( spl0_683
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f1558,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
    | ~ spl0_30
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f301]) ).

fof(f15568,plain,
    ( spl0_682
    | ~ spl0_20
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1562,f1545,f257,f15566]) ).

fof(f15566,plain,
    ( spl0_682
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(X3))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f1562,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(X3))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
    | ~ spl0_20
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f258]) ).

fof(f15564,plain,
    ( spl0_681
    | ~ spl0_44
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1536,f1512,f396,f15562]) ).

fof(f15562,plain,
    ( spl0_681
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f1536,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
        | cross_product(X0,X1) = null_class )
    | ~ spl0_44
    | ~ spl0_173 ),
    inference(superposition,[],[f397,f1513]) ).

fof(f15547,plain,
    ( spl0_680
    | ~ spl0_92
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1567,f1545,f686,f15545]) ).

fof(f15545,plain,
    ( spl0_680
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),identity_relation)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f1567,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),identity_relation)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_92
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f687]) ).

fof(f15543,plain,
    ( spl0_679
    | ~ spl0_116
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1538,f1512,f882,f15541]) ).

fof(f15541,plain,
    ( spl0_679
  <=> ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f1538,plain,
    ( ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_116
    | ~ spl0_173 ),
    inference(superposition,[],[f883,f1513]) ).

fof(f15049,plain,
    ( spl0_678
    | ~ spl0_37
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1509,f1505,f339,f15047]) ).

fof(f15047,plain,
    ( spl0_678
  <=> ! [X0,X1] :
        ( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(successor_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f1509,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(successor_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) )
    | ~ spl0_37
    | ~ spl0_172 ),
    inference(resolution,[],[f1506,f340]) ).

fof(f15045,plain,
    ( ~ spl0_677
    | ~ spl0_99
    | spl0_670 ),
    inference(avatar_split_clause,[],[f15016,f15005,f746,f15042]) ).

fof(f15042,plain,
    ( spl0_677
  <=> subclass(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f15016,plain,
    ( ~ subclass(universal_class,subset_relation)
    | ~ spl0_99
    | spl0_670 ),
    inference(resolution,[],[f15007,f747]) ).

fof(f15040,plain,
    ( spl0_676
    | ~ spl0_29
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1490,f1465,f296,f15038]) ).

fof(f15038,plain,
    ( spl0_676
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f1490,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_29
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f297]) ).

fof(f15036,plain,
    ( spl0_675
    | ~ spl0_30
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1489,f1465,f300,f15034]) ).

fof(f15034,plain,
    ( spl0_675
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1489,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_30
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f301]) ).

fof(f15032,plain,
    ( spl0_674
    | ~ spl0_29
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1472,f1461,f296,f15030]) ).

fof(f15030,plain,
    ( spl0_674
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f1472,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_29
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f297]) ).

fof(f15028,plain,
    ( spl0_673
    | ~ spl0_30
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1471,f1461,f300,f15026]) ).

fof(f15026,plain,
    ( spl0_673
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f1471,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
    | ~ spl0_30
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f301]) ).

fof(f15024,plain,
    ( spl0_672
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1263,f1216,f500,f404,f15022]) ).

fof(f15022,plain,
    ( spl0_672
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f1263,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) )
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_142 ),
    inference(forward_demodulation,[],[f1251,f405]) ).

fof(f1251,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class),X2) )
    | ~ spl0_63
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f501]) ).

fof(f15013,plain,
    ( ~ spl0_671
    | ~ spl0_110
    | spl0_187 ),
    inference(avatar_split_clause,[],[f12321,f1748,f856,f15010]) ).

fof(f15010,plain,
    ( spl0_671
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f1748,plain,
    ( spl0_187
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f12321,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),element_relation)
    | ~ spl0_110
    | spl0_187 ),
    inference(superposition,[],[f1750,f858]) ).

fof(f1750,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),cross_product(universal_class,universal_class))
    | spl0_187 ),
    inference(avatar_component_clause,[],[f1748]) ).

fof(f15008,plain,
    ( ~ spl0_670
    | ~ spl0_101
    | spl0_187 ),
    inference(avatar_split_clause,[],[f1754,f1748,f754,f15005]) ).

fof(f1754,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),subset_relation)
    | ~ spl0_101
    | spl0_187 ),
    inference(resolution,[],[f1750,f755]) ).

fof(f14923,plain,
    ( ~ spl0_669
    | ~ spl0_220
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f13875,f11626,f2123,f14920]) ).

fof(f2123,plain,
    ( spl0_220
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f13875,plain,
    ( ~ member(regular(identity_relation),null_class)
    | ~ spl0_220
    | ~ spl0_590 ),
    inference(resolution,[],[f11627,f2125]) ).

fof(f2125,plain,
    ( member(regular(identity_relation),subset_relation)
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f2123]) ).

fof(f14918,plain,
    ( spl0_668
    | ~ spl0_110
    | ~ spl0_667 ),
    inference(avatar_split_clause,[],[f14913,f14909,f856,f14915]) ).

fof(f14909,plain,
    ( spl0_667
  <=> not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f14913,plain,
    ( not_subclass_element(element_relation,successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,successor_relation)),first(not_subclass_element(element_relation,successor_relation))),unordered_pair(first(not_subclass_element(element_relation,successor_relation)),unordered_pair(second(not_subclass_element(element_relation,successor_relation)),second(not_subclass_element(element_relation,successor_relation)))))
    | ~ spl0_110
    | ~ spl0_667 ),
    inference(forward_demodulation,[],[f14911,f858]) ).

fof(f14911,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
    | ~ spl0_667 ),
    inference(avatar_component_clause,[],[f14909]) ).

fof(f14912,plain,
    ( spl0_667
    | spl0_113
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1575,f1570,f869,f14909]) ).

fof(f869,plain,
    ( spl0_113
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1575,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
    | spl0_113
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f871]) ).

fof(f871,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_113 ),
    inference(avatar_component_clause,[],[f869]) ).

fof(f14423,plain,
    ( spl0_361
    | ~ spl0_8
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f9109,f7452,f206,f4702]) ).

fof(f14382,plain,
    ( spl0_666
    | ~ spl0_110
    | ~ spl0_561 ),
    inference(avatar_split_clause,[],[f14058,f11034,f856,f14380]) ).

fof(f14380,plain,
    ( spl0_666
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f11034,plain,
    ( spl0_561
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f14058,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_110
    | ~ spl0_561 ),
    inference(forward_demodulation,[],[f11035,f858]) ).

fof(f11035,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_561 ),
    inference(avatar_component_clause,[],[f11034]) ).

fof(f14378,plain,
    ( spl0_665
    | ~ spl0_110
    | ~ spl0_563 ),
    inference(avatar_split_clause,[],[f14057,f11054,f856,f14376]) ).

fof(f14376,plain,
    ( spl0_665
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f11054,plain,
    ( spl0_563
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f14057,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_110
    | ~ spl0_563 ),
    inference(forward_demodulation,[],[f11055,f858]) ).

fof(f11055,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_563 ),
    inference(avatar_component_clause,[],[f11054]) ).

fof(f14199,plain,
    ( spl0_664
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_663 ),
    inference(avatar_split_clause,[],[f14195,f14191,f3255,f856,f14197]) ).

fof(f14195,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_663 ),
    inference(forward_demodulation,[],[f14194,f12338]) ).

fof(f14194,plain,
    ( ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_663 ),
    inference(forward_demodulation,[],[f14192,f12338]) ).

fof(f14193,plain,
    ( spl0_663
    | ~ spl0_110
    | ~ spl0_555 ),
    inference(avatar_split_clause,[],[f12144,f10898,f856,f14191]) ).

fof(f10898,plain,
    ( spl0_555
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f12144,plain,
    ( ! [X0] :
        ( subclass(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation) )
    | ~ spl0_110
    | ~ spl0_555 ),
    inference(forward_demodulation,[],[f12143,f858]) ).

fof(f12143,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_110
    | ~ spl0_555 ),
    inference(forward_demodulation,[],[f10899,f858]) ).

fof(f10899,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_555 ),
    inference(avatar_component_clause,[],[f10898]) ).

fof(f14056,plain,
    ( ~ spl0_361
    | ~ spl0_162
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f13879,f11626,f1372,f4702]) ).

fof(f13879,plain,
    ( ~ member(u,null_class)
    | ~ spl0_162
    | ~ spl0_590 ),
    inference(resolution,[],[f11627,f1373]) ).

fof(f13984,plain,
    ( spl0_662
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_661 ),
    inference(avatar_split_clause,[],[f13980,f13976,f3255,f856,f13982]) ).

fof(f13980,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_661 ),
    inference(forward_demodulation,[],[f13979,f12338]) ).

fof(f13979,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_661 ),
    inference(forward_demodulation,[],[f13977,f12338]) ).

fof(f13978,plain,
    ( spl0_661
    | ~ spl0_110
    | ~ spl0_543 ),
    inference(avatar_split_clause,[],[f12151,f10683,f856,f13976]) ).

fof(f10683,plain,
    ( spl0_543
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f12151,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) )
    | ~ spl0_110
    | ~ spl0_543 ),
    inference(forward_demodulation,[],[f12150,f858]) ).

fof(f12150,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_110
    | ~ spl0_543 ),
    inference(forward_demodulation,[],[f10684,f858]) ).

fof(f10684,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_543 ),
    inference(avatar_component_clause,[],[f10683]) ).

fof(f13974,plain,
    ( ~ spl0_660
    | ~ spl0_110
    | spl0_598 ),
    inference(avatar_split_clause,[],[f12111,f11935,f856,f13971]) ).

fof(f13971,plain,
    ( spl0_660
  <=> not_subclass_element(element_relation,element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(element_relation,element_relation)),first(not_subclass_element(element_relation,element_relation))),unordered_pair(first(not_subclass_element(element_relation,element_relation)),unordered_pair(second(not_subclass_element(element_relation,element_relation)),second(not_subclass_element(element_relation,element_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f11935,plain,
    ( spl0_598
  <=> not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f12111,plain,
    ( not_subclass_element(element_relation,element_relation) != unordered_pair(unordered_pair(first(not_subclass_element(element_relation,element_relation)),first(not_subclass_element(element_relation,element_relation))),unordered_pair(first(not_subclass_element(element_relation,element_relation)),unordered_pair(second(not_subclass_element(element_relation,element_relation)),second(not_subclass_element(element_relation,element_relation)))))
    | ~ spl0_110
    | spl0_598 ),
    inference(forward_demodulation,[],[f11936,f858]) ).

fof(f11936,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),element_relation) != unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
    | spl0_598 ),
    inference(avatar_component_clause,[],[f11935]) ).

fof(f13940,plain,
    ( spl0_659
    | ~ spl0_329
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f10134,f10129,f3612,f13938]) ).

fof(f13938,plain,
    ( spl0_659
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f10134,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_329
    | ~ spl0_516 ),
    inference(forward_demodulation,[],[f10133,f3614]) ).

fof(f3614,plain,
    ( null_class = unordered_pair(u,u)
    | ~ spl0_329 ),
    inference(avatar_component_clause,[],[f3612]) ).

fof(f10133,plain,
    ( ! [X0] :
        ( ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_329
    | ~ spl0_516 ),
    inference(forward_demodulation,[],[f10132,f3614]) ).

fof(f10132,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_329
    | ~ spl0_516 ),
    inference(forward_demodulation,[],[f10130,f3614]) ).

fof(f13866,plain,
    ( spl0_658
    | ~ spl0_329
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f10119,f10114,f3612,f13864]) ).

fof(f13864,plain,
    ( spl0_658
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f10119,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_329
    | ~ spl0_514 ),
    inference(forward_demodulation,[],[f10118,f3614]) ).

fof(f10118,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_329
    | ~ spl0_514 ),
    inference(forward_demodulation,[],[f10117,f3614]) ).

fof(f10117,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_329
    | ~ spl0_514 ),
    inference(forward_demodulation,[],[f10115,f3614]) ).

fof(f13853,plain,
    ( spl0_657
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_656 ),
    inference(avatar_split_clause,[],[f13849,f13846,f3255,f856,f13851]) ).

fof(f13851,plain,
    ( spl0_657
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f13846,plain,
    ( spl0_656
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f13849,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_656 ),
    inference(forward_demodulation,[],[f13847,f12338]) ).

fof(f13847,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1) )
    | ~ spl0_656 ),
    inference(avatar_component_clause,[],[f13846]) ).

fof(f13848,plain,
    ( spl0_656
    | ~ spl0_110
    | ~ spl0_525 ),
    inference(avatar_split_clause,[],[f12155,f10288,f856,f13846]) ).

fof(f10288,plain,
    ( spl0_525
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f12155,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1) )
    | ~ spl0_110
    | ~ spl0_525 ),
    inference(forward_demodulation,[],[f12154,f858]) ).

fof(f12154,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,X1) )
    | ~ spl0_110
    | ~ spl0_525 ),
    inference(forward_demodulation,[],[f10289,f858]) ).

fof(f10289,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1) )
    | ~ spl0_525 ),
    inference(avatar_component_clause,[],[f10288]) ).

fof(f13789,plain,
    ( spl0_655
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_654 ),
    inference(avatar_split_clause,[],[f13785,f13782,f3255,f856,f13787]) ).

fof(f13787,plain,
    ( spl0_655
  <=> ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),subset_relation)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f13782,plain,
    ( spl0_654
  <=> ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),subset_relation)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f13785,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),subset_relation)
        | null_class = X0 )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_654 ),
    inference(forward_demodulation,[],[f13783,f12338]) ).

fof(f13783,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),subset_relation)
        | null_class = X0 )
    | ~ spl0_654 ),
    inference(avatar_component_clause,[],[f13782]) ).

fof(f13784,plain,
    ( spl0_654
    | ~ spl0_110
    | ~ spl0_510 ),
    inference(avatar_split_clause,[],[f12158,f9999,f856,f13782]) ).

fof(f9999,plain,
    ( spl0_510
  <=> ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f12158,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),subset_relation)
        | null_class = X0 )
    | ~ spl0_110
    | ~ spl0_510 ),
    inference(forward_demodulation,[],[f12157,f858]) ).

fof(f12157,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),subset_relation)
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 )
    | ~ spl0_110
    | ~ spl0_510 ),
    inference(forward_demodulation,[],[f10000,f858]) ).

fof(f10000,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | member(regular(X0),subset_relation)
        | null_class = X0 )
    | ~ spl0_510 ),
    inference(avatar_component_clause,[],[f9999]) ).

fof(f13716,plain,
    ( spl0_653
    | ~ spl0_110
    | ~ spl0_502 ),
    inference(avatar_split_clause,[],[f12165,f9879,f856,f13714]) ).

fof(f13714,plain,
    ( spl0_653
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),element_relation)
        | ~ member(not_subclass_element(X0,subset_relation),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f9879,plain,
    ( spl0_502
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f12165,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),element_relation)
        | ~ member(not_subclass_element(X0,subset_relation),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,subset_relation) )
    | ~ spl0_110
    | ~ spl0_502 ),
    inference(forward_demodulation,[],[f12164,f858]) ).

fof(f12164,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) )
    | ~ spl0_110
    | ~ spl0_502 ),
    inference(forward_demodulation,[],[f9880,f858]) ).

fof(f9880,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) )
    | ~ spl0_502 ),
    inference(avatar_component_clause,[],[f9879]) ).

fof(f13648,plain,
    ( spl0_652
    | ~ spl0_110
    | ~ spl0_492 ),
    inference(avatar_split_clause,[],[f12183,f9703,f856,f13646]) ).

fof(f13646,plain,
    ( spl0_652
  <=> ! [X0,X1] :
        ( ~ member(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X1,element_relation)
        | ~ subclass(subset_relation,X0)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f9703,plain,
    ( spl0_492
  <=> ! [X0,X1] :
        ( ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f12183,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X1,element_relation)
        | ~ subclass(subset_relation,X0)
        | member(X1,X0) )
    | ~ spl0_110
    | ~ spl0_492 ),
    inference(forward_demodulation,[],[f12182,f858]) ).

fof(f12182,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,element_relation)
        | ~ subclass(subset_relation,X0)
        | ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X1,X0) )
    | ~ spl0_110
    | ~ spl0_492 ),
    inference(forward_demodulation,[],[f9704,f858]) ).

fof(f9704,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ subclass(subset_relation,X0)
        | member(X1,X0) )
    | ~ spl0_492 ),
    inference(avatar_component_clause,[],[f9703]) ).

fof(f13480,plain,
    ( spl0_651
    | ~ spl0_110
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f12388,f1361,f856,f13478]) ).

fof(f13478,plain,
    ( spl0_651
  <=> ! [X2,X0,X1] :
        ( ~ subclass(element_relation,X0)
        | ~ member(X1,universal_class)
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f12388,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(element_relation,X0)
        | ~ member(X1,universal_class)
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0) )
    | ~ spl0_110
    | ~ spl0_160 ),
    inference(superposition,[],[f1362,f858]) ).

fof(f13411,plain,
    ( spl0_650
    | ~ spl0_71
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12386,f856,f558,f13409]) ).

fof(f13409,plain,
    ( spl0_650
  <=> ! [X0] :
        ( ~ member(X0,element_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f12386,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
    | ~ spl0_71
    | ~ spl0_110 ),
    inference(superposition,[],[f559,f858]) ).

fof(f13406,plain,
    ( spl0_649
    | ~ spl0_110
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f12318,f1368,f856,f13404]) ).

fof(f13404,plain,
    ( spl0_649
  <=> ! [X0] :
        ( ~ member(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X0,subset_relation)
        | ~ member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f12318,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X0,subset_relation)
        | ~ member(X0,element_relation) )
    | ~ spl0_110
    | ~ spl0_161 ),
    inference(superposition,[],[f1369,f858]) ).

fof(f13395,plain,
    ( spl0_648
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f13391,f13388,f3255,f856,f13393]) ).

fof(f13391,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_647 ),
    inference(forward_demodulation,[],[f13389,f12338]) ).

fof(f13390,plain,
    ( spl0_647
    | ~ spl0_110
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f12216,f7282,f856,f13388]) ).

fof(f7282,plain,
    ( spl0_424
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f12216,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_110
    | ~ spl0_424 ),
    inference(forward_demodulation,[],[f7283,f858]) ).

fof(f7283,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_424 ),
    inference(avatar_component_clause,[],[f7282]) ).

fof(f13383,plain,
    ( spl0_646
    | ~ spl0_110
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f12233,f6732,f856,f13381]) ).

fof(f6732,plain,
    ( spl0_409
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f12233,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_110
    | ~ spl0_409 ),
    inference(forward_demodulation,[],[f6733,f858]) ).

fof(f6733,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f6732]) ).

fof(f13361,plain,
    ( spl0_645
    | ~ spl0_68
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12385,f856,f538,f13359]) ).

fof(f13359,plain,
    ( spl0_645
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f12385,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_110 ),
    inference(superposition,[],[f539,f858]) ).

fof(f13308,plain,
    ( spl0_644
    | ~ spl0_37
    | ~ spl0_606 ),
    inference(avatar_split_clause,[],[f12471,f12438,f339,f13306]) ).

fof(f12471,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(u,X0) )
    | ~ spl0_37
    | ~ spl0_606 ),
    inference(resolution,[],[f12440,f340]) ).

fof(f13304,plain,
    ( spl0_643
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_642 ),
    inference(avatar_split_clause,[],[f13300,f13297,f3255,f856,f13302]) ).

fof(f13302,plain,
    ( spl0_643
  <=> ! [X0] :
        ( ~ member(X0,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,element_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f13297,plain,
    ( spl0_642
  <=> ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,subset_relation)
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f13300,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,element_relation)
        | member(X0,subset_relation) )
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_642 ),
    inference(forward_demodulation,[],[f13298,f12338]) ).

fof(f13298,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | member(X0,subset_relation)
        | ~ member(X0,element_relation) )
    | ~ spl0_642 ),
    inference(avatar_component_clause,[],[f13297]) ).

fof(f13299,plain,
    ( spl0_642
    | ~ spl0_110
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f12244,f6514,f856,f13297]) ).

fof(f6514,plain,
    ( spl0_405
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f12244,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,subset_relation)
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_110
    | ~ spl0_405 ),
    inference(forward_demodulation,[],[f6515,f858]) ).

fof(f6515,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,cross_product(universal_class,universal_class))
        | member(X0,subset_relation) )
    | ~ spl0_405 ),
    inference(avatar_component_clause,[],[f6514]) ).

fof(f13233,plain,
    ( spl0_641
    | ~ spl0_110
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f12314,f1202,f856,f13231]) ).

fof(f12314,plain,
    ( ! [X0] :
        ( member(X0,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_110
    | ~ spl0_140 ),
    inference(superposition,[],[f1203,f858]) ).

fof(f13167,plain,
    ( spl0_640
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_639 ),
    inference(avatar_split_clause,[],[f13162,f13158,f3255,f856,f13164]) ).

fof(f13158,plain,
    ( spl0_639
  <=> subset_relation = intersection(element_relation,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f13162,plain,
    ( subset_relation = intersection(element_relation,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_639 ),
    inference(forward_demodulation,[],[f13160,f12338]) ).

fof(f13160,plain,
    ( subset_relation = intersection(element_relation,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_639 ),
    inference(avatar_component_clause,[],[f13158]) ).

fof(f13161,plain,
    ( spl0_639
    | ~ spl0_67
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12301,f856,f533,f13158]) ).

fof(f12301,plain,
    ( subset_relation = intersection(element_relation,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_67
    | ~ spl0_110 ),
    inference(superposition,[],[f535,f858]) ).

fof(f13153,plain,
    ( ~ spl0_638
    | ~ spl0_110
    | ~ spl0_297
    | spl0_637 ),
    inference(avatar_split_clause,[],[f13148,f13144,f3255,f856,f13150]) ).

fof(f13148,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | ~ spl0_110
    | ~ spl0_297
    | spl0_637 ),
    inference(forward_demodulation,[],[f13146,f12338]) ).

fof(f13147,plain,
    ( ~ spl0_637
    | ~ spl0_110
    | spl0_548 ),
    inference(avatar_split_clause,[],[f12148,f10806,f856,f13144]) ).

fof(f10806,plain,
    ( spl0_548
  <=> member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f12148,plain,
    ( ~ member(regular(complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | ~ spl0_110
    | spl0_548 ),
    inference(forward_demodulation,[],[f10808,f858]) ).

fof(f10808,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | spl0_548 ),
    inference(avatar_component_clause,[],[f10806]) ).

fof(f13126,plain,
    ( spl0_636
    | ~ spl0_61
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12384,f856,f492,f13124]) ).

fof(f13124,plain,
    ( spl0_636
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f492,plain,
    ( spl0_61
  <=> ! [X0,X3,X2,X1] :
        ( member(X3,X1)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f12384,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X1,universal_class) )
    | ~ spl0_61
    | ~ spl0_110 ),
    inference(superposition,[],[f493,f858]) ).

fof(f493,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X3,X1) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f492]) ).

fof(f13122,plain,
    ( spl0_635
    | ~ spl0_60
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12383,f856,f488,f13120]) ).

fof(f13120,plain,
    ( spl0_635
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f488,plain,
    ( spl0_60
  <=> ! [X0,X3,X2,X1] :
        ( member(X2,X0)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f12383,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,universal_class) )
    | ~ spl0_60
    | ~ spl0_110 ),
    inference(superposition,[],[f489,f858]) ).

fof(f489,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f488]) ).

fof(f13112,plain,
    ( spl0_634
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_633 ),
    inference(avatar_split_clause,[],[f13107,f13103,f3255,f856,f13109]) ).

fof(f13103,plain,
    ( spl0_633
  <=> member(regular(subset_relation),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f13107,plain,
    ( member(regular(subset_relation),intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_297
    | ~ spl0_633 ),
    inference(forward_demodulation,[],[f13105,f12338]) ).

fof(f13105,plain,
    ( member(regular(subset_relation),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_633 ),
    inference(avatar_component_clause,[],[f13103]) ).

fof(f13106,plain,
    ( spl0_633
    | ~ spl0_110
    | ~ spl0_399 ),
    inference(avatar_split_clause,[],[f12245,f6479,f856,f13103]) ).

fof(f6479,plain,
    ( spl0_399
  <=> member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f12245,plain,
    ( member(regular(subset_relation),intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_399 ),
    inference(forward_demodulation,[],[f6481,f858]) ).

fof(f6481,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_399 ),
    inference(avatar_component_clause,[],[f6479]) ).

fof(f13101,plain,
    ( ~ spl0_632
    | ~ spl0_110
    | ~ spl0_297
    | spl0_631 ),
    inference(avatar_split_clause,[],[f13096,f13092,f3255,f856,f13098]) ).

fof(f13098,plain,
    ( spl0_632
  <=> null_class = complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f13092,plain,
    ( spl0_631
  <=> null_class = complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f13096,plain,
    ( null_class != complement(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_297
    | spl0_631 ),
    inference(forward_demodulation,[],[f13094,f12338]) ).

fof(f13094,plain,
    ( null_class != complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_631 ),
    inference(avatar_component_clause,[],[f13092]) ).

fof(f13095,plain,
    ( ~ spl0_631
    | ~ spl0_110
    | spl0_547 ),
    inference(avatar_split_clause,[],[f12147,f10802,f856,f13092]) ).

fof(f12147,plain,
    ( null_class != complement(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | spl0_547 ),
    inference(forward_demodulation,[],[f10803,f858]) ).

fof(f10803,plain,
    ( null_class != complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_547 ),
    inference(avatar_component_clause,[],[f10802]) ).

fof(f13090,plain,
    ( ~ spl0_630
    | ~ spl0_110
    | spl0_404 ),
    inference(avatar_split_clause,[],[f13048,f6509,f856,f13087]) ).

fof(f13087,plain,
    ( spl0_630
  <=> subclass(element_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f6509,plain,
    ( spl0_404
  <=> subclass(cross_product(universal_class,universal_class),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f13048,plain,
    ( ~ subclass(element_relation,null_class)
    | ~ spl0_110
    | spl0_404 ),
    inference(forward_demodulation,[],[f6511,f858]) ).

fof(f6511,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),null_class)
    | spl0_404 ),
    inference(avatar_component_clause,[],[f6509]) ).

fof(f13085,plain,
    ( ~ spl0_629
    | ~ spl0_110
    | ~ spl0_297
    | spl0_628 ),
    inference(avatar_split_clause,[],[f13080,f13076,f3255,f856,f13082]) ).

fof(f13082,plain,
    ( spl0_629
  <=> subclass(universal_class,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f13076,plain,
    ( spl0_628
  <=> subclass(universal_class,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f13080,plain,
    ( ~ subclass(universal_class,intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_297
    | spl0_628 ),
    inference(forward_demodulation,[],[f13078,f12338]) ).

fof(f13078,plain,
    ( ~ subclass(universal_class,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_628 ),
    inference(avatar_component_clause,[],[f13076]) ).

fof(f13079,plain,
    ( ~ spl0_628
    | ~ spl0_110
    | spl0_504 ),
    inference(avatar_split_clause,[],[f12159,f9918,f856,f13076]) ).

fof(f12159,plain,
    ( ~ subclass(universal_class,intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | spl0_504 ),
    inference(forward_demodulation,[],[f9920,f858]) ).

fof(f9920,plain,
    ( ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_504 ),
    inference(avatar_component_clause,[],[f9918]) ).

fof(f13072,plain,
    ( ~ spl0_627
    | ~ spl0_110
    | ~ spl0_297
    | spl0_626 ),
    inference(avatar_split_clause,[],[f13067,f13063,f3255,f856,f13069]) ).

fof(f13069,plain,
    ( spl0_627
  <=> function(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f13063,plain,
    ( spl0_626
  <=> function(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f13067,plain,
    ( ~ function(intersection(element_relation,complement(compose(null_class,domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | ~ spl0_297
    | spl0_626 ),
    inference(forward_demodulation,[],[f13065,f12338]) ).

fof(f13065,plain,
    ( ~ function(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_626 ),
    inference(avatar_component_clause,[],[f13063]) ).

fof(f13066,plain,
    ( ~ spl0_626
    | ~ spl0_110
    | spl0_164 ),
    inference(avatar_split_clause,[],[f12319,f1398,f856,f13063]) ).

fof(f1398,plain,
    ( spl0_164
  <=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f12319,plain,
    ( ~ function(intersection(element_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_110
    | spl0_164 ),
    inference(superposition,[],[f1400,f858]) ).

fof(f1400,plain,
    ( ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | spl0_164 ),
    inference(avatar_component_clause,[],[f1398]) ).

fof(f13061,plain,
    ( spl0_625
    | ~ spl0_110
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f12313,f1137,f856,f13059]) ).

fof(f13059,plain,
    ( spl0_625
  <=> ! [X0] :
        ( ~ subclass(cross_product(element_relation,universal_class),flip(X0))
        | flip(X0) = cross_product(element_relation,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f12313,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(element_relation,universal_class),flip(X0))
        | flip(X0) = cross_product(element_relation,universal_class) )
    | ~ spl0_110
    | ~ spl0_135 ),
    inference(superposition,[],[f1138,f858]) ).

fof(f12938,plain,
    ( spl0_218
    | ~ spl0_245
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f12903,f6509,f2400,f2110]) ).

fof(f12903,plain,
    ( member(null_class,null_class)
    | ~ spl0_245
    | ~ spl0_404 ),
    inference(resolution,[],[f6510,f2401]) ).

fof(f6510,plain,
    ( subclass(cross_product(universal_class,universal_class),null_class)
    | ~ spl0_404 ),
    inference(avatar_component_clause,[],[f6509]) ).

fof(f12937,plain,
    ( spl0_624
    | ~ spl0_110
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f12312,f1133,f856,f12935]) ).

fof(f12935,plain,
    ( spl0_624
  <=> ! [X0] :
        ( ~ subclass(cross_product(element_relation,universal_class),rotate(X0))
        | rotate(X0) = cross_product(element_relation,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f12312,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(element_relation,universal_class),rotate(X0))
        | rotate(X0) = cross_product(element_relation,universal_class) )
    | ~ spl0_110
    | ~ spl0_134 ),
    inference(superposition,[],[f1134,f858]) ).

fof(f12933,plain,
    ( ~ spl0_623
    | ~ spl0_110
    | spl0_157 ),
    inference(avatar_split_clause,[],[f12316,f1346,f856,f12930]) ).

fof(f12930,plain,
    ( spl0_623
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f1346,plain,
    ( spl0_157
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f12316,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class)))))
    | ~ spl0_110
    | spl0_157 ),
    inference(superposition,[],[f1348,f858]) ).

fof(f1348,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | spl0_157 ),
    inference(avatar_component_clause,[],[f1346]) ).

fof(f12927,plain,
    ( ~ spl0_621
    | spl0_622
    | ~ spl0_54
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12360,f856,f458,f12924,f12920]) ).

fof(f12920,plain,
    ( spl0_621
  <=> operation(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f12924,plain,
    ( spl0_622
  <=> subclass(domain_of(domain_of(flip(element_relation))),domain_of(domain_of(universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f458,plain,
    ( spl0_54
  <=> ! [X8] :
        ( ~ operation(X8)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f12360,plain,
    ( subclass(domain_of(domain_of(flip(element_relation))),domain_of(domain_of(universal_class)))
    | ~ operation(universal_class)
    | ~ spl0_54
    | ~ spl0_110 ),
    inference(superposition,[],[f459,f858]) ).

fof(f459,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f458]) ).

fof(f12918,plain,
    ( spl0_620
    | ~ spl0_110
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f12311,f1098,f856,f12916]) ).

fof(f12916,plain,
    ( spl0_620
  <=> ! [X0,X1] :
        ( ~ subclass(element_relation,compose(X0,X1))
        | element_relation = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f12311,plain,
    ( ! [X0,X1] :
        ( ~ subclass(element_relation,compose(X0,X1))
        | element_relation = compose(X0,X1) )
    | ~ spl0_110
    | ~ spl0_131 ),
    inference(superposition,[],[f1099,f858]) ).

fof(f12901,plain,
    ( ~ spl0_618
    | spl0_619
    | ~ spl0_47
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12357,f856,f408,f12898,f12894]) ).

fof(f12894,plain,
    ( spl0_618
  <=> single_valued_class(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f12898,plain,
    ( spl0_619
  <=> subclass(compose(universal_class,domain_of(flip(element_relation))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f408,plain,
    ( spl0_47
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f12357,plain,
    ( subclass(compose(universal_class,domain_of(flip(element_relation))),identity_relation)
    | ~ single_valued_class(universal_class)
    | ~ spl0_47
    | ~ spl0_110 ),
    inference(superposition,[],[f409,f858]) ).

fof(f409,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f408]) ).

fof(f12881,plain,
    ( spl0_617
    | ~ spl0_110
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f12310,f1003,f856,f12879]) ).

fof(f12879,plain,
    ( spl0_617
  <=> ! [X0] :
        ( ~ subclass(element_relation,X0)
        | element_relation = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f12310,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | element_relation = X0
        | ~ function(X0) )
    | ~ spl0_110
    | ~ spl0_126 ),
    inference(superposition,[],[f1004,f858]) ).

fof(f12706,plain,
    ( spl0_616
    | ~ spl0_46
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12382,f856,f404,f12704]) ).

fof(f12704,plain,
    ( spl0_616
  <=> ! [X0] : intersection(element_relation,X0) = intersection(X0,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f12382,plain,
    ( ! [X0] : intersection(element_relation,X0) = intersection(X0,element_relation)
    | ~ spl0_46
    | ~ spl0_110 ),
    inference(superposition,[],[f405,f858]) ).

fof(f12702,plain,
    ( spl0_615
    | ~ spl0_106
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12307,f856,f821,f12700]) ).

fof(f12700,plain,
    ( spl0_615
  <=> ! [X0] :
        ( ~ subclass(X0,element_relation)
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f12307,plain,
    ( ! [X0] :
        ( ~ subclass(X0,element_relation)
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_106
    | ~ spl0_110 ),
    inference(superposition,[],[f822,f858]) ).

fof(f12608,plain,
    ( ~ spl0_613
    | spl0_614
    | ~ spl0_34
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12355,f856,f317,f12605,f12601]) ).

fof(f12601,plain,
    ( spl0_613
  <=> one_to_one(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f12605,plain,
    ( spl0_614
  <=> function(domain_of(flip(element_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f317,plain,
    ( spl0_34
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f12355,plain,
    ( function(domain_of(flip(element_relation)))
    | ~ one_to_one(universal_class)
    | ~ spl0_34
    | ~ spl0_110 ),
    inference(superposition,[],[f318,f858]) ).

fof(f318,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f317]) ).

fof(f12599,plain,
    ( spl0_612
    | ~ spl0_101
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12306,f856,f754,f12597]) ).

fof(f12306,plain,
    ( ! [X0] :
        ( member(X0,element_relation)
        | ~ member(X0,subset_relation) )
    | ~ spl0_101
    | ~ spl0_110 ),
    inference(superposition,[],[f755,f858]) ).

fof(f12595,plain,
    ( spl0_611
    | ~ spl0_32
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12300,f856,f308,f12593]) ).

fof(f12593,plain,
    ( spl0_611
  <=> ! [X0] : subclass(flip(X0),cross_product(element_relation,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f308,plain,
    ( spl0_32
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f12300,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(element_relation,universal_class))
    | ~ spl0_32
    | ~ spl0_110 ),
    inference(superposition,[],[f309,f858]) ).

fof(f309,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f308]) ).

fof(f12591,plain,
    ( spl0_610
    | ~ spl0_31
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12299,f856,f304,f12589]) ).

fof(f12589,plain,
    ( spl0_610
  <=> ! [X0] : subclass(rotate(X0),cross_product(element_relation,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f304,plain,
    ( spl0_31
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f12299,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(element_relation,universal_class))
    | ~ spl0_31
    | ~ spl0_110 ),
    inference(superposition,[],[f305,f858]) ).

fof(f305,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f12465,plain,
    ( spl0_609
    | ~ spl0_22
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12298,f856,f265,f12463]) ).

fof(f12463,plain,
    ( spl0_609
  <=> ! [X0] :
        ( subclass(X0,element_relation)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f265,plain,
    ( spl0_22
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f12298,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_110 ),
    inference(superposition,[],[f266,f858]) ).

fof(f266,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f12461,plain,
    ( spl0_608
    | ~ spl0_21
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12297,f856,f261,f12459]) ).

fof(f12459,plain,
    ( spl0_608
  <=> ! [X0,X1] : subclass(compose(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f261,plain,
    ( spl0_21
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f12297,plain,
    ( ! [X0,X1] : subclass(compose(X0,X1),element_relation)
    | ~ spl0_21
    | ~ spl0_110 ),
    inference(superposition,[],[f262,f858]) ).

fof(f262,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f12447,plain,
    ( spl0_364
    | ~ spl0_110
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f12317,f1350,f856,f4751]) ).

fof(f12317,plain,
    ( member(null_class,element_relation)
    | ~ spl0_110
    | ~ spl0_158 ),
    inference(superposition,[],[f1351,f858]) ).

fof(f1351,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1350]) ).

fof(f12446,plain,
    ( ~ spl0_607
    | ~ spl0_110
    | spl0_113 ),
    inference(avatar_split_clause,[],[f12309,f869,f856,f12443]) ).

fof(f12443,plain,
    ( spl0_607
  <=> subclass(element_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f12309,plain,
    ( ~ subclass(element_relation,successor_relation)
    | ~ spl0_110
    | spl0_113 ),
    inference(superposition,[],[f871,f858]) ).

fof(f12441,plain,
    ( spl0_606
    | ~ spl0_110
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f12315,f1224,f856,f12438]) ).

fof(f12315,plain,
    ( member(u,element_relation)
    | ~ spl0_110
    | ~ spl0_144 ),
    inference(superposition,[],[f1226,f858]) ).

fof(f12436,plain,
    ( ~ spl0_605
    | ~ spl0_110
    | spl0_112 ),
    inference(avatar_split_clause,[],[f12308,f865,f856,f12433]) ).

fof(f12433,plain,
    ( spl0_605
  <=> element_relation = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f865,plain,
    ( spl0_112
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f12308,plain,
    ( element_relation != successor_relation
    | ~ spl0_110
    | spl0_112 ),
    inference(superposition,[],[f866,f858]) ).

fof(f866,plain,
    ( cross_product(universal_class,universal_class) != successor_relation
    | spl0_112 ),
    inference(avatar_component_clause,[],[f865]) ).

fof(f12431,plain,
    ( spl0_604
    | ~ spl0_13
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f12296,f856,f227,f12428]) ).

fof(f12428,plain,
    ( spl0_604
  <=> subclass(successor_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f227,plain,
    ( spl0_13
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f12296,plain,
    ( subclass(successor_relation,element_relation)
    | ~ spl0_13
    | ~ spl0_110 ),
    inference(superposition,[],[f229,f858]) ).

fof(f229,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f227]) ).

fof(f12426,plain,
    ( ~ spl0_603
    | ~ spl0_110
    | spl0_243 ),
    inference(avatar_split_clause,[],[f12329,f2384,f856,f12423]) ).

fof(f12423,plain,
    ( spl0_603
  <=> member(subset_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f2384,plain,
    ( spl0_243
  <=> member(subset_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f12329,plain,
    ( ~ member(subset_relation,element_relation)
    | ~ spl0_110
    | spl0_243 ),
    inference(superposition,[],[f2385,f858]) ).

fof(f2385,plain,
    ( ~ member(subset_relation,cross_product(universal_class,universal_class))
    | spl0_243 ),
    inference(avatar_component_clause,[],[f2384]) ).

fof(f12109,plain,
    ( spl0_218
    | ~ spl0_158
    | ~ spl0_599 ),
    inference(avatar_split_clause,[],[f11971,f11945,f1350,f2110]) ).

fof(f11945,plain,
    ( spl0_599
  <=> cross_product(universal_class,universal_class) = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f11971,plain,
    ( member(null_class,null_class)
    | ~ spl0_158
    | ~ spl0_599 ),
    inference(superposition,[],[f1351,f11947]) ).

fof(f11947,plain,
    ( cross_product(universal_class,universal_class) = null_class
    | ~ spl0_599 ),
    inference(avatar_component_clause,[],[f11945]) ).

fof(f12108,plain,
    ( ~ spl0_602
    | spl0_113
    | ~ spl0_599 ),
    inference(avatar_split_clause,[],[f11963,f11945,f869,f12105]) ).

fof(f11963,plain,
    ( ~ subclass(null_class,successor_relation)
    | spl0_113
    | ~ spl0_599 ),
    inference(superposition,[],[f871,f11947]) ).

fof(f12103,plain,
    ( ~ spl0_601
    | spl0_112
    | ~ spl0_599 ),
    inference(avatar_split_clause,[],[f11962,f11945,f865,f12100]) ).

fof(f11962,plain,
    ( null_class != successor_relation
    | spl0_112
    | ~ spl0_599 ),
    inference(superposition,[],[f866,f11947]) ).

fof(f12098,plain,
    ( spl0_600
    | ~ spl0_13
    | ~ spl0_599 ),
    inference(avatar_split_clause,[],[f11950,f11945,f227,f12095]) ).

fof(f11950,plain,
    ( subclass(successor_relation,null_class)
    | ~ spl0_13
    | ~ spl0_599 ),
    inference(superposition,[],[f229,f11947]) ).

fof(f11948,plain,
    ( spl0_599
    | ~ spl0_110
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f11941,f4776,f856,f11945]) ).

fof(f11941,plain,
    ( cross_product(universal_class,universal_class) = null_class
    | ~ spl0_110
    | ~ spl0_367 ),
    inference(forward_demodulation,[],[f858,f4778]) ).

fof(f4778,plain,
    ( element_relation = null_class
    | ~ spl0_367 ),
    inference(avatar_component_clause,[],[f4776]) ).

fof(f11942,plain,
    ( spl0_404
    | ~ spl0_111
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f11940,f4776,f860,f6509]) ).

fof(f860,plain,
    ( spl0_111
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f11940,plain,
    ( subclass(cross_product(universal_class,universal_class),null_class)
    | ~ spl0_111
    | ~ spl0_367 ),
    inference(forward_demodulation,[],[f861,f4778]) ).

fof(f861,plain,
    ( subclass(cross_product(universal_class,universal_class),element_relation)
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f860]) ).

fof(f11938,plain,
    ( spl0_598
    | spl0_111
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1574,f1570,f860,f11935]) ).

fof(f1574,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
    | spl0_111
    | ~ spl0_176 ),
    inference(resolution,[],[f1571,f862]) ).

fof(f862,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_111 ),
    inference(avatar_component_clause,[],[f860]) ).

fof(f11773,plain,
    ( spl0_597
    | ~ spl0_367
    | ~ spl0_596 ),
    inference(avatar_split_clause,[],[f11706,f11702,f4776,f11771]) ).

fof(f11771,plain,
    ( spl0_597
  <=> ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(null_class,cross_product(universal_class,X0))),domain_of(intersection(null_class,cross_product(universal_class,X0)))),universal_class))))
        | null_class = cross_product(unordered_pair(domain_of(intersection(null_class,cross_product(universal_class,X0))),domain_of(intersection(null_class,cross_product(universal_class,X0)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f11702,plain,
    ( spl0_596
  <=> ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f11706,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(null_class,cross_product(universal_class,X0))),domain_of(intersection(null_class,cross_product(universal_class,X0)))),universal_class))))
        | null_class = cross_product(unordered_pair(domain_of(intersection(null_class,cross_product(universal_class,X0))),domain_of(intersection(null_class,cross_product(universal_class,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_367
    | ~ spl0_596 ),
    inference(forward_demodulation,[],[f11705,f4778]) ).

fof(f11705,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(null_class,cross_product(universal_class,X0))),domain_of(intersection(null_class,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_367
    | ~ spl0_596 ),
    inference(forward_demodulation,[],[f11703,f4778]) ).

fof(f11703,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_596 ),
    inference(avatar_component_clause,[],[f11702]) ).

fof(f11704,plain,
    ( spl0_596
    | ~ spl0_133
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1163,f1145,f1109,f11702]) ).

fof(f1163,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_133
    | ~ spl0_137 ),
    inference(resolution,[],[f1146,f1110]) ).

fof(f11700,plain,
    ( spl0_595
    | ~ spl0_81
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f779,f746,f629,f11698]) ).

fof(f11698,plain,
    ( spl0_595
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f779,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
    | ~ spl0_81
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f630]) ).

fof(f11696,plain,
    ( spl0_594
    | ~ spl0_80
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f778,f746,f622,f11694]) ).

fof(f11694,plain,
    ( spl0_594
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f778,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
    | ~ spl0_80
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f623]) ).

fof(f11689,plain,
    ( spl0_593
    | ~ spl0_69
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1553,f1545,f549,f11687]) ).

fof(f11687,plain,
    ( spl0_593
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),successor_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f549,plain,
    ( spl0_69
  <=> ! [X0,X1] :
        ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f1553,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),successor_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) )
    | ~ spl0_69
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f550]) ).

fof(f550,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f549]) ).

fof(f11646,plain,
    ( spl0_592
    | ~ spl0_367
    | ~ spl0_591 ),
    inference(avatar_split_clause,[],[f11642,f11638,f4776,f11644]) ).

fof(f11644,plain,
    ( spl0_592
  <=> ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f11638,plain,
    ( spl0_591
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f11642,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | null_class = X0 )
    | ~ spl0_367
    | ~ spl0_591 ),
    inference(forward_demodulation,[],[f11641,f4778]) ).

fof(f11641,plain,
    ( ! [X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 )
    | ~ spl0_367
    | ~ spl0_591 ),
    inference(forward_demodulation,[],[f11639,f4778]) ).

fof(f11639,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | null_class = X0 )
    | ~ spl0_591 ),
    inference(avatar_component_clause,[],[f11638]) ).

fof(f11640,plain,
    ( spl0_591
    | ~ spl0_128
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1328,f1284,f1052,f11638]) ).

fof(f1328,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 )
    | ~ spl0_128
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f1053]) ).

fof(f11628,plain,
    ( spl0_590
    | ~ spl0_20
    | ~ spl0_500 ),
    inference(avatar_split_clause,[],[f10159,f9870,f257,f11626]) ).

fof(f10159,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,subset_relation) )
    | ~ spl0_20
    | ~ spl0_500 ),
    inference(superposition,[],[f258,f9872]) ).

fof(f11624,plain,
    ( spl0_589
    | ~ spl0_121
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1539,f1512,f933,f11622]) ).

fof(f11622,plain,
    ( spl0_589
  <=> ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f933,plain,
    ( spl0_121
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f1539,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_121
    | ~ spl0_173 ),
    inference(superposition,[],[f934,f1513]) ).

fof(f934,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f933]) ).

fof(f11620,plain,
    ( spl0_588
    | ~ spl0_69
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1524,f1512,f549,f11618]) ).

fof(f11618,plain,
    ( spl0_588
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),successor_relation)
        | second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f1524,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),successor_relation)
        | second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_69
    | ~ spl0_173 ),
    inference(superposition,[],[f550,f1513]) ).

fof(f11559,plain,
    ( spl0_587
    | ~ spl0_367
    | ~ spl0_586 ),
    inference(avatar_split_clause,[],[f11555,f11552,f4776,f11557]) ).

fof(f11557,plain,
    ( spl0_587
  <=> ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f11552,plain,
    ( spl0_586
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f11555,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class) )
    | ~ spl0_367
    | ~ spl0_586 ),
    inference(forward_demodulation,[],[f11553,f4778]) ).

fof(f11553,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_586 ),
    inference(avatar_component_clause,[],[f11552]) ).

fof(f11554,plain,
    ( spl0_586
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1493,f1465,f257,f11552]) ).

fof(f1493,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f258]) ).

fof(f11492,plain,
    ( spl0_585
    | ~ spl0_367
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f11488,f11485,f4776,f11490]) ).

fof(f11490,plain,
    ( spl0_585
  <=> ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1)
        | null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f11485,plain,
    ( spl0_584
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f11488,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1)
        | null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class) )
    | ~ spl0_367
    | ~ spl0_584 ),
    inference(forward_demodulation,[],[f11486,f4778]) ).

fof(f11486,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1)
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_584 ),
    inference(avatar_component_clause,[],[f11485]) ).

fof(f11487,plain,
    ( spl0_584
    | ~ spl0_20
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1475,f1461,f257,f11485]) ).

fof(f1475,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_20
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f258]) ).

fof(f11427,plain,
    ( spl0_583
    | ~ spl0_20
    | ~ spl0_494 ),
    inference(avatar_split_clause,[],[f10084,f9712,f257,f11425]) ).

fof(f11425,plain,
    ( spl0_583
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f9712,plain,
    ( spl0_494
  <=> null_class = complement(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f10084,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,identity_relation) )
    | ~ spl0_20
    | ~ spl0_494 ),
    inference(superposition,[],[f258,f9714]) ).

fof(f9714,plain,
    ( null_class = complement(identity_relation)
    | ~ spl0_494 ),
    inference(avatar_component_clause,[],[f9712]) ).

fof(f11420,plain,
    ( spl0_582
    | ~ spl0_367
    | ~ spl0_581 ),
    inference(avatar_split_clause,[],[f11416,f11413,f4776,f11418]) ).

fof(f11418,plain,
    ( spl0_582
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),null_class)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f11413,plain,
    ( spl0_581
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f11416,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),null_class)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_367
    | ~ spl0_581 ),
    inference(forward_demodulation,[],[f11414,f4778]) ).

fof(f11414,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_581 ),
    inference(avatar_component_clause,[],[f11413]) ).

fof(f11415,plain,
    ( spl0_581
    | ~ spl0_153
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1532,f1512,f1296,f11413]) ).

fof(f1532,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_153
    | ~ spl0_173 ),
    inference(superposition,[],[f1297,f1513]) ).

fof(f11361,plain,
    ( spl0_580
    | ~ spl0_367
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f11357,f11354,f4776,f11359]) ).

fof(f11359,plain,
    ( spl0_580
  <=> ! [X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f11354,plain,
    ( spl0_579
  <=> ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f11357,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | null_class = X1 )
    | ~ spl0_367
    | ~ spl0_579 ),
    inference(forward_demodulation,[],[f11355,f4778]) ).

fof(f11355,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | ~ member(intersection(null_class,X0),universal_class)
        | null_class = intersection(null_class,X0)
        | null_class = X1 )
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f11354]) ).

fof(f11356,plain,
    ( spl0_579
    | ~ spl0_105
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1494,f1465,f817,f11354]) ).

fof(f817,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f1494,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_105
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f818]) ).

fof(f818,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f817]) ).

fof(f11293,plain,
    ( spl0_578
    | ~ spl0_367
    | ~ spl0_577 ),
    inference(avatar_split_clause,[],[f11289,f11286,f4776,f11291]) ).

fof(f11291,plain,
    ( spl0_578
  <=> ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f11286,plain,
    ( spl0_577
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f11289,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2) )
    | ~ spl0_367
    | ~ spl0_577 ),
    inference(forward_demodulation,[],[f11287,f4778]) ).

fof(f11287,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_577 ),
    inference(avatar_component_clause,[],[f11286]) ).

fof(f11288,plain,
    ( spl0_577
    | ~ spl0_37
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1486,f1465,f339,f11286]) ).

fof(f1486,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
    | ~ spl0_37
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f340]) ).

fof(f11232,plain,
    ( spl0_576
    | ~ spl0_20
    | ~ spl0_490 ),
    inference(avatar_split_clause,[],[f9948,f9426,f257,f11230]) ).

fof(f9426,plain,
    ( spl0_490
  <=> null_class = complement(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f9948,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,successor_relation) )
    | ~ spl0_20
    | ~ spl0_490 ),
    inference(superposition,[],[f258,f9428]) ).

fof(f9428,plain,
    ( null_class = complement(successor_relation)
    | ~ spl0_490 ),
    inference(avatar_component_clause,[],[f9426]) ).

fof(f11228,plain,
    ( spl0_575
    | ~ spl0_367
    | ~ spl0_574 ),
    inference(avatar_split_clause,[],[f11224,f11221,f4776,f11226]) ).

fof(f11226,plain,
    ( spl0_575
  <=> ! [X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f11221,plain,
    ( spl0_574
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f11224,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | null_class = X1 )
    | ~ spl0_367
    | ~ spl0_574 ),
    inference(forward_demodulation,[],[f11222,f4778]) ).

fof(f11222,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | ~ member(intersection(X0,null_class),universal_class)
        | null_class = intersection(X0,null_class)
        | null_class = X1 )
    | ~ spl0_574 ),
    inference(avatar_component_clause,[],[f11221]) ).

fof(f11223,plain,
    ( spl0_574
    | ~ spl0_105
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1476,f1461,f817,f11221]) ).

fof(f1476,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_105
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f818]) ).

fof(f11160,plain,
    ( spl0_573
    | ~ spl0_367
    | ~ spl0_572 ),
    inference(avatar_split_clause,[],[f11156,f11153,f4776,f11158]) ).

fof(f11158,plain,
    ( spl0_573
  <=> ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f11153,plain,
    ( spl0_572
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f11156,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2) )
    | ~ spl0_367
    | ~ spl0_572 ),
    inference(forward_demodulation,[],[f11154,f4778]) ).

fof(f11154,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_572 ),
    inference(avatar_component_clause,[],[f11153]) ).

fof(f11155,plain,
    ( spl0_572
    | ~ spl0_37
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1468,f1461,f339,f11153]) ).

fof(f1468,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
    | ~ spl0_37
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f340]) ).

fof(f11139,plain,
    ( spl0_571
    | ~ spl0_367
    | ~ spl0_570 ),
    inference(avatar_split_clause,[],[f11135,f11132,f4776,f11137]) ).

fof(f11137,plain,
    ( spl0_571
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f11132,plain,
    ( spl0_570
  <=> ! [X0] :
        ( null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f11135,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | null_class = X0 )
    | ~ spl0_367
    | ~ spl0_570 ),
    inference(forward_demodulation,[],[f11133,f4778]) ).

fof(f11133,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | ~ member(complement(regular(X0)),universal_class)
        | null_class = complement(regular(X0))
        | null_class = X0 )
    | ~ spl0_570 ),
    inference(avatar_component_clause,[],[f11132]) ).

fof(f11134,plain,
    ( spl0_570
    | ~ spl0_114
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1456,f1443,f874,f11132]) ).

fof(f1456,plain,
    ( ! [X0] :
        ( null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = X0 )
    | ~ spl0_114
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f875]) ).

fof(f11130,plain,
    ( ~ spl0_504
    | spl0_569
    | ~ spl0_133
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1386,f1368,f1109,f11128,f9918]) ).

fof(f11128,plain,
    ( spl0_569
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation)
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f1386,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class) )
    | ~ spl0_133
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f1110]) ).

fof(f11091,plain,
    ( spl0_568
    | ~ spl0_367
    | ~ spl0_567 ),
    inference(avatar_split_clause,[],[f11087,f11083,f4776,f11089]) ).

fof(f11089,plain,
    ( spl0_568
  <=> ! [X2,X0,X1] :
        ( complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))) = X1
        | complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f11083,plain,
    ( spl0_567
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f11087,plain,
    ( ! [X2,X0,X1] :
        ( complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))) = X1
        | complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class) )
    | ~ spl0_367
    | ~ spl0_567 ),
    inference(forward_demodulation,[],[f11086,f4778]) ).

fof(f11086,plain,
    ( ! [X2,X0,X1] :
        ( complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
    | ~ spl0_367
    | ~ spl0_567 ),
    inference(forward_demodulation,[],[f11084,f4778]) ).

fof(f11084,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
    | ~ spl0_567 ),
    inference(avatar_component_clause,[],[f11083]) ).

fof(f11085,plain,
    ( spl0_567
    | ~ spl0_44
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1317,f1284,f396,f11083]) ).

fof(f1317,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
    | ~ spl0_44
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f397]) ).

fof(f11081,plain,
    ( spl0_566
    | ~ spl0_128
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1311,f1280,f1052,f11079]) ).

fof(f11079,plain,
    ( spl0_566
  <=> ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f1311,plain,
    ( ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | null_class = X1 )
    | ~ spl0_128
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f1053]) ).

fof(f11077,plain,
    ( spl0_565
    | ~ spl0_71
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f978,f929,f558,f11075]) ).

fof(f11075,plain,
    ( spl0_565
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f978,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) )
    | ~ spl0_71
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f559]) ).

fof(f11061,plain,
    ( spl0_564
    | ~ spl0_329
    | ~ spl0_563 ),
    inference(avatar_split_clause,[],[f11057,f11054,f3612,f11059]) ).

fof(f11059,plain,
    ( spl0_564
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f11057,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_329
    | ~ spl0_563 ),
    inference(forward_demodulation,[],[f11055,f3614]) ).

fof(f11056,plain,
    ( spl0_563
    | ~ spl0_96
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1790,f1761,f728,f11054]) ).

fof(f1790,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_96
    | ~ spl0_189 ),
    inference(resolution,[],[f1762,f729]) ).

fof(f11041,plain,
    ( spl0_562
    | ~ spl0_329
    | ~ spl0_561 ),
    inference(avatar_split_clause,[],[f11037,f11034,f3612,f11039]) ).

fof(f11039,plain,
    ( spl0_562
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f11037,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_329
    | ~ spl0_561 ),
    inference(forward_demodulation,[],[f11035,f3614]) ).

fof(f11036,plain,
    ( spl0_561
    | ~ spl0_96
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1772,f1757,f728,f11034]) ).

fof(f1772,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_96
    | ~ spl0_188 ),
    inference(resolution,[],[f1758,f729]) ).

fof(f11032,plain,
    ( spl0_560
    | ~ spl0_4
    | ~ spl0_542 ),
    inference(avatar_split_clause,[],[f10887,f10575,f187,f11029]) ).

fof(f187,plain,
    ( spl0_4
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f10575,plain,
    ( spl0_542
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f10887,plain,
    ( null_class = complement(omega)
    | ~ spl0_4
    | ~ spl0_542 ),
    inference(resolution,[],[f10576,f189]) ).

fof(f189,plain,
    ( inductive(omega)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f10576,plain,
    ( ! [X0] :
        ( ~ inductive(X0)
        | complement(X0) = null_class )
    | ~ spl0_542 ),
    inference(avatar_component_clause,[],[f10575]) ).

fof(f10927,plain,
    ( spl0_559
    | ~ spl0_27
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1534,f1512,f288,f10925]) ).

fof(f10925,plain,
    ( spl0_559
  <=> ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f1534,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_27
    | ~ spl0_173 ),
    inference(superposition,[],[f289,f1513]) ).

fof(f10923,plain,
    ( spl0_558
    | ~ spl0_44
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1300,f1280,f396,f10921]) ).

fof(f10921,plain,
    ( spl0_558
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,unordered_pair(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f1300,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,unordered_pair(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 )
    | ~ spl0_44
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f397]) ).

fof(f10919,plain,
    ( spl0_557
    | ~ spl0_45
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1247,f1216,f400,f10917]) ).

fof(f10917,plain,
    ( spl0_557
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
        | subclass(X0,intersection(X1,intersection(X2,X3)))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f1247,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
        | subclass(X0,intersection(X1,intersection(X2,X3)))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) )
    | ~ spl0_45
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f401]) ).

fof(f10906,plain,
    ( spl0_556
    | ~ spl0_367
    | ~ spl0_555 ),
    inference(avatar_split_clause,[],[f10902,f10898,f4776,f10904]) ).

fof(f10902,plain,
    ( ! [X0] :
        ( subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0)
        | ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation) )
    | ~ spl0_367
    | ~ spl0_555 ),
    inference(forward_demodulation,[],[f10901,f4778]) ).

fof(f10901,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_367
    | ~ spl0_555 ),
    inference(forward_demodulation,[],[f10899,f4778]) ).

fof(f10900,plain,
    ( spl0_555
    | ~ spl0_107
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1209,f1202,f844,f10898]) ).

fof(f844,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f1209,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_107
    | ~ spl0_140 ),
    inference(resolution,[],[f1203,f845]) ).

fof(f845,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f844]) ).

fof(f10886,plain,
    ( spl0_554
    | ~ spl0_367
    | ~ spl0_553 ),
    inference(avatar_split_clause,[],[f10882,f10879,f4776,f10884]) ).

fof(f10884,plain,
    ( spl0_554
  <=> ! [X0] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f10879,plain,
    ( spl0_553
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f10882,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class) )
    | ~ spl0_367
    | ~ spl0_553 ),
    inference(forward_demodulation,[],[f10880,f4778]) ).

fof(f10880,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_553 ),
    inference(avatar_component_clause,[],[f10879]) ).

fof(f10881,plain,
    ( spl0_553
    | ~ spl0_92
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1497,f1465,f686,f10879]) ).

fof(f1497,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_92
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f687]) ).

fof(f10867,plain,
    ( spl0_552
    | ~ spl0_367
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f10863,f10860,f4776,f10865]) ).

fof(f10865,plain,
    ( spl0_552
  <=> ! [X0] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation)
        | null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f10860,plain,
    ( spl0_551
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f10863,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation)
        | null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class) )
    | ~ spl0_367
    | ~ spl0_551 ),
    inference(forward_demodulation,[],[f10861,f4778]) ).

fof(f10861,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | null_class = intersection(X0,identity_relation) )
    | ~ spl0_551 ),
    inference(avatar_component_clause,[],[f10860]) ).

fof(f10862,plain,
    ( spl0_551
    | ~ spl0_92
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1479,f1461,f686,f10860]) ).

fof(f1479,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_92
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f687]) ).

fof(f10822,plain,
    ( ~ spl0_550
    | ~ spl0_367
    | spl0_548 ),
    inference(avatar_split_clause,[],[f10810,f10806,f4776,f10819]) ).

fof(f10810,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))),subset_relation)
    | ~ spl0_367
    | spl0_548 ),
    inference(forward_demodulation,[],[f10808,f4778]) ).

fof(f10817,plain,
    ( ~ spl0_549
    | ~ spl0_367
    | spl0_547 ),
    inference(avatar_split_clause,[],[f10811,f10802,f4776,f10814]) ).

fof(f10811,plain,
    ( null_class != complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_367
    | spl0_547 ),
    inference(forward_demodulation,[],[f10803,f4778]) ).

fof(f10812,plain,
    ( spl0_297
    | ~ spl0_158
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9212,f9161,f1350,f3255]) ).

fof(f9212,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ spl0_158
    | ~ spl0_475 ),
    inference(resolution,[],[f9162,f1351]) ).

fof(f10809,plain,
    ( spl0_547
    | ~ spl0_548
    | ~ spl0_104
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1210,f1202,f813,f10806,f10802]) ).

fof(f813,plain,
    ( spl0_104
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f1210,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_104
    | ~ spl0_140 ),
    inference(resolution,[],[f1203,f814]) ).

fof(f814,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f813]) ).

fof(f10732,plain,
    ( spl0_545
    | spl0_546
    | ~ spl0_71
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f784,f746,f558,f10730,f10727]) ).

fof(f10727,plain,
    ( spl0_545
  <=> ! [X2,X3] : unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f784,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) )
    | ~ spl0_71
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f559]) ).

fof(f10691,plain,
    ( spl0_544
    | ~ spl0_367
    | ~ spl0_543 ),
    inference(avatar_split_clause,[],[f10687,f10683,f4776,f10689]) ).

fof(f10687,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation) )
    | ~ spl0_367
    | ~ spl0_543 ),
    inference(forward_demodulation,[],[f10686,f4778]) ).

fof(f10686,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_367
    | ~ spl0_543 ),
    inference(forward_demodulation,[],[f10684,f4778]) ).

fof(f10685,plain,
    ( spl0_543
    | ~ spl0_26
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1208,f1202,f284,f10683]) ).

fof(f284,plain,
    ( spl0_26
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1208,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_26
    | ~ spl0_140 ),
    inference(resolution,[],[f1203,f285]) ).

fof(f285,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f284]) ).

fof(f10577,plain,
    ( spl0_542
    | ~ spl0_14
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9206,f9161,f232,f10575]) ).

fof(f9206,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ inductive(X0) )
    | ~ spl0_14
    | ~ spl0_475 ),
    inference(resolution,[],[f9162,f233]) ).

fof(f10573,plain,
    ( spl0_541
    | ~ spl0_370
    | ~ spl0_417
    | ~ spl0_540 ),
    inference(avatar_split_clause,[],[f10569,f10566,f6780,f4795,f10571]) ).

fof(f10566,plain,
    ( spl0_540
  <=> ! [X0,X1] :
        ( ~ member(null_class,compose(X0,X1))
        | member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f10569,plain,
    ( ! [X0,X1] :
        ( member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(u,universal_class),X1),universal_class)))),universal_class),X0),universal_class)))))
        | ~ member(null_class,compose(X0,X1)) )
    | ~ spl0_370
    | ~ spl0_417
    | ~ spl0_540 ),
    inference(forward_demodulation,[],[f10567,f6978]) ).

fof(f10567,plain,
    ( ! [X0,X1] :
        ( member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X1),universal_class)))),universal_class),X0),universal_class)))))
        | ~ member(null_class,compose(X0,X1)) )
    | ~ spl0_540 ),
    inference(avatar_component_clause,[],[f10566]) ).

fof(f10568,plain,
    ( spl0_540
    | ~ spl0_76
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4717,f1291,f591,f10566]) ).

fof(f4717,plain,
    ( ! [X0,X1] :
        ( ~ member(null_class,compose(X0,X1))
        | member(second(null_class),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(null_class),first(null_class)),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_76
    | ~ spl0_152 ),
    inference(superposition,[],[f592,f1293]) ).

fof(f10563,plain,
    ( spl0_539
    | ~ spl0_105
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1436,f1425,f817,f10561]) ).

fof(f10561,plain,
    ( spl0_539
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,null_class)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f1436,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,null_class)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_105
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f818]) ).

fof(f10476,plain,
    ( spl0_538
    | ~ spl0_367
    | ~ spl0_537 ),
    inference(avatar_split_clause,[],[f10472,f10469,f4776,f10474]) ).

fof(f10474,plain,
    ( spl0_538
  <=> ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2)
        | null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f10469,plain,
    ( spl0_537
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f10472,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2)
        | null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2) )
    | ~ spl0_367
    | ~ spl0_537 ),
    inference(forward_demodulation,[],[f10470,f4778]) ).

fof(f10470,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_537 ),
    inference(avatar_component_clause,[],[f10469]) ).

fof(f10471,plain,
    ( spl0_537
    | ~ spl0_37
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1428,f1425,f339,f10469]) ).

fof(f1428,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_37
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f340]) ).

fof(f10467,plain,
    ( spl0_536
    | ~ spl0_115
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1252,f1216,f878,f10465]) ).

fof(f10465,plain,
    ( spl0_536
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1252,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
    | ~ spl0_115
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f879]) ).

fof(f10463,plain,
    ( spl0_535
    | ~ spl0_125
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1091,f1056,f999,f10461]) ).

fof(f10461,plain,
    ( spl0_535
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
        | member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
        | subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1091,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
        | member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
        | subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) )
    | ~ spl0_125
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f1000]) ).

fof(f10459,plain,
    ( spl0_534
    | ~ spl0_124
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1084,f1056,f995,f10457]) ).

fof(f10457,plain,
    ( spl0_534
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
        | member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
        | subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f1084,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
        | member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
        | subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) )
    | ~ spl0_124
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f996]) ).

fof(f10369,plain,
    ( spl0_533
    | ~ spl0_367
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f10365,f10362,f4776,f10367]) ).

fof(f10367,plain,
    ( spl0_533
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),null_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f10362,plain,
    ( spl0_532
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f10365,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),null_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_367
    | ~ spl0_532 ),
    inference(forward_demodulation,[],[f10363,f4778]) ).

fof(f10363,plain,
    ( ! [X0,X1] :
        ( ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_532 ),
    inference(avatar_component_clause,[],[f10362]) ).

fof(f10364,plain,
    ( spl0_532
    | ~ spl0_75
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1525,f1512,f585,f10362]) ).

fof(f1525,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_75
    | ~ spl0_173 ),
    inference(superposition,[],[f586,f1513]) ).

fof(f10344,plain,
    ( spl0_531
    | ~ spl0_367
    | ~ spl0_530 ),
    inference(avatar_split_clause,[],[f10340,f10337,f4776,f10342]) ).

fof(f10342,plain,
    ( spl0_531
  <=> ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f10337,plain,
    ( spl0_530
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f10340,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class) )
    | ~ spl0_367
    | ~ spl0_530 ),
    inference(forward_demodulation,[],[f10338,f4778]) ).

fof(f10338,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_530 ),
    inference(avatar_component_clause,[],[f10337]) ).

fof(f10339,plain,
    ( spl0_530
    | ~ spl0_29
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1432,f1425,f296,f10337]) ).

fof(f1432,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_29
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f297]) ).

fof(f10318,plain,
    ( spl0_529
    | ~ spl0_367
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f10314,f10311,f4776,f10316]) ).

fof(f10316,plain,
    ( spl0_529
  <=> ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2)
        | null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f10311,plain,
    ( spl0_528
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f10314,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2)
        | null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class) )
    | ~ spl0_367
    | ~ spl0_528 ),
    inference(forward_demodulation,[],[f10312,f4778]) ).

fof(f10312,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_528 ),
    inference(avatar_component_clause,[],[f10311]) ).

fof(f10313,plain,
    ( spl0_528
    | ~ spl0_30
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1431,f1425,f300,f10311]) ).

fof(f1431,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_30
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f301]) ).

fof(f10309,plain,
    ( spl0_527
    | ~ spl0_251
    | ~ spl0_329
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9234,f9161,f3612,f2509,f10306]) ).

fof(f9234,plain,
    ( null_class = complement(complement(null_class))
    | ~ spl0_251
    | ~ spl0_329
    | ~ spl0_475 ),
    inference(forward_demodulation,[],[f9220,f3614]) ).

fof(f10295,plain,
    ( spl0_526
    | ~ spl0_367
    | ~ spl0_525 ),
    inference(avatar_split_clause,[],[f10291,f10288,f4776,f10293]) ).

fof(f10293,plain,
    ( spl0_526
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f10291,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | subclass(X0,X1) )
    | ~ spl0_367
    | ~ spl0_525 ),
    inference(forward_demodulation,[],[f10289,f4778]) ).

fof(f10290,plain,
    ( spl0_525
    | ~ spl0_120
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1390,f1368,f929,f10288]) ).

fof(f1390,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,X1) )
    | ~ spl0_120
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f930]) ).

fof(f10286,plain,
    ( spl0_524
    | ~ spl0_41
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1250,f1216,f379,f10284]) ).

fof(f10284,plain,
    ( spl0_524
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
        | subclass(X0,intersection(X1,complement(X2)))
        | member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f1250,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
        | subclass(X0,intersection(X1,complement(X2)))
        | member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) )
    | ~ spl0_41
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f380]) ).

fof(f10282,plain,
    ( spl0_523
    | ~ spl0_71
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f901,f848,f558,f10280]) ).

fof(f10280,plain,
    ( spl0_523
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | null_class = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f901,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | null_class = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) )
    | ~ spl0_71
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f559]) ).

fof(f10189,plain,
    ( spl0_522
    | ~ spl0_367
    | ~ spl0_521 ),
    inference(avatar_split_clause,[],[f10158,f10155,f4776,f10187]) ).

fof(f10187,plain,
    ( spl0_522
  <=> ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f10155,plain,
    ( spl0_521
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f10158,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_367
    | ~ spl0_521 ),
    inference(forward_demodulation,[],[f10156,f4778]) ).

fof(f10156,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | null_class = X0 )
    | ~ spl0_521 ),
    inference(avatar_component_clause,[],[f10155]) ).

fof(f10157,plain,
    ( spl0_521
    | ~ spl0_20
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1435,f1425,f257,f10155]) ).

fof(f1435,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_20
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f258]) ).

fof(f10153,plain,
    ( spl0_520
    | ~ spl0_119
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1090,f1056,f925,f10151]) ).

fof(f10151,plain,
    ( spl0_520
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
        | member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f1090,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
        | member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_119
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f926]) ).

fof(f10149,plain,
    ( spl0_519
    | ~ spl0_118
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1088,f1056,f921,f10147]) ).

fof(f10147,plain,
    ( spl0_519
  <=> ! [X0] :
        ( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
        | member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f1088,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
        | member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_118
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f922]) ).

fof(f10145,plain,
    ( spl0_518
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f893,f844,f500,f404,f10143]) ).

fof(f10143,plain,
    ( spl0_518
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
        | subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f893,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
        | subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) )
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_107 ),
    inference(forward_demodulation,[],[f889,f405]) ).

fof(f889,plain,
    ( ! [X0,X1] :
        ( subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class),X0) )
    | ~ spl0_63
    | ~ spl0_107 ),
    inference(resolution,[],[f845,f501]) ).

fof(f10139,plain,
    ( spl0_517
    | ~ spl0_329
    | ~ spl0_367
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f10135,f10129,f4776,f3612,f10137]) ).

fof(f10135,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | null_class = intersection(intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_329
    | ~ spl0_367
    | ~ spl0_516 ),
    inference(forward_demodulation,[],[f10134,f4778]) ).

fof(f10131,plain,
    ( spl0_516
    | ~ spl0_93
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1491,f1465,f701,f10129]) ).

fof(f1491,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)
        | ~ member(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_93
    | ~ spl0_171 ),
    inference(resolution,[],[f1466,f702]) ).

fof(f10124,plain,
    ( spl0_515
    | ~ spl0_329
    | ~ spl0_367
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f10120,f10114,f4776,f3612,f10122]) ).

fof(f10120,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class)
        | ~ member(intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | null_class = intersection(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_329
    | ~ spl0_367
    | ~ spl0_514 ),
    inference(forward_demodulation,[],[f10119,f4778]) ).

fof(f10116,plain,
    ( spl0_514
    | ~ spl0_93
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1473,f1461,f701,f10114]) ).

fof(f1473,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_93
    | ~ spl0_170 ),
    inference(resolution,[],[f1462,f702]) ).

fof(f10024,plain,
    ( spl0_513
    | ~ spl0_367
    | ~ spl0_512 ),
    inference(avatar_split_clause,[],[f10020,f10017,f4776,f10022]) ).

fof(f10022,plain,
    ( spl0_513
  <=> ! [X0] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f10017,plain,
    ( spl0_512
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f10020,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_367
    | ~ spl0_512 ),
    inference(forward_demodulation,[],[f10018,f4778]) ).

fof(f10018,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | null_class = X0 )
    | ~ spl0_512 ),
    inference(avatar_component_clause,[],[f10017]) ).

fof(f10019,plain,
    ( spl0_512
    | ~ spl0_92
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1440,f1425,f686,f10017]) ).

fof(f1440,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_92
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f687]) ).

fof(f10006,plain,
    ( spl0_511
    | ~ spl0_367
    | ~ spl0_510 ),
    inference(avatar_split_clause,[],[f10002,f9999,f4776,f10004]) ).

fof(f10004,plain,
    ( spl0_511
  <=> ! [X0] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f10002,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | null_class = X0 )
    | ~ spl0_367
    | ~ spl0_510 ),
    inference(forward_demodulation,[],[f10000,f4778]) ).

fof(f10001,plain,
    ( spl0_510
    | ~ spl0_108
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1387,f1368,f848,f9999]) ).

fof(f1387,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 )
    | ~ spl0_108
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f849]) ).

fof(f9997,plain,
    ( spl0_509
    | ~ spl0_76
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f776,f746,f591,f9995]) ).

fof(f9995,plain,
    ( spl0_509
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f776,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_76
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f592]) ).

fof(f9938,plain,
    ( spl0_508
    | ~ spl0_68
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1523,f1512,f538,f9936]) ).

fof(f9936,plain,
    ( spl0_508
  <=> ! [X0,X3,X2,X1] :
        ( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),X3)
        | ~ member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f1523,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),X3)
        | ~ member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_68
    | ~ spl0_173 ),
    inference(superposition,[],[f539,f1513]) ).

fof(f9934,plain,
    ( spl0_507
    | ~ spl0_133
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1447,f1443,f1109,f9932]) ).

fof(f9932,plain,
    ( spl0_507
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(complement(X0),universal_class)
        | ~ subclass(universal_class,X0)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f1447,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(complement(X0),universal_class)
        | ~ subclass(universal_class,X0)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_133
    | ~ spl0_169 ),
    inference(resolution,[],[f1444,f1110]) ).

fof(f9930,plain,
    ( ~ spl0_506
    | ~ spl0_367
    | spl0_504 ),
    inference(avatar_split_clause,[],[f9925,f9918,f4776,f9927]) ).

fof(f9925,plain,
    ( ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_367
    | spl0_504 ),
    inference(forward_demodulation,[],[f9920,f4778]) ).

fof(f9924,plain,
    ( ~ spl0_504
    | spl0_505
    | ~ spl0_99
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1389,f1368,f746,f9922,f9918]) ).

fof(f9922,plain,
    ( spl0_505
  <=> ! [X0,X1] :
        ( member(unordered_pair(X0,X1),subset_relation)
        | ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f1389,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(X0,X1),subset_relation)
        | ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_99
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f747]) ).

fof(f9886,plain,
    ( spl0_503
    | ~ spl0_367
    | ~ spl0_502 ),
    inference(avatar_split_clause,[],[f9882,f9879,f4776,f9884]) ).

fof(f9884,plain,
    ( spl0_503
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f9882,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) )
    | ~ spl0_367
    | ~ spl0_502 ),
    inference(forward_demodulation,[],[f9880,f4778]) ).

fof(f9881,plain,
    ( spl0_502
    | ~ spl0_67
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1258,f1216,f533,f9879]) ).

fof(f1258,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) )
    | ~ spl0_67
    | ~ spl0_142 ),
    inference(superposition,[],[f1217,f535]) ).

fof(f9877,plain,
    ( spl0_501
    | ~ spl0_120
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1165,f1145,f929,f9875]) ).

fof(f9875,plain,
    ( spl0_501
  <=> ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f1165,plain,
    ( ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_120
    | ~ spl0_137 ),
    inference(resolution,[],[f1146,f930]) ).

fof(f9873,plain,
    ( spl0_500
    | ~ spl0_200
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9232,f9161,f1896,f9870]) ).

fof(f9232,plain,
    ( null_class = complement(subset_relation)
    | ~ spl0_200
    | ~ spl0_475 ),
    inference(resolution,[],[f9162,f1897]) ).

fof(f1897,plain,
    ( member(null_class,subset_relation)
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f1896]) ).

fof(f9839,plain,
    ( spl0_499
    | ~ spl0_329
    | ~ spl0_498 ),
    inference(avatar_split_clause,[],[f9835,f9829,f3612,f9837]) ).

fof(f9837,plain,
    ( spl0_499
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | subclass(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f9829,plain,
    ( spl0_498
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1)
        | subclass(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f9835,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | subclass(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1) )
    | ~ spl0_329
    | ~ spl0_498 ),
    inference(forward_demodulation,[],[f9834,f3614]) ).

fof(f9834,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | subclass(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class) )
    | ~ spl0_329
    | ~ spl0_498 ),
    inference(forward_demodulation,[],[f9833,f3614]) ).

fof(f9833,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1)
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class) )
    | ~ spl0_329
    | ~ spl0_498 ),
    inference(forward_demodulation,[],[f9832,f3614]) ).

fof(f9832,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1)
        | subclass(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class) )
    | ~ spl0_329
    | ~ spl0_498 ),
    inference(forward_demodulation,[],[f9830,f3614]) ).

fof(f9830,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class)
        | subclass(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1) )
    | ~ spl0_498 ),
    inference(avatar_component_clause,[],[f9829]) ).

fof(f9831,plain,
    ( spl0_498
    | ~ spl0_96
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1248,f1216,f728,f9829]) ).

fof(f1248,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),X1)
        | subclass(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))
        | member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),universal_class) )
    | ~ spl0_96
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f729]) ).

fof(f9819,plain,
    ( spl0_497
    | ~ spl0_106
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1241,f1212,f821,f9817]) ).

fof(f9817,plain,
    ( spl0_497
  <=> ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
        | not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
        | function(unordered_pair(X0,X1))
        | ~ single_valued_class(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f1241,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
        | not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
        | function(unordered_pair(X0,X1))
        | ~ single_valued_class(unordered_pair(X0,X1)) )
    | ~ spl0_106
    | ~ spl0_141 ),
    inference(resolution,[],[f1213,f822]) ).

fof(f9786,plain,
    ( spl0_496
    | ~ spl0_367
    | ~ spl0_495 ),
    inference(avatar_split_clause,[],[f9782,f9778,f4776,f9784]) ).

fof(f9784,plain,
    ( spl0_496
  <=> ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,X1))),X0)
        | member(domain_of(intersection(null_class,cross_product(universal_class,X1))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f9778,plain,
    ( spl0_495
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f9782,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,X1))),X0)
        | member(domain_of(intersection(null_class,cross_product(universal_class,X1))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | null_class = X0 )
    | ~ spl0_367
    | ~ spl0_495 ),
    inference(forward_demodulation,[],[f9781,f4778]) ).

fof(f9781,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,X1))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 )
    | ~ spl0_367
    | ~ spl0_495 ),
    inference(forward_demodulation,[],[f9779,f4778]) ).

fof(f9779,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ subclass(universal_class,regular(X0))
        | null_class = X0 )
    | ~ spl0_495 ),
    inference(avatar_component_clause,[],[f9778]) ).

fof(f9780,plain,
    ( spl0_495
    | ~ spl0_128
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1131,f1109,f1052,f9778]) ).

fof(f1131,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 )
    | ~ spl0_128
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f1053]) ).

fof(f9715,plain,
    ( spl0_494
    | ~ spl0_286
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9230,f9161,f3029,f9712]) ).

fof(f9230,plain,
    ( null_class = complement(identity_relation)
    | ~ spl0_286
    | ~ spl0_475 ),
    inference(resolution,[],[f9162,f3031]) ).

fof(f9710,plain,
    ( spl0_493
    | ~ spl0_367
    | ~ spl0_492 ),
    inference(avatar_split_clause,[],[f9706,f9703,f4776,f9708]) ).

fof(f9706,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | member(X1,X0) )
    | ~ spl0_367
    | ~ spl0_492 ),
    inference(forward_demodulation,[],[f9704,f4778]) ).

fof(f9705,plain,
    ( spl0_492
    | ~ spl0_67
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1119,f1102,f533,f9703]) ).

fof(f1102,plain,
    ( spl0_132
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1119,plain,
    ( ! [X0,X1] :
        ( ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X1,X0) )
    | ~ spl0_67
    | ~ spl0_132 ),
    inference(superposition,[],[f1103,f535]) ).

fof(f1103,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1102]) ).

fof(f9701,plain,
    ( spl0_491
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f830,f813,f500,f404,f9699]) ).

fof(f9699,plain,
    ( spl0_491
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f830,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) )
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_104 ),
    inference(forward_demodulation,[],[f828,f405]) ).

fof(f828,plain,
    ( ! [X0] :
        ( null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
    | ~ spl0_63
    | ~ spl0_104 ),
    inference(resolution,[],[f814,f501]) ).

fof(f9429,plain,
    ( spl0_490
    | ~ spl0_387
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f9229,f9161,f5537,f9426]) ).

fof(f9229,plain,
    ( null_class = complement(successor_relation)
    | ~ spl0_387
    | ~ spl0_475 ),
    inference(resolution,[],[f9162,f5538]) ).

fof(f9261,plain,
    ( spl0_489
    | ~ spl0_367
    | ~ spl0_488 ),
    inference(avatar_split_clause,[],[f9257,f9254,f4776,f9259]) ).

fof(f9259,plain,
    ( spl0_489
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),null_class)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f9254,plain,
    ( spl0_488
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f9257,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),null_class)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_367
    | ~ spl0_488 ),
    inference(forward_demodulation,[],[f9255,f4778]) ).

fof(f9255,plain,
    ( ! [X2,X0,X1] :
        ( member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2))
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | ~ compatible(X0,X1,X2) )
    | ~ spl0_488 ),
    inference(avatar_component_clause,[],[f9254]) ).

fof(f9256,plain,
    ( spl0_488
    | ~ spl0_56
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1551,f1545,f471,f9254]) ).

fof(f471,plain,
    ( spl0_56
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1551,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_56
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f472]) ).

fof(f472,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f471]) ).

fof(f9252,plain,
    ( spl0_487
    | ~ spl0_124
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1416,f1394,f995,f9250]) ).

fof(f9250,plain,
    ( spl0_487
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f1394,plain,
    ( spl0_163
  <=> ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f1416,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0)) )
    | ~ spl0_124
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1411]) ).

fof(f1411,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0))
        | subclass(intersection(universal_class,X1),domain_of(X0)) )
    | ~ spl0_124
    | ~ spl0_163 ),
    inference(resolution,[],[f1395,f996]) ).

fof(f1395,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1394]) ).

fof(f9248,plain,
    ( spl0_486
    | ~ spl0_125
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1415,f1394,f999,f9246]) ).

fof(f9246,plain,
    ( spl0_486
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f1415,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0)) )
    | ~ spl0_125
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1412]) ).

fof(f1412,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0))
        | subclass(intersection(X1,universal_class),domain_of(X0)) )
    | ~ spl0_125
    | ~ spl0_163 ),
    inference(resolution,[],[f1395,f1000]) ).

fof(f9244,plain,
    ( spl0_485
    | ~ spl0_58
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1265,f1229,f479,f9242]) ).

fof(f9242,plain,
    ( spl0_485
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f479,plain,
    ( spl0_58
  <=> ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f1229,plain,
    ( spl0_145
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1265,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | ~ inductive(X1) )
    | ~ spl0_58
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f480]) ).

fof(f480,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f479]) ).

fof(f1230,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),X2)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,X2) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1229]) ).

fof(f9240,plain,
    ( spl0_484
    | ~ spl0_114
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1253,f1216,f874,f9238]) ).

fof(f9238,plain,
    ( spl0_484
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
        | subclass(X0,intersection(X1,regular(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f1253,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
        | subclass(X0,intersection(X1,regular(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f875]) ).

fof(f9204,plain,
    ( spl0_483
    | ~ spl0_101
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1246,f1216,f754,f9202]) ).

fof(f1246,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) )
    | ~ spl0_101
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f755]) ).

fof(f9200,plain,
    ( spl0_482
    | ~ spl0_25
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1083,f1056,f280,f9198]) ).

fof(f9198,plain,
    ( spl0_482
  <=> ! [X0] :
        ( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
        | member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
        | subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f1083,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
        | member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
        | subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_25
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f281]) ).

fof(f9196,plain,
    ( spl0_481
    | ~ spl0_125
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1076,f1052,f999,f9194]) ).

fof(f9194,plain,
    ( spl0_481
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | null_class = X1
        | subclass(intersection(X0,regular(X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f1076,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | null_class = X1
        | subclass(intersection(X0,regular(X1)),X2) )
    | ~ spl0_125
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f1000]) ).

fof(f9192,plain,
    ( spl0_480
    | ~ spl0_124
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1069,f1052,f995,f9190]) ).

fof(f9190,plain,
    ( spl0_480
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | null_class = X0
        | subclass(intersection(regular(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f1069,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | null_class = X0
        | subclass(intersection(regular(X0),X1),X2) )
    | ~ spl0_124
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f996]) ).

fof(f9188,plain,
    ( spl0_479
    | ~ spl0_44
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1025,f999,f396,f9186]) ).

fof(f9186,plain,
    ( spl0_479
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f1025,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 )
    | ~ spl0_44
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f397]) ).

fof(f9184,plain,
    ( spl0_478
    | ~ spl0_44
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1008,f995,f396,f9182]) ).

fof(f9182,plain,
    ( spl0_478
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(unordered_pair(X0,X1),X2),X3)
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f1008,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(unordered_pair(X0,X1),X2),X3)
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 )
    | ~ spl0_44
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f397]) ).

fof(f9172,plain,
    ( spl0_477
    | ~ spl0_367
    | ~ spl0_476 ),
    inference(avatar_split_clause,[],[f9168,f9165,f4776,f9170]) ).

fof(f9170,plain,
    ( spl0_477
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | ~ member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f9165,plain,
    ( spl0_476
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f9168,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | ~ member(X0,X1) )
    | ~ spl0_367
    | ~ spl0_476 ),
    inference(forward_demodulation,[],[f9166,f4778]) ).

fof(f9166,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_476 ),
    inference(avatar_component_clause,[],[f9165]) ).

fof(f9167,plain,
    ( spl0_476
    | ~ spl0_75
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f798,f754,f585,f9165]) ).

fof(f798,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_75
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f586]) ).

fof(f9163,plain,
    ( spl0_475
    | ~ spl0_20
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f2326,f2238,f257,f9161]) ).

fof(f2238,plain,
    ( spl0_229
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f2326,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(null_class,X0) )
    | ~ spl0_20
    | ~ spl0_229 ),
    inference(resolution,[],[f2239,f258]) ).

fof(f2239,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_229 ),
    inference(avatar_component_clause,[],[f2238]) ).

fof(f9159,plain,
    ( ~ spl0_4
    | ~ spl0_473
    | spl0_474
    | ~ spl0_58
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f792,f750,f479,f9156,f9152,f187]) ).

fof(f9152,plain,
    ( spl0_473
  <=> inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f9156,plain,
    ( spl0_474
  <=> omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f750,plain,
    ( spl0_100
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f792,plain,
    ( omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))
    | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))))
    | ~ inductive(omega)
    | ~ spl0_58
    | ~ spl0_100 ),
    inference(resolution,[],[f751,f480]) ).

fof(f751,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f750]) ).

fof(f9150,plain,
    ( ~ spl0_472
    | ~ spl0_367
    | spl0_471 ),
    inference(avatar_split_clause,[],[f9145,f9141,f4776,f9147]) ).

fof(f9141,plain,
    ( spl0_471
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f9145,plain,
    ( ~ member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_367
    | spl0_471 ),
    inference(forward_demodulation,[],[f9142,f4778]) ).

fof(f9142,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | spl0_471 ),
    inference(avatar_component_clause,[],[f9141]) ).

fof(f9144,plain,
    ( spl0_219
    | ~ spl0_470
    | spl0_471
    | ~ spl0_74
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f698,f686,f575,f9141,f9137,f2119]) ).

fof(f9137,plain,
    ( spl0_470
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f698,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ member(identity_relation,universal_class)
    | null_class = identity_relation
    | ~ spl0_74
    | ~ spl0_92 ),
    inference(resolution,[],[f687,f576]) ).

fof(f9108,plain,
    ( spl0_469
    | ~ spl0_60
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1549,f1545,f488,f9106]) ).

fof(f9106,plain,
    ( spl0_469
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f1549,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),X3) )
    | ~ spl0_60
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f489]) ).

fof(f9104,plain,
    ( spl0_468
    | ~ spl0_61
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1548,f1545,f492,f9102]) ).

fof(f9102,plain,
    ( spl0_468
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f1548,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),X4) )
    | ~ spl0_61
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f493]) ).

fof(f9100,plain,
    ( spl0_467
    | ~ spl0_38
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1239,f1212,f343,f9098]) ).

fof(f9098,plain,
    ( spl0_467
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | ~ subclass(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f1239,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | ~ subclass(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = X2 )
    | ~ spl0_38
    | ~ spl0_141 ),
    inference(resolution,[],[f1213,f344]) ).

fof(f9096,plain,
    ( spl0_466
    | ~ spl0_99
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1164,f1145,f746,f9094]) ).

fof(f9094,plain,
    ( spl0_466
  <=> ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f1164,plain,
    ( ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) )
    | ~ spl0_99
    | ~ spl0_137 ),
    inference(resolution,[],[f1146,f747]) ).

fof(f9088,plain,
    ( spl0_465
    | ~ spl0_367
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f9084,f9080,f4776,f9086]) ).

fof(f9086,plain,
    ( spl0_465
  <=> ! [X2,X0,X1] :
        ( domain_of(intersection(null_class,cross_product(universal_class,X2))) = X1
        | domain_of(intersection(null_class,cross_product(universal_class,X2))) = X0
        | ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f9080,plain,
    ( spl0_464
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f9084,plain,
    ( ! [X2,X0,X1] :
        ( domain_of(intersection(null_class,cross_product(universal_class,X2))) = X1
        | domain_of(intersection(null_class,cross_product(universal_class,X2))) = X0
        | ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class) )
    | ~ spl0_367
    | ~ spl0_464 ),
    inference(forward_demodulation,[],[f9083,f4778]) ).

fof(f9083,plain,
    ( ! [X2,X0,X1] :
        ( domain_of(intersection(null_class,cross_product(universal_class,X2))) = X0
        | ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
    | ~ spl0_367
    | ~ spl0_464 ),
    inference(forward_demodulation,[],[f9081,f4778]) ).

fof(f9081,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
    | ~ spl0_464 ),
    inference(avatar_component_clause,[],[f9080]) ).

fof(f9082,plain,
    ( spl0_464
    | ~ spl0_44
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1121,f1109,f396,f9080]) ).

fof(f1121,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
    | ~ spl0_44
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f397]) ).

fof(f8497,plain,
    ( spl0_463
    | ~ spl0_22
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1366,f1361,f265,f8495]) ).

fof(f8495,plain,
    ( spl0_463
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ function(cross_product(X1,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f1366,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ function(cross_product(X1,X3)) )
    | ~ spl0_22
    | ~ spl0_160 ),
    inference(resolution,[],[f1362,f266]) ).

fof(f8418,plain,
    ( spl0_462
    | ~ spl0_367
    | ~ spl0_461 ),
    inference(avatar_split_clause,[],[f8414,f8411,f4776,f8416]) ).

fof(f8416,plain,
    ( spl0_462
  <=> ! [X2,X0,X1] :
        ( ~ subclass(null_class,X2)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f8411,plain,
    ( spl0_461
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(element_relation,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f8414,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X2)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_367
    | ~ spl0_461 ),
    inference(forward_demodulation,[],[f8412,f4778]) ).

fof(f8412,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(element_relation,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_461 ),
    inference(avatar_component_clause,[],[f8411]) ).

fof(f8413,plain,
    ( spl0_461
    | ~ spl0_37
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1331,f1296,f339,f8411]) ).

fof(f1331,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(element_relation,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_37
    | ~ spl0_153 ),
    inference(resolution,[],[f1297,f340]) ).

fof(f8409,plain,
    ( spl0_460
    | ~ spl0_37
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f8309,f1372,f339,f8407]) ).

fof(f8309,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(u,X0) )
    | ~ spl0_37
    | ~ spl0_162 ),
    inference(resolution,[],[f1373,f340]) ).

fof(f8341,plain,
    ( spl0_459
    | ~ spl0_367
    | ~ spl0_458 ),
    inference(avatar_split_clause,[],[f8337,f8334,f4776,f8339]) ).

fof(f8334,plain,
    ( spl0_458
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f8337,plain,
    ( ! [X2,X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X2)
        | ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2) )
    | ~ spl0_367
    | ~ spl0_458 ),
    inference(forward_demodulation,[],[f8335,f4778]) ).

fof(f8335,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,universal_class)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X2)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) )
    | ~ spl0_458 ),
    inference(avatar_component_clause,[],[f8334]) ).

fof(f8336,plain,
    ( spl0_458
    | ~ spl0_37
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1316,f1284,f339,f8334]) ).

fof(f1316,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) )
    | ~ spl0_37
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f340]) ).

fof(f8332,plain,
    ( spl0_457
    | ~ spl0_37
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1299,f1280,f339,f8330]) ).

fof(f8330,plain,
    ( spl0_457
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,X1)
        | ~ member(X2,universal_class)
        | ~ subclass(X1,X3)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f1299,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,X1)
        | ~ member(X2,universal_class)
        | ~ subclass(X1,X3)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
    | ~ spl0_37
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f340]) ).

fof(f8328,plain,
    ( spl0_456
    | ~ spl0_54
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1264,f1229,f458,f8326]) ).

fof(f8326,plain,
    ( spl0_456
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,domain_of(domain_of(X1)))
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f1264,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,domain_of(domain_of(X1)))
        | ~ operation(X1) )
    | ~ spl0_54
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f459]) ).

fof(f8324,plain,
    ( spl0_455
    | ~ spl0_100
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1240,f1212,f750,f8322]) ).

fof(f8322,plain,
    ( spl0_455
  <=> ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),omega) = X1
        | not_subclass_element(unordered_pair(X0,X1),omega) = X0
        | unordered_pair(X0,X1) = omega
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f1240,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),omega) = X1
        | not_subclass_element(unordered_pair(X0,X1),omega) = X0
        | unordered_pair(X0,X1) = omega
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_100
    | ~ spl0_141 ),
    inference(resolution,[],[f1213,f751]) ).

fof(f8320,plain,
    ( spl0_454
    | ~ spl0_108
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1162,f1145,f848,f8318]) ).

fof(f8318,plain,
    ( spl0_454
  <=> ! [X0] :
        ( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f1162,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
        | null_class = X0 )
    | ~ spl0_108
    | ~ spl0_137 ),
    inference(resolution,[],[f1146,f849]) ).

fof(f8304,plain,
    ( spl0_451
    | spl0_452
    | ~ spl0_453
    | ~ spl0_23
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1087,f1056,f269,f8301,f8297,f8293]) ).

fof(f8297,plain,
    ( spl0_452
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f8301,plain,
    ( spl0_453
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f1087,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
    | member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_23
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f270]) ).

fof(f8291,plain,
    ( spl0_450
    | ~ spl0_119
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1075,f1052,f925,f8289]) ).

fof(f8289,plain,
    ( spl0_450
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),null_class)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | null_class = X1
        | null_class = intersection(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f1075,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),null_class)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | null_class = X1
        | null_class = intersection(X0,regular(X1)) )
    | ~ spl0_119
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f926]) ).

fof(f8287,plain,
    ( spl0_449
    | ~ spl0_118
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1073,f1052,f921,f8285]) ).

fof(f8285,plain,
    ( spl0_449
  <=> ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),null_class)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | null_class = X0
        | null_class = intersection(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1073,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),null_class)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | null_class = X0
        | null_class = intersection(regular(X0),X1) )
    | ~ spl0_118
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f922]) ).

fof(f8283,plain,
    ( spl0_448
    | ~ spl0_44
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f960,f925,f396,f8281]) ).

fof(f8281,plain,
    ( spl0_448
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f960,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
    | ~ spl0_44
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f397]) ).

fof(f8278,plain,
    ( ~ spl0_446
    | spl0_248
    | spl0_447
    | ~ spl0_67
    | ~ spl0_171
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f8256,f4776,f1465,f533,f8275,f2433,f8271]) ).

fof(f8275,plain,
    ( spl0_447
  <=> member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f8256,plain,
    ( member(domain_of(intersection(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_67
    | ~ spl0_171
    | ~ spl0_367 ),
    inference(forward_demodulation,[],[f1503,f4778]) ).

fof(f8266,plain,
    ( spl0_445
    | ~ spl0_367
    | ~ spl0_442 ),
    inference(avatar_split_clause,[],[f7580,f7577,f4776,f8264]) ).

fof(f7577,plain,
    ( spl0_442
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f7580,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),null_class)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_367
    | ~ spl0_442 ),
    inference(forward_demodulation,[],[f7578,f4778]) ).

fof(f7578,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(regular(cross_product(X0,X1)),element_relation)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_442 ),
    inference(avatar_component_clause,[],[f7577]) ).

fof(f8202,plain,
    ( spl0_248
    | spl0_162
    | ~ spl0_426 ),
    inference(avatar_split_clause,[],[f7505,f7296,f1372,f2433]) ).

fof(f8200,plain,
    ( spl0_444
    | ~ spl0_44
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f941,f921,f396,f8198]) ).

fof(f941,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
    | ~ spl0_44
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f397]) ).

fof(f7586,plain,
    ( spl0_443
    | spl0_162
    | ~ spl0_367
    | ~ spl0_426
    | ~ spl0_442 ),
    inference(avatar_split_clause,[],[f7582,f7577,f7296,f4776,f1372,f7584]) ).

fof(f7582,plain,
    ( ! [X0,X1] :
        ( cross_product(X0,X1) = subset_relation
        | ~ member(regular(cross_product(X0,X1)),subset_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))) )
    | spl0_162
    | ~ spl0_367
    | ~ spl0_426
    | ~ spl0_442 ),
    inference(forward_demodulation,[],[f7581,f7505]) ).

fof(f7581,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),subset_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | spl0_162
    | ~ spl0_367
    | ~ spl0_426
    | ~ spl0_442 ),
    inference(forward_demodulation,[],[f7580,f7505]) ).

fof(f7579,plain,
    ( spl0_442
    | ~ spl0_56
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1520,f1512,f471,f7577]) ).

fof(f1520,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_56
    | ~ spl0_173 ),
    inference(superposition,[],[f472,f1513]) ).

fof(f7503,plain,
    ( spl0_441
    | ~ spl0_120
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1414,f1394,f929,f7501]) ).

fof(f7501,plain,
    ( spl0_441
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f1414,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class) )
    | ~ spl0_120
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1413]) ).

fof(f1413,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class)
        | subclass(X1,domain_of(X0)) )
    | ~ spl0_120
    | ~ spl0_163 ),
    inference(resolution,[],[f1395,f930]) ).

fof(f7492,plain,
    ( spl0_440
    | ~ spl0_367
    | ~ spl0_439 ),
    inference(avatar_split_clause,[],[f7488,f7485,f4776,f7490]) ).

fof(f7490,plain,
    ( spl0_440
  <=> ! [X2,X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))),X0)
        | ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f7485,plain,
    ( spl0_439
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f7488,plain,
    ( ! [X2,X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))),X0)
        | ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class) )
    | ~ spl0_367
    | ~ spl0_439 ),
    inference(forward_demodulation,[],[f7486,f4778]) ).

fof(f7486,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) )
    | ~ spl0_439 ),
    inference(avatar_component_clause,[],[f7485]) ).

fof(f7487,plain,
    ( spl0_439
    | ~ spl0_29
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1320,f1284,f296,f7485]) ).

fof(f1320,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) )
    | ~ spl0_29
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f297]) ).

fof(f7475,plain,
    ( spl0_438
    | ~ spl0_367
    | ~ spl0_437 ),
    inference(avatar_split_clause,[],[f7471,f7468,f4776,f7473]) ).

fof(f7473,plain,
    ( spl0_438
  <=> ! [X2,X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))),X1)
        | ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f7468,plain,
    ( spl0_437
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f7471,plain,
    ( ! [X2,X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X2),universal_class)),universal_class))))),X1)
        | ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class) )
    | ~ spl0_367
    | ~ spl0_437 ),
    inference(forward_demodulation,[],[f7469,f4778]) ).

fof(f7469,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) )
    | ~ spl0_437 ),
    inference(avatar_component_clause,[],[f7468]) ).

fof(f7470,plain,
    ( spl0_437
    | ~ spl0_30
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1319,f1284,f300,f7468]) ).

fof(f1319,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) )
    | ~ spl0_30
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f301]) ).

fof(f7466,plain,
    ( spl0_436
    | ~ spl0_29
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1303,f1280,f296,f7464]) ).

fof(f7464,plain,
    ( spl0_436
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1303,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) )
    | ~ spl0_29
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f297]) ).

fof(f7462,plain,
    ( spl0_435
    | ~ spl0_30
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1302,f1280,f300,f7460]) ).

fof(f7460,plain,
    ( spl0_435
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1302,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) )
    | ~ spl0_30
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f301]) ).

fof(f7458,plain,
    ( spl0_434
    | ~ spl0_128
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1197,f1167,f1052,f7456]) ).

fof(f7456,plain,
    ( spl0_434
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f1197,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_128
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1176]) ).

fof(f1176,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_128
    | ~ spl0_138 ),
    inference(superposition,[],[f1053,f1168]) ).

fof(f7454,plain,
    ( spl0_433
    | ~ spl0_37
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f6439,f4702,f339,f7452]) ).

fof(f6439,plain,
    ( ! [X0] :
        ( ~ subclass(null_class,X0)
        | member(u,X0) )
    | ~ spl0_37
    | ~ spl0_361 ),
    inference(resolution,[],[f4704,f340]) ).

fof(f4704,plain,
    ( member(u,null_class)
    | ~ spl0_361 ),
    inference(avatar_component_clause,[],[f4702]) ).

fof(f7450,plain,
    ( spl0_432
    | ~ spl0_128
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1192,f1167,f1052,f7448]) ).

fof(f7448,plain,
    ( spl0_432
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f1192,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_128
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1181]) ).

fof(f1181,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_128
    | ~ spl0_138 ),
    inference(superposition,[],[f1053,f1168]) ).

fof(f7446,plain,
    ( spl0_431
    | ~ spl0_45
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f886,f844,f400,f7444]) ).

fof(f7444,plain,
    ( spl0_431
  <=> ! [X2,X0,X1] :
        ( subclass(complement(intersection(X0,X1)),X2)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f886,plain,
    ( ! [X2,X0,X1] :
        ( subclass(complement(intersection(X0,X1)),X2)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) )
    | ~ spl0_45
    | ~ spl0_107 ),
    inference(resolution,[],[f845,f401]) ).

fof(f7315,plain,
    ( spl0_430
    | ~ spl0_367
    | ~ spl0_429 ),
    inference(avatar_split_clause,[],[f7311,f7308,f4776,f7313]) ).

fof(f7308,plain,
    ( spl0_429
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f7311,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class) )
    | ~ spl0_367
    | ~ spl0_429 ),
    inference(forward_demodulation,[],[f7309,f4778]) ).

fof(f7309,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | ~ member(X1,universal_class)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_429 ),
    inference(avatar_component_clause,[],[f7308]) ).

fof(f7310,plain,
    ( spl0_429
    | ~ spl0_20
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1322,f1284,f257,f7308]) ).

fof(f1322,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) )
    | ~ spl0_20
    | ~ spl0_150 ),
    inference(resolution,[],[f1285,f258]) ).

fof(f7306,plain,
    ( spl0_428
    | ~ spl0_20
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1305,f1280,f257,f7304]) ).

fof(f7304,plain,
    ( spl0_428
  <=> ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(X1))
        | ~ member(X2,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f1305,plain,
    ( ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(X1))
        | ~ member(X2,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) )
    | ~ spl0_20
    | ~ spl0_149 ),
    inference(resolution,[],[f1281,f258]) ).

fof(f7302,plain,
    ( spl0_427
    | ~ spl0_98
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1238,f1212,f742,f7300]) ).

fof(f7300,plain,
    ( spl0_427
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(null_class,X2)
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f742,plain,
    ( spl0_98
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1238,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(null_class,X2)
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_98
    | ~ spl0_141 ),
    inference(resolution,[],[f1213,f743]) ).

fof(f743,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f742]) ).

fof(f7298,plain,
    ( spl0_426
    | ~ spl0_105
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f6436,f4702,f817,f7296]) ).

fof(f6436,plain,
    ( ! [X0] :
        ( member(u,X0)
        | null_class = X0 )
    | ~ spl0_105
    | ~ spl0_361 ),
    inference(resolution,[],[f4704,f818]) ).

fof(f7289,plain,
    ( spl0_425
    | ~ spl0_367
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f7285,f7282,f4776,f7287]) ).

fof(f7285,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_367
    | ~ spl0_424 ),
    inference(forward_demodulation,[],[f7283,f4778]) ).

fof(f7284,plain,
    ( spl0_424
    | ~ spl0_37
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1207,f1202,f339,f7282]) ).

fof(f1207,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | member(X0,X1) )
    | ~ spl0_37
    | ~ spl0_140 ),
    inference(resolution,[],[f1203,f340]) ).

fof(f7280,plain,
    ( spl0_423
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1094,f1056,f500,f404,f7278]) ).

fof(f7278,plain,
    ( spl0_423
  <=> ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f1094,plain,
    ( ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_46
    | ~ spl0_63
    | ~ spl0_129 ),
    inference(forward_demodulation,[],[f1081,f405]) ).

fof(f1081,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
    | ~ spl0_63
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f501]) ).

fof(f6814,plain,
    ( spl0_422
    | ~ spl0_44
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4734,f1291,f396,f6812]) ).

fof(f6812,plain,
    ( spl0_422
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | unordered_pair(first(null_class),first(null_class)) = X0
        | unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f4734,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | unordered_pair(first(null_class),first(null_class)) = X0
        | unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))) = X0 )
    | ~ spl0_44
    | ~ spl0_152 ),
    inference(superposition,[],[f397,f1293]) ).

fof(f6802,plain,
    ( ~ spl0_11
    | spl0_420 ),
    inference(avatar_contradiction_clause,[],[f6800]) ).

fof(f6800,plain,
    ( $false
    | ~ spl0_11
    | spl0_420 ),
    inference(resolution,[],[f6794,f219]) ).

fof(f6794,plain,
    ( ~ member(unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))),universal_class)
    | spl0_420 ),
    inference(avatar_component_clause,[],[f6792]) ).

fof(f6792,plain,
    ( spl0_420
  <=> member(unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f6799,plain,
    ( ~ spl0_420
    | spl0_421
    | ~ spl0_28
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4733,f1291,f292,f6796,f6792]) ).

fof(f4733,plain,
    ( member(unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))),null_class)
    | ~ member(unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))),universal_class)
    | ~ spl0_28
    | ~ spl0_152 ),
    inference(superposition,[],[f293,f1293]) ).

fof(f6790,plain,
    ( spl0_419
    | ~ spl0_61
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1522,f1512,f492,f6788]) ).

fof(f6788,plain,
    ( spl0_419
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f1522,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_61
    | ~ spl0_173 ),
    inference(superposition,[],[f493,f1513]) ).

fof(f6786,plain,
    ( spl0_418
    | ~ spl0_60
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1521,f1512,f488,f6784]) ).

fof(f6784,plain,
    ( spl0_418
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f1521,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_60
    | ~ spl0_173 ),
    inference(superposition,[],[f489,f1513]) ).

fof(f6782,plain,
    ( spl0_417
    | ~ spl0_44
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f4038,f3612,f396,f6780]) ).

fof(f4038,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | u = X0 )
    | ~ spl0_44
    | ~ spl0_329 ),
    inference(duplicate_literal_removal,[],[f3964]) ).

fof(f3964,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | u = X0
        | u = X0 )
    | ~ spl0_44
    | ~ spl0_329 ),
    inference(superposition,[],[f397,f3614]) ).

fof(f6778,plain,
    ( spl0_416
    | ~ spl0_22
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1268,f1229,f265,f6776]) ).

fof(f6776,plain,
    ( spl0_416
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f1268,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(X1)) )
    | ~ spl0_22
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f266]) ).

fof(f6774,plain,
    ( spl0_415
    | ~ spl0_121
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1237,f1212,f933,f6772]) ).

fof(f6772,plain,
    ( spl0_415
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f1237,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_121
    | ~ spl0_141 ),
    inference(resolution,[],[f1213,f934]) ).

fof(f6770,plain,
    ( spl0_414
    | ~ spl0_122
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1236,f1212,f937,f6768]) ).

fof(f6768,plain,
    ( spl0_414
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f1236,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_122
    | ~ spl0_141 ),
    inference(resolution,[],[f1213,f938]) ).

fof(f6766,plain,
    ( spl0_413
    | ~ spl0_37
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1198,f1171,f339,f6764]) ).

fof(f6764,plain,
    ( spl0_413
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f1171,plain,
    ( spl0_139
  <=> ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f1198,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) )
    | ~ spl0_37
    | ~ spl0_139 ),
    inference(resolution,[],[f1172,f340]) ).

fof(f1172,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1171]) ).

fof(f6762,plain,
    ( spl0_412
    | ~ spl0_120
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1093,f1056,f929,f6760]) ).

fof(f6760,plain,
    ( spl0_412
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),subset_relation)
        | member(not_subclass_element(X0,X1),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f1093,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),subset_relation)
        | member(not_subclass_element(X0,X1),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_120
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f930]) ).

fof(f6758,plain,
    ( spl0_411
    | ~ spl0_120
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1078,f1052,f929,f6756]) ).

fof(f6756,plain,
    ( spl0_411
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | ~ member(not_subclass_element(X0,X1),X2)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f1078,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | ~ member(not_subclass_element(X0,X1),X2)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) )
    | ~ spl0_120
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f930]) ).

fof(f6739,plain,
    ( spl0_410
    | ~ spl0_367
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f6735,f6732,f4776,f6737]) ).

fof(f6735,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_367
    | ~ spl0_409 ),
    inference(forward_demodulation,[],[f6733,f4778]) ).

fof(f6734,plain,
    ( spl0_409
    | ~ spl0_67
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1038,f999,f533,f6732]) ).

fof(f1038,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_67
    | ~ spl0_125 ),
    inference(superposition,[],[f1000,f535]) ).

fof(f6730,plain,
    ( spl0_408
    | ~ spl0_45
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f825,f813,f400,f6728]) ).

fof(f825,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_45
    | ~ spl0_104 ),
    inference(resolution,[],[f814,f401]) ).

fof(f6580,plain,
    ( spl0_407
    | ~ spl0_25
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1417,f1394,f280,f6578]) ).

fof(f6578,plain,
    ( spl0_407
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f1417,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0)) )
    | ~ spl0_25
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1410]) ).

fof(f1410,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0))
        | subclass(universal_class,domain_of(X0)) )
    | ~ spl0_25
    | ~ spl0_163 ),
    inference(resolution,[],[f1395,f281]) ).

fof(f6521,plain,
    ( spl0_406
    | ~ spl0_367
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f6517,f6514,f4776,f6519]) ).

fof(f6519,plain,
    ( spl0_406
  <=> ! [X0] :
        ( ~ member(X0,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))
        | member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f6517,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class))))))
        | member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_367
    | ~ spl0_405 ),
    inference(forward_demodulation,[],[f6515,f4778]) ).

fof(f6516,plain,
    ( spl0_405
    | ~ spl0_45
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1392,f1368,f400,f6514]) ).

fof(f1392,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_45
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1377]) ).

fof(f1377,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_45
    | ~ spl0_161 ),
    inference(resolution,[],[f1369,f401]) ).

fof(f6512,plain,
    ( ~ spl0_404
    | spl0_111
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f5027,f4776,f860,f6509]) ).

fof(f5027,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),null_class)
    | spl0_111
    | ~ spl0_367 ),
    inference(superposition,[],[f862,f4778]) ).

fof(f6507,plain,
    ( spl0_403
    | ~ spl0_108
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1195,f1167,f848,f6505]) ).

fof(f6505,plain,
    ( spl0_403
  <=> ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f1195,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_108
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1178]) ).

fof(f1178,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_108
    | ~ spl0_138 ),
    inference(superposition,[],[f849,f1168]) ).

fof(f6503,plain,
    ( spl0_402
    | ~ spl0_108
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1190,f1167,f848,f6501]) ).

fof(f6501,plain,
    ( spl0_402
  <=> ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f1190,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_108
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1183]) ).

fof(f1183,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_108
    | ~ spl0_138 ),
    inference(superposition,[],[f849,f1168]) ).

fof(f6499,plain,
    ( spl0_401
    | ~ spl0_25
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1068,f1052,f280,f6497]) ).

fof(f6497,plain,
    ( spl0_401
  <=> ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),null_class)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | null_class = X0
        | subclass(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f1068,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),null_class)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | null_class = X0
        | subclass(regular(X0),X1) )
    | ~ spl0_25
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f281]) ).

fof(f6488,plain,
    ( spl0_400
    | ~ spl0_367
    | ~ spl0_399 ),
    inference(avatar_split_clause,[],[f6483,f6479,f4776,f6485]) ).

fof(f6483,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(null_class),domain_of(flip(cross_product(null_class,universal_class)))))))
    | ~ spl0_367
    | ~ spl0_399 ),
    inference(forward_demodulation,[],[f6481,f4778]) ).

fof(f6482,plain,
    ( spl0_248
    | spl0_399
    | ~ spl0_67
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f973,f925,f533,f6479,f2433]) ).

fof(f973,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = subset_relation
    | ~ spl0_67
    | ~ spl0_119 ),
    inference(superposition,[],[f926,f535]) ).

fof(f6477,plain,
    ( spl0_398
    | ~ spl0_41
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f888,f844,f379,f6475]) ).

fof(f6475,plain,
    ( spl0_398
  <=> ! [X0,X1] :
        ( subclass(complement(complement(X0)),X1)
        | member(not_subclass_element(complement(complement(X0)),X1),X0)
        | ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f888,plain,
    ( ! [X0,X1] :
        ( subclass(complement(complement(X0)),X1)
        | member(not_subclass_element(complement(complement(X0)),X1),X0)
        | ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) )
    | ~ spl0_41
    | ~ spl0_107 ),
    inference(resolution,[],[f845,f380]) ).

fof(f6473,plain,
    ( spl0_397
    | ~ spl0_71
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f795,f754,f558,f6471]) ).

fof(f6471,plain,
    ( spl0_397
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f795,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
    | ~ spl0_71
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f559]) ).

fof(f6443,plain,
    ( spl0_396
    | ~ spl0_329
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f6433,f6428,f3612,f6441]) ).

fof(f6441,plain,
    ( spl0_396
  <=> ! [X0] :
        ( subclass(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f6428,plain,
    ( spl0_395
  <=> ! [X0] :
        ( member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f6433,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class) )
    | ~ spl0_329
    | ~ spl0_395 ),
    inference(forward_demodulation,[],[f6432,f3614]) ).

fof(f6432,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
        | subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_329
    | ~ spl0_395 ),
    inference(forward_demodulation,[],[f6431,f3614]) ).

fof(f6431,plain,
    ( ! [X0] :
        ( member(not_subclass_element(X0,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_329
    | ~ spl0_395 ),
    inference(forward_demodulation,[],[f6429,f3614]) ).

fof(f6429,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
        | subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_395 ),
    inference(avatar_component_clause,[],[f6428]) ).

fof(f6430,plain,
    ( spl0_395
    | ~ spl0_26
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f740,f728,f284,f6428]) ).

fof(f740,plain,
    ( ! [X0] :
        ( member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
        | ~ member(not_subclass_element(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),universal_class)
        | subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_26
    | ~ spl0_96 ),
    inference(resolution,[],[f729,f285]) ).

fof(f6201,plain,
    ( spl0_394
    | ~ spl0_39
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1194,f1167,f347,f6199]) ).

fof(f6199,plain,
    ( spl0_394
  <=> ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1194,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_39
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1179]) ).

fof(f1179,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_39
    | ~ spl0_138 ),
    inference(superposition,[],[f348,f1168]) ).

fof(f6197,plain,
    ( spl0_393
    | ~ spl0_39
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1189,f1167,f347,f6195]) ).

fof(f6195,plain,
    ( spl0_393
  <=> ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f1189,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_39
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1184]) ).

fof(f1184,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_39
    | ~ spl0_138 ),
    inference(superposition,[],[f348,f1168]) ).

fof(f6193,plain,
    ( spl0_392
    | ~ spl0_108
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1089,f1056,f848,f6191]) ).

fof(f6191,plain,
    ( spl0_392
  <=> ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1089,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_108
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f849]) ).

fof(f6124,plain,
    ( spl0_391
    | ~ spl0_229
    | spl0_387
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f6120,f6115,f5537,f2238,f6122]) ).

fof(f6122,plain,
    ( spl0_391
  <=> ! [X0,X1] :
        ( successor_relation = X0
        | successor_relation = X1
        | member(regular(X0),successor_relation)
        | ~ member(regular(X0),X1)
        | ~ subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f6115,plain,
    ( spl0_390
  <=> ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f6120,plain,
    ( ! [X0,X1] :
        ( successor_relation = X0
        | successor_relation = X1
        | member(regular(X0),successor_relation)
        | ~ member(regular(X0),X1)
        | ~ subclass(X0,regular(X1)) )
    | ~ spl0_229
    | spl0_387
    | ~ spl0_390 ),
    inference(forward_demodulation,[],[f6119,f5541]) ).

fof(f5541,plain,
    ( null_class = successor_relation
    | ~ spl0_229
    | spl0_387 ),
    inference(resolution,[],[f5539,f2239]) ).

fof(f5539,plain,
    ( ~ member(null_class,successor_relation)
    | spl0_387 ),
    inference(avatar_component_clause,[],[f5537]) ).

fof(f6119,plain,
    ( ! [X0,X1] :
        ( successor_relation = X1
        | member(regular(X0),successor_relation)
        | ~ member(regular(X0),X1)
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_229
    | spl0_387
    | ~ spl0_390 ),
    inference(forward_demodulation,[],[f6118,f5541]) ).

fof(f6118,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),successor_relation)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_229
    | spl0_387
    | ~ spl0_390 ),
    inference(forward_demodulation,[],[f6116,f5541]) ).

fof(f6116,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | member(regular(X0),null_class)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f6115]) ).

fof(f6117,plain,
    ( spl0_390
    | ~ spl0_108
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1074,f1052,f848,f6115]) ).

fof(f1074,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_108
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f849]) ).

fof(f6113,plain,
    ( spl0_389
    | ~ spl0_44
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f977,f929,f396,f6111]) ).

fof(f6111,plain,
    ( spl0_389
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = X1
        | not_subclass_element(X0,X3) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f977,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = X1
        | not_subclass_element(X0,X3) = X2 )
    | ~ spl0_44
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f397]) ).

fof(f6109,plain,
    ( spl0_388
    | ~ spl0_107
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f916,f878,f844,f6107]) ).

fof(f6107,plain,
    ( spl0_388
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f916,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_107
    | ~ spl0_115 ),
    inference(resolution,[],[f879,f845]) ).

fof(f5540,plain,
    ( spl0_386
    | ~ spl0_387
    | ~ spl0_69
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4715,f1291,f549,f5537,f5533]) ).

fof(f4715,plain,
    ( ~ member(null_class,successor_relation)
    | second(null_class) = complement(intersection(complement(first(null_class)),complement(unordered_pair(first(null_class),first(null_class)))))
    | ~ spl0_69
    | ~ spl0_152 ),
    inference(superposition,[],[f550,f1293]) ).

fof(f5531,plain,
    ( spl0_385
    | ~ spl0_40
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1256,f1216,f351,f5529]) ).

fof(f5529,plain,
    ( spl0_385
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f1256,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_40
    | ~ spl0_142 ),
    inference(superposition,[],[f1217,f353]) ).

fof(f5527,plain,
    ( spl0_384
    | ~ spl0_39
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1254,f1216,f347,f5525]) ).

fof(f5525,plain,
    ( spl0_384
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),regular(X0))
        | ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f1254,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),regular(X0))
        | ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | null_class = X0 )
    | ~ spl0_39
    | ~ spl0_142 ),
    inference(superposition,[],[f1217,f348]) ).

fof(f5523,plain,
    ( spl0_383
    | ~ spl0_114
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1196,f1167,f874,f5521]) ).

fof(f5521,plain,
    ( spl0_383
  <=> ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f1196,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_114
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1177]) ).

fof(f1177,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_114
    | ~ spl0_138 ),
    inference(superposition,[],[f875,f1168]) ).

fof(f5519,plain,
    ( spl0_382
    | ~ spl0_114
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1191,f1167,f874,f5517]) ).

fof(f5517,plain,
    ( spl0_382
  <=> ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f1191,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_114
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1182]) ).

fof(f1182,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_114
    | ~ spl0_138 ),
    inference(superposition,[],[f875,f1168]) ).

fof(f5515,plain,
    ( ~ spl0_381
    | spl0_202
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f5040,f4776,f1906,f5512]) ).

fof(f1906,plain,
    ( spl0_202
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f5040,plain,
    ( ~ function(null_class)
    | spl0_202
    | ~ spl0_367 ),
    inference(superposition,[],[f1907,f4778]) ).

fof(f1907,plain,
    ( ~ function(element_relation)
    | spl0_202 ),
    inference(avatar_component_clause,[],[f1906]) ).

fof(f5448,plain,
    ( spl0_380
    | ~ spl0_367
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f5444,f5441,f4776,f5446]) ).

fof(f5444,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(intersection(null_class,cross_product(universal_class,X1))),X2)
        | ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2) )
    | ~ spl0_367
    | ~ spl0_379 ),
    inference(forward_demodulation,[],[f5442,f4778]) ).

fof(f5443,plain,
    ( spl0_379
    | ~ spl0_37
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1120,f1109,f339,f5441]) ).

fof(f1120,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
    | ~ spl0_37
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f340]) ).

fof(f5439,plain,
    ( ~ spl0_377
    | spl0_378
    | ~ spl0_99
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1092,f1056,f746,f5437,f5433]) ).

fof(f5433,plain,
    ( spl0_377
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f5437,plain,
    ( spl0_378
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f1092,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation)
        | ~ subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_99
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f747]) ).

fof(f5431,plain,
    ( spl0_376
    | ~ spl0_99
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1077,f1052,f746,f5429]) ).

fof(f5429,plain,
    ( spl0_376
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | ~ member(unordered_pair(X0,X1),X2)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f1077,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | ~ member(unordered_pair(X0,X1),X2)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) )
    | ~ spl0_99
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f747]) ).

fof(f5427,plain,
    ( spl0_375
    | ~ spl0_23
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1072,f1052,f269,f5425]) ).

fof(f5425,plain,
    ( spl0_375
  <=> ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f1072,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) )
    | ~ spl0_23
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f270]) ).

fof(f5421,plain,
    ( spl0_373
    | ~ spl0_374
    | ~ spl0_104
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f918,f878,f813,f5418,f5414]) ).

fof(f5418,plain,
    ( spl0_374
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f918,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_104
    | ~ spl0_115 ),
    inference(resolution,[],[f879,f814]) ).

fof(f5412,plain,
    ( ~ spl0_372
    | spl0_201
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f5039,f4776,f1902,f5409]) ).

fof(f1902,plain,
    ( spl0_201
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f5039,plain,
    ( ~ single_valued_class(null_class)
    | spl0_201
    | ~ spl0_367 ),
    inference(superposition,[],[f1904,f4778]) ).

fof(f1904,plain,
    ( ~ single_valued_class(element_relation)
    | spl0_201 ),
    inference(avatar_component_clause,[],[f1902]) ).

fof(f5407,plain,
    ( spl0_371
    | ~ spl0_41
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f827,f813,f379,f5405]) ).

fof(f5405,plain,
    ( spl0_371
  <=> ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f827,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_41
    | ~ spl0_104 ),
    inference(resolution,[],[f814,f380]) ).

fof(f4801,plain,
    ( ~ spl0_11
    | spl0_369 ),
    inference(avatar_contradiction_clause,[],[f4799]) ).

fof(f4799,plain,
    ( $false
    | ~ spl0_11
    | spl0_369 ),
    inference(resolution,[],[f4793,f219]) ).

fof(f4793,plain,
    ( ~ member(unordered_pair(first(null_class),first(null_class)),universal_class)
    | spl0_369 ),
    inference(avatar_component_clause,[],[f4791]) ).

fof(f4791,plain,
    ( spl0_369
  <=> member(unordered_pair(first(null_class),first(null_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f4798,plain,
    ( ~ spl0_369
    | spl0_370
    | ~ spl0_27
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4732,f1291,f288,f4795,f4791]) ).

fof(f4732,plain,
    ( member(unordered_pair(first(null_class),first(null_class)),null_class)
    | ~ member(unordered_pair(first(null_class),first(null_class)),universal_class)
    | ~ spl0_27
    | ~ spl0_152 ),
    inference(superposition,[],[f289,f1293]) ).

fof(f4783,plain,
    ( spl0_368
    | ~ spl0_68
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4714,f1291,f538,f4781]) ).

fof(f4781,plain,
    ( spl0_368
  <=> ! [X0,X1] :
        ( member(null_class,cross_product(X0,X1))
        | ~ member(second(null_class),X1)
        | ~ member(first(null_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f4714,plain,
    ( ! [X0,X1] :
        ( member(null_class,cross_product(X0,X1))
        | ~ member(second(null_class),X1)
        | ~ member(first(null_class),X0) )
    | ~ spl0_68
    | ~ spl0_152 ),
    inference(superposition,[],[f539,f1293]) ).

fof(f4779,plain,
    ( spl0_367
    | ~ spl0_229
    | spl0_364 ),
    inference(avatar_split_clause,[],[f4755,f4751,f2238,f4776]) ).

fof(f4755,plain,
    ( element_relation = null_class
    | ~ spl0_229
    | spl0_364 ),
    inference(resolution,[],[f4753,f2239]) ).

fof(f4753,plain,
    ( ~ member(null_class,element_relation)
    | spl0_364 ),
    inference(avatar_component_clause,[],[f4751]) ).

fof(f4764,plain,
    ( spl0_366
    | ~ spl0_61
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4713,f1291,f492,f4762]) ).

fof(f4762,plain,
    ( spl0_366
  <=> ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(second(null_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f4713,plain,
    ( ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(second(null_class),X1) )
    | ~ spl0_61
    | ~ spl0_152 ),
    inference(superposition,[],[f493,f1293]) ).

fof(f4760,plain,
    ( spl0_365
    | ~ spl0_60
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4712,f1291,f488,f4758]) ).

fof(f4758,plain,
    ( spl0_365
  <=> ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(first(null_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f4712,plain,
    ( ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(first(null_class),X0) )
    | ~ spl0_60
    | ~ spl0_152 ),
    inference(superposition,[],[f489,f1293]) ).

fof(f4754,plain,
    ( spl0_363
    | ~ spl0_364
    | ~ spl0_56
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f4711,f1291,f471,f4751,f4747]) ).

fof(f4747,plain,
    ( spl0_363
  <=> member(first(null_class),second(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f4711,plain,
    ( ~ member(null_class,element_relation)
    | member(first(null_class),second(null_class))
    | ~ spl0_56
    | ~ spl0_152 ),
    inference(superposition,[],[f472,f1293]) ).

fof(f4710,plain,
    ( spl0_152
    | ~ spl0_71
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f2389,f1350,f558,f1291]) ).

fof(f2389,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | ~ spl0_71
    | ~ spl0_158 ),
    inference(resolution,[],[f1351,f559]) ).

fof(f4709,plain,
    ( spl0_362
    | ~ spl0_124
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1261,f1216,f995,f4707]) ).

fof(f4707,plain,
    ( spl0_362
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f1261,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_124
    | ~ spl0_142 ),
    inference(duplicate_literal_removal,[],[f1243]) ).

fof(f1243,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0))
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_124
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f996]) ).

fof(f4705,plain,
    ( ~ spl0_70
    | spl0_361
    | ~ spl0_27
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f3962,f3612,f288,f4702,f553]) ).

fof(f3962,plain,
    ( member(u,null_class)
    | ~ member(u,universal_class)
    | ~ spl0_27
    | ~ spl0_329 ),
    inference(superposition,[],[f289,f3614]) ).

fof(f4700,plain,
    ( spl0_360
    | ~ spl0_125
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1260,f1216,f999,f4698]) ).

fof(f4698,plain,
    ( spl0_360
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f1260,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_125
    | ~ spl0_142 ),
    inference(duplicate_literal_removal,[],[f1244]) ).

fof(f1244,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1))
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_125
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f1000]) ).

fof(f4696,plain,
    ( spl0_359
    | ~ spl0_23
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1193,f1167,f269,f4694]) ).

fof(f4694,plain,
    ( spl0_359
  <=> ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f1193,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_23
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1180]) ).

fof(f1180,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_138 ),
    inference(superposition,[],[f270,f1168]) ).

fof(f4692,plain,
    ( spl0_358
    | ~ spl0_23
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1188,f1167,f269,f4690]) ).

fof(f4690,plain,
    ( spl0_358
  <=> ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f1188,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_23
    | ~ spl0_138 ),
    inference(duplicate_literal_removal,[],[f1185]) ).

fof(f1185,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_138 ),
    inference(superposition,[],[f270,f1168]) ).

fof(f4688,plain,
    ( spl0_357
    | ~ spl0_29
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1124,f1109,f296,f4686]) ).

fof(f4686,plain,
    ( spl0_357
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f1124,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) )
    | ~ spl0_29
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f297]) ).

fof(f4684,plain,
    ( spl0_356
    | ~ spl0_30
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1123,f1109,f300,f4682]) ).

fof(f4682,plain,
    ( spl0_356
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f1123,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) )
    | ~ spl0_30
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f301]) ).

fof(f4680,plain,
    ( spl0_355
    | ~ spl0_40
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1117,f1102,f351,f4678]) ).

fof(f4678,plain,
    ( spl0_355
  <=> ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f1117,plain,
    ( ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_40
    | ~ spl0_132 ),
    inference(superposition,[],[f1103,f353]) ).

fof(f4676,plain,
    ( spl0_354
    | ~ spl0_39
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1115,f1102,f347,f4674]) ).

fof(f4674,plain,
    ( spl0_354
  <=> ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f1115,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 )
    | ~ spl0_39
    | ~ spl0_132 ),
    inference(superposition,[],[f1103,f348]) ).

fof(f4672,plain,
    ( spl0_353
    | ~ spl0_29
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1028,f999,f296,f4670]) ).

fof(f4670,plain,
    ( spl0_353
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f1028,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_29
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f297]) ).

fof(f4668,plain,
    ( spl0_352
    | ~ spl0_30
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1027,f999,f300,f4666]) ).

fof(f4666,plain,
    ( spl0_352
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f1027,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_30
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f301]) ).

fof(f4664,plain,
    ( spl0_351
    | ~ spl0_29
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1011,f995,f296,f4662]) ).

fof(f4662,plain,
    ( spl0_351
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f1011,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_29
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f297]) ).

fof(f4660,plain,
    ( spl0_218
    | ~ spl0_8
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f4509,f2279,f206,f2110]) ).

fof(f2279,plain,
    ( spl0_239
  <=> ! [X0] :
        ( ~ subclass(null_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f4509,plain,
    ( member(null_class,null_class)
    | ~ spl0_8
    | ~ spl0_239 ),
    inference(resolution,[],[f2280,f207]) ).

fof(f2280,plain,
    ( ! [X0] :
        ( ~ subclass(null_class,X0)
        | member(null_class,X0) )
    | ~ spl0_239 ),
    inference(avatar_component_clause,[],[f2279]) ).

fof(f4659,plain,
    ( spl0_350
    | ~ spl0_30
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1010,f995,f300,f4657]) ).

fof(f4657,plain,
    ( spl0_350
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f1010,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_30
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f301]) ).

fof(f4655,plain,
    ( spl0_349
    | ~ spl0_26
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f915,f878,f284,f4653]) ).

fof(f4653,plain,
    ( spl0_349
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f915,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_26
    | ~ spl0_115 ),
    inference(resolution,[],[f879,f285]) ).

fof(f4651,plain,
    ( spl0_348
    | ~ spl0_44
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f900,f848,f396,f4649]) ).

fof(f4649,plain,
    ( spl0_348
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f900,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_44
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f397]) ).

fof(f4644,plain,
    ( spl0_347
    | ~ spl0_329
    | ~ spl0_346 ),
    inference(avatar_split_clause,[],[f4640,f4637,f3612,f4642]) ).

fof(f4640,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class) )
    | ~ spl0_329
    | ~ spl0_346 ),
    inference(forward_demodulation,[],[f4638,f3614]) ).

fof(f4639,plain,
    ( spl0_346
    | ~ spl0_93
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f1560,f1545,f701,f4637]) ).

fof(f1560,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class) )
    | ~ spl0_93
    | ~ spl0_175 ),
    inference(resolution,[],[f1546,f702]) ).

fof(f4186,plain,
    ( spl0_345
    | ~ spl0_120
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1259,f1216,f929,f4184]) ).

fof(f4184,plain,
    ( spl0_345
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f1259,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_120
    | ~ spl0_142 ),
    inference(duplicate_literal_removal,[],[f1245]) ).

fof(f1245,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_120
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f930]) ).

fof(f4178,plain,
    ( ~ spl0_343
    | spl0_344
    | ~ spl0_14
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1161,f1145,f232,f4175,f4171]) ).

fof(f4171,plain,
    ( spl0_343
  <=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f4175,plain,
    ( spl0_344
  <=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f1161,plain,
    ( null_class = cross_product(unordered_pair(null_class,null_class),universal_class)
    | ~ inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class))))
    | ~ spl0_14
    | ~ spl0_137 ),
    inference(resolution,[],[f1146,f233]) ).

fof(f4169,plain,
    ( spl0_342
    | ~ spl0_20
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1126,f1109,f257,f4167]) ).

fof(f1126,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) )
    | ~ spl0_20
    | ~ spl0_133 ),
    inference(resolution,[],[f1110,f258]) ).

fof(f4165,plain,
    ( spl0_341
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1114,f1102,f265,f4163]) ).

fof(f4163,plain,
    ( spl0_341
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f1114,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) )
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(resolution,[],[f1103,f266]) ).

fof(f4161,plain,
    ( spl0_340
    | ~ spl0_105
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1031,f999,f817,f4159]) ).

fof(f4159,plain,
    ( spl0_340
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f1031,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 )
    | ~ spl0_105
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f818]) ).

fof(f4157,plain,
    ( spl0_339
    | ~ spl0_37
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1024,f999,f339,f4155]) ).

fof(f4155,plain,
    ( spl0_339
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f1024,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_37
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f340]) ).

fof(f4153,plain,
    ( spl0_338
    | ~ spl0_105
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1014,f995,f817,f4151]) ).

fof(f4151,plain,
    ( spl0_338
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f1014,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 )
    | ~ spl0_105
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f818]) ).

fof(f4149,plain,
    ( spl0_337
    | ~ spl0_37
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1007,f995,f339,f4147]) ).

fof(f4147,plain,
    ( spl0_337
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f1007,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_37
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f340]) ).

fof(f4145,plain,
    ( spl0_336
    | ~ spl0_29
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f963,f925,f296,f4143]) ).

fof(f4143,plain,
    ( spl0_336
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f963,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_29
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f297]) ).

fof(f4141,plain,
    ( spl0_335
    | ~ spl0_251
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f3949,f3612,f2509,f4138]) ).

fof(f3949,plain,
    ( member(null_class,complement(null_class))
    | ~ spl0_251
    | ~ spl0_329 ),
    inference(superposition,[],[f2511,f3614]) ).

fof(f4136,plain,
    ( spl0_334
    | ~ spl0_30
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f962,f925,f300,f4134]) ).

fof(f4134,plain,
    ( spl0_334
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f962,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_30
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f301]) ).

fof(f4132,plain,
    ( spl0_333
    | ~ spl0_29
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f944,f921,f296,f4130]) ).

fof(f4130,plain,
    ( spl0_333
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f944,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_29
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f297]) ).

fof(f4128,plain,
    ( spl0_332
    | ~ spl0_30
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f943,f921,f300,f4126]) ).

fof(f4126,plain,
    ( spl0_332
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f943,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_30
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f301]) ).

fof(f4124,plain,
    ( spl0_331
    | ~ spl0_107
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f912,f874,f844,f4122]) ).

fof(f4122,plain,
    ( spl0_331
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f912,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) )
    | ~ spl0_107
    | ~ spl0_114 ),
    inference(resolution,[],[f875,f845]) ).

fof(f4120,plain,
    ( spl0_330
    | ~ spl0_44
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f783,f746,f396,f4118]) ).

fof(f4118,plain,
    ( spl0_330
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f783,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_44
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f397]) ).

fof(f3615,plain,
    ( spl0_329
    | ~ spl0_229
    | spl0_294 ),
    inference(avatar_split_clause,[],[f3550,f3238,f2238,f3612]) ).

fof(f3238,plain,
    ( spl0_294
  <=> member(null_class,unordered_pair(u,u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f3550,plain,
    ( null_class = unordered_pair(u,u)
    | ~ spl0_229
    | spl0_294 ),
    inference(resolution,[],[f2239,f3240]) ).

fof(f3240,plain,
    ( ~ member(null_class,unordered_pair(u,u))
    | spl0_294 ),
    inference(avatar_component_clause,[],[f3238]) ).

fof(f3590,plain,
    ( spl0_328
    | ~ spl0_99
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1537,f1512,f746,f3588]) ).

fof(f3588,plain,
    ( spl0_328
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f1537,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_99
    | ~ spl0_173 ),
    inference(superposition,[],[f747,f1513]) ).

fof(f3586,plain,
    ( spl0_327
    | ~ spl0_30
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1205,f1202,f300,f3584]) ).

fof(f3584,plain,
    ( spl0_327
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f1205,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_30
    | ~ spl0_140 ),
    inference(resolution,[],[f1203,f301]) ).

fof(f3582,plain,
    ( spl0_326
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1187,f1167,f3580]) ).

fof(f3580,plain,
    ( spl0_326
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f1187,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_138 ),
    inference(equality_factoring,[],[f1168]) ).

fof(f3578,plain,
    ( spl0_325
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1186,f1167,f3576]) ).

fof(f3576,plain,
    ( spl0_325
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f1186,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_138 ),
    inference(equality_factoring,[],[f1168]) ).

fof(f3574,plain,
    ( spl0_324
    | ~ spl0_124
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1158,f1141,f995,f3572]) ).

fof(f3572,plain,
    ( spl0_324
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f1141,plain,
    ( spl0_136
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1158,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_124
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1152]) ).

fof(f1152,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1))
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_124
    | ~ spl0_136 ),
    inference(resolution,[],[f1142,f996]) ).

fof(f1142,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1)) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1141]) ).

fof(f3548,plain,
    ( spl0_323
    | ~ spl0_125
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1157,f1141,f999,f3546]) ).

fof(f3546,plain,
    ( spl0_323
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f1157,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_125
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1153]) ).

fof(f1153,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1))
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_125
    | ~ spl0_136 ),
    inference(resolution,[],[f1142,f1000]) ).

fof(f3544,plain,
    ( spl0_322
    | ~ spl0_22
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1065,f1048,f265,f3542]) ).

fof(f3542,plain,
    ( spl0_322
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f1048,plain,
    ( spl0_127
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1065,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_22
    | ~ spl0_127 ),
    inference(resolution,[],[f1049,f266]) ).

fof(f1049,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1048]) ).

fof(f3540,plain,
    ( spl0_321
    | ~ spl0_20
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1030,f999,f257,f3538]) ).

fof(f1030,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_20
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f258]) ).

fof(f3536,plain,
    ( spl0_320
    | ~ spl0_20
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1013,f995,f257,f3534]) ).

fof(f1013,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_20
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f258]) ).

fof(f3532,plain,
    ( spl0_319
    | ~ spl0_105
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f983,f929,f817,f3530]) ).

fof(f3530,plain,
    ( spl0_319
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f983,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 )
    | ~ spl0_105
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f818]) ).

fof(f3528,plain,
    ( spl0_318
    | ~ spl0_37
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f976,f929,f339,f3526]) ).

fof(f3526,plain,
    ( spl0_318
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f976,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_37
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f340]) ).

fof(f3524,plain,
    ( spl0_317
    | ~ spl0_105
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f966,f925,f817,f3522]) ).

fof(f3522,plain,
    ( spl0_317
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f966,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 )
    | ~ spl0_105
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f818]) ).

fof(f3520,plain,
    ( spl0_316
    | ~ spl0_37
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f959,f925,f339,f3518]) ).

fof(f3518,plain,
    ( spl0_316
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f959,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_37
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f340]) ).

fof(f3516,plain,
    ( spl0_315
    | ~ spl0_105
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f947,f921,f817,f3514]) ).

fof(f3514,plain,
    ( spl0_315
  <=> ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f947,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 )
    | ~ spl0_105
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f818]) ).

fof(f3512,plain,
    ( spl0_314
    | ~ spl0_37
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f940,f921,f339,f3510]) ).

fof(f3510,plain,
    ( spl0_314
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f940,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_37
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f340]) ).

fof(f3508,plain,
    ( spl0_313
    | ~ spl0_104
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f913,f874,f813,f3506]) ).

fof(f3506,plain,
    ( spl0_313
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f913,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) )
    | ~ spl0_104
    | ~ spl0_114 ),
    inference(resolution,[],[f875,f814]) ).

fof(f3504,plain,
    ( spl0_312
    | ~ spl0_101
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f885,f844,f754,f3502]) ).

fof(f885,plain,
    ( ! [X0] :
        ( subclass(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) )
    | ~ spl0_101
    | ~ spl0_107 ),
    inference(resolution,[],[f845,f755]) ).

fof(f3500,plain,
    ( spl0_311
    | ~ spl0_60
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f800,f754,f488,f3498]) ).

fof(f3498,plain,
    ( spl0_311
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f800,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_60
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f489]) ).

fof(f3496,plain,
    ( spl0_310
    | ~ spl0_61
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f799,f754,f492,f3494]) ).

fof(f3494,plain,
    ( spl0_310
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f799,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_61
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f493]) ).

fof(f3492,plain,
    ( spl0_309
    | ~ spl0_54
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f761,f742,f458,f3490]) ).

fof(f3490,plain,
    ( spl0_309
  <=> ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f761,plain,
    ( ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_54
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f459]) ).

fof(f3379,plain,
    ( ~ spl0_308
    | ~ spl0_14
    | spl0_294 ),
    inference(avatar_split_clause,[],[f3281,f3238,f232,f3376]) ).

fof(f3376,plain,
    ( spl0_308
  <=> inductive(unordered_pair(u,u)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f3281,plain,
    ( ~ inductive(unordered_pair(u,u))
    | ~ spl0_14
    | spl0_294 ),
    inference(resolution,[],[f3240,f233]) ).

fof(f3301,plain,
    ( spl0_307
    | ~ spl0_120
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1156,f1141,f929,f3299]) ).

fof(f1156,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_120
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1154]) ).

fof(f1154,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_120
    | ~ spl0_136 ),
    inference(resolution,[],[f1142,f930]) ).

fof(f3297,plain,
    ( spl0_306
    | ~ spl0_29
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f980,f929,f296,f3295]) ).

fof(f3295,plain,
    ( spl0_306
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f980,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_29
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f297]) ).

fof(f3293,plain,
    ( spl0_305
    | ~ spl0_30
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f979,f929,f300,f3291]) ).

fof(f3291,plain,
    ( spl0_305
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f979,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_30
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f301]) ).

fof(f3289,plain,
    ( spl0_304
    | ~ spl0_20
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f965,f925,f257,f3287]) ).

fof(f965,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_20
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f258]) ).

fof(f3285,plain,
    ( spl0_303
    | ~ spl0_20
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f946,f921,f257,f3283]) ).

fof(f946,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_20
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f258]) ).

fof(f3280,plain,
    ( spl0_302
    | ~ spl0_37
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f914,f878,f339,f3278]) ).

fof(f3278,plain,
    ( spl0_302
  <=> ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f914,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_37
    | ~ spl0_115 ),
    inference(resolution,[],[f879,f340]) ).

fof(f3276,plain,
    ( spl0_301
    | ~ spl0_26
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f911,f874,f284,f3274]) ).

fof(f3274,plain,
    ( spl0_301
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f911,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_26
    | ~ spl0_114 ),
    inference(resolution,[],[f875,f285]) ).

fof(f3272,plain,
    ( spl0_300
    | ~ spl0_37
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f910,f874,f339,f3270]) ).

fof(f3270,plain,
    ( spl0_300
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f910,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_37
    | ~ spl0_114 ),
    inference(resolution,[],[f875,f340]) ).

fof(f3268,plain,
    ( spl0_299
    | ~ spl0_105
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f906,f848,f817,f3266]) ).

fof(f3266,plain,
    ( spl0_299
  <=> ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f906,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 )
    | ~ spl0_105
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f818]) ).

fof(f3264,plain,
    ( spl0_298
    | ~ spl0_37
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f899,f848,f339,f3262]) ).

fof(f3262,plain,
    ( spl0_298
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f899,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_37
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f340]) ).

fof(f3258,plain,
    ( ~ spl0_296
    | spl0_297
    | ~ spl0_101
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f824,f813,f754,f3255,f3251]) ).

fof(f824,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | ~ spl0_101
    | ~ spl0_104 ),
    inference(resolution,[],[f814,f755]) ).

fof(f3245,plain,
    ( spl0_295
    | spl0_286
    | ~ spl0_48
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f768,f742,f412,f3029,f3243]) ).

fof(f3243,plain,
    ( spl0_295
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f412,plain,
    ( spl0_48
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f768,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_48
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f413]) ).

fof(f413,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f412]) ).

fof(f3241,plain,
    ( ~ spl0_294
    | ~ spl0_20
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f3187,f2509,f257,f3238]) ).

fof(f3187,plain,
    ( ~ member(null_class,unordered_pair(u,u))
    | ~ spl0_20
    | ~ spl0_251 ),
    inference(resolution,[],[f2511,f258]) ).

fof(f3223,plain,
    ( spl0_293
    | ~ spl0_93
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1029,f999,f701,f3221]) ).

fof(f1029,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1)
        | ~ member(not_subclass_element(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),X1),null_class) )
    | ~ spl0_93
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f702]) ).

fof(f3219,plain,
    ( spl0_292
    | ~ spl0_93
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1012,f995,f701,f3217]) ).

fof(f1012,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1)
        | ~ member(not_subclass_element(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),X1),null_class) )
    | ~ spl0_93
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f702]) ).

fof(f3204,plain,
    ( spl0_291
    | ~ spl0_93
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f964,f925,f701,f3202]) ).

fof(f964,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(regular(intersection(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),null_class) )
    | ~ spl0_93
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f702]) ).

fof(f3200,plain,
    ( spl0_290
    | ~ spl0_93
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f945,f921,f701,f3198]) ).

fof(f945,plain,
    ( ! [X0] :
        ( null_class = intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)
        | ~ member(regular(intersection(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0)),null_class) )
    | ~ spl0_93
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f702]) ).

fof(f3045,plain,
    ( spl0_289
    | ~ spl0_8
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1270,f1233,f206,f3043]) ).

fof(f3043,plain,
    ( spl0_289
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f1233,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1270,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_8
    | ~ spl0_146 ),
    inference(resolution,[],[f1234,f207]) ).

fof(f1234,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1)))
        | ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,X1) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1233]) ).

fof(f3041,plain,
    ( spl0_288
    | ~ spl0_54
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1269,f1233,f458,f3039]) ).

fof(f3039,plain,
    ( spl0_288
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f1269,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_54
    | ~ spl0_146 ),
    inference(resolution,[],[f1234,f459]) ).

fof(f3037,plain,
    ( spl0_287
    | ~ spl0_25
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1262,f1216,f280,f3035]) ).

fof(f3035,plain,
    ( spl0_287
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f1262,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_25
    | ~ spl0_142 ),
    inference(duplicate_literal_removal,[],[f1242]) ).

fof(f1242,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0))
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_25
    | ~ spl0_142 ),
    inference(resolution,[],[f1217,f281]) ).

fof(f3032,plain,
    ( ~ spl0_285
    | spl0_286
    | ~ spl0_200
    | ~ spl0_14
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1085,f1056,f232,f1896,f3029,f3025]) ).

fof(f3025,plain,
    ( spl0_285
  <=> inductive(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f1085,plain,
    ( ~ member(null_class,subset_relation)
    | member(null_class,identity_relation)
    | ~ inductive(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_14
    | ~ spl0_129 ),
    inference(resolution,[],[f1057,f233]) ).

fof(f3019,plain,
    ( spl0_284
    | spl0_218
    | ~ spl0_14
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1070,f1052,f232,f2110,f3017]) ).

fof(f3017,plain,
    ( spl0_284
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f1070,plain,
    ( ! [X0] :
        ( member(null_class,null_class)
        | ~ member(null_class,X0)
        | null_class = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_14
    | ~ spl0_128 ),
    inference(resolution,[],[f1053,f233]) ).

fof(f3015,plain,
    ( spl0_283
    | ~ spl0_92
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1033,f999,f686,f3013]) ).

fof(f1033,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_92
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f687]) ).

fof(f3011,plain,
    ( spl0_282
    | ~ spl0_40
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1019,f995,f351,f3009]) ).

fof(f3009,plain,
    ( spl0_282
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f1019,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_40
    | ~ spl0_124 ),
    inference(superposition,[],[f996,f353]) ).

fof(f3006,plain,
    ( spl0_281
    | ~ spl0_92
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1016,f995,f686,f3004]) ).

fof(f1016,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_92
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f687]) ).

fof(f3002,plain,
    ( spl0_280
    | ~ spl0_22
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f993,f937,f265,f3000]) ).

fof(f3000,plain,
    ( spl0_280
  <=> ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f993,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_22
    | ~ spl0_122 ),
    inference(resolution,[],[f938,f266]) ).

fof(f2998,plain,
    ( spl0_279
    | ~ spl0_22
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f990,f933,f265,f2996]) ).

fof(f2996,plain,
    ( spl0_279
  <=> ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f990,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_121 ),
    inference(resolution,[],[f934,f266]) ).

fof(f2994,plain,
    ( spl0_278
    | ~ spl0_20
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f982,f929,f257,f2992]) ).

fof(f982,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_20
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f258]) ).

fof(f2990,plain,
    ( spl0_277
    | ~ spl0_29
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f903,f848,f296,f2988]) ).

fof(f2988,plain,
    ( spl0_277
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f903,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_29
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f297]) ).

fof(f2986,plain,
    ( spl0_276
    | ~ spl0_30
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f902,f848,f300,f2984]) ).

fof(f2984,plain,
    ( spl0_276
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f902,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_30
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f301]) ).

fof(f2982,plain,
    ( spl0_275
    | ~ spl0_26
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f797,f754,f284,f2980]) ).

fof(f797,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_26
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f285]) ).

fof(f2969,plain,
    ( spl0_274
    | ~ spl0_93
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1433,f1425,f701,f2967]) ).

fof(f1433,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class) )
    | ~ spl0_93
    | ~ spl0_168 ),
    inference(resolution,[],[f1426,f702]) ).

fof(f2965,plain,
    ( ~ spl0_218
    | ~ spl0_35
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f2419,f701,f330,f2110]) ).

fof(f2419,plain,
    ( ~ member(null_class,null_class)
    | ~ spl0_35
    | ~ spl0_93 ),
    inference(resolution,[],[f331,f702]) ).

fof(f2964,plain,
    ( spl0_273
    | ~ spl0_25
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f705,f701,f280,f2962]) ).

fof(f705,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0),null_class)
        | subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X0) )
    | ~ spl0_25
    | ~ spl0_93 ),
    inference(resolution,[],[f702,f281]) ).

fof(f2959,plain,
    ( spl0_271
    | ~ spl0_272
    | ~ spl0_23
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f708,f701,f269,f2956,f2952]) ).

fof(f2952,plain,
    ( spl0_271
  <=> null_class = intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f708,plain,
    ( ~ member(regular(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),null_class)
    | null_class = intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))
    | ~ spl0_23
    | ~ spl0_93 ),
    inference(resolution,[],[f702,f270]) ).

fof(f2881,plain,
    ( spl0_270
    | ~ spl0_11
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1533,f1512,f218,f2879]) ).

fof(f2879,plain,
    ( spl0_270
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f1533,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_11
    | ~ spl0_173 ),
    inference(superposition,[],[f219,f1513]) ).

fof(f2877,plain,
    ( spl0_269
    | ~ spl0_92
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f985,f929,f686,f2875]) ).

fof(f2875,plain,
    ( spl0_269
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f985,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_92
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f687]) ).

fof(f2873,plain,
    ( spl0_268
    | ~ spl0_92
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f968,f925,f686,f2871]) ).

fof(f968,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_92
    | ~ spl0_119 ),
    inference(resolution,[],[f926,f687]) ).

fof(f2858,plain,
    ( ~ spl0_218
    | spl0_35
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f2857,f2238,f330,f2110]) ).

fof(f2857,plain,
    ( ~ member(null_class,null_class)
    | spl0_35
    | ~ spl0_229 ),
    inference(forward_demodulation,[],[f332,f2315]) ).

fof(f2315,plain,
    ( null_class = intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))
    | spl0_35
    | ~ spl0_229 ),
    inference(resolution,[],[f2239,f332]) ).

fof(f332,plain,
    ( ~ member(null_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
    | spl0_35 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f2855,plain,
    ( spl0_267
    | ~ spl0_35
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2850,f2119,f330,f2852]) ).

fof(f2852,plain,
    ( spl0_267
  <=> member(identity_relation,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(identity_relation))))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2850,plain,
    ( member(identity_relation,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(identity_relation)))))))))
    | ~ spl0_35
    | ~ spl0_219 ),
    inference(forward_demodulation,[],[f331,f2121]) ).

fof(f2121,plain,
    ( null_class = identity_relation
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2119]) ).

fof(f2808,plain,
    ( spl0_266
    | ~ spl0_218
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2784,f2119,f2110,f2805]) ).

fof(f2805,plain,
    ( spl0_266
  <=> member(identity_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f2784,plain,
    ( member(identity_relation,identity_relation)
    | ~ spl0_218
    | ~ spl0_219 ),
    inference(superposition,[],[f2112,f2121]) ).

fof(f2112,plain,
    ( member(null_class,null_class)
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f2110]) ).

fof(f2764,plain,
    ( spl0_219
    | spl0_265
    | ~ spl0_40
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f952,f921,f351,f2761,f2119]) ).

fof(f2761,plain,
    ( spl0_265
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f952,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ spl0_40
    | ~ spl0_118 ),
    inference(superposition,[],[f922,f353]) ).

fof(f2759,plain,
    ( spl0_264
    | ~ spl0_92
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f949,f921,f686,f2757]) ).

fof(f949,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) )
    | ~ spl0_92
    | ~ spl0_118 ),
    inference(resolution,[],[f922,f687]) ).

fof(f2755,plain,
    ( spl0_263
    | ~ spl0_20
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f905,f848,f257,f2753]) ).

fof(f905,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_20
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f258]) ).

fof(f2751,plain,
    ( spl0_262
    | ~ spl0_37
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f796,f754,f339,f2749]) ).

fof(f796,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_37
    | ~ spl0_101 ),
    inference(resolution,[],[f755,f340]) ).

fof(f2747,plain,
    ( spl0_261
    | ~ spl0_37
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f782,f746,f339,f2745]) ).

fof(f2745,plain,
    ( spl0_261
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f782,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_37
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f340]) ).

fof(f2688,plain,
    ( spl0_260
    | ~ spl0_25
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1159,f1141,f280,f2686]) ).

fof(f1159,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_25
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1151]) ).

fof(f1151,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_25
    | ~ spl0_136 ),
    inference(resolution,[],[f1142,f281]) ).

fof(f2684,plain,
    ( spl0_259
    | ~ spl0_67
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1021,f995,f533,f2682]) ).

fof(f1021,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_67
    | ~ spl0_124 ),
    inference(superposition,[],[f996,f535]) ).

fof(f2680,plain,
    ( spl0_258
    | ~ spl0_92
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f908,f848,f686,f2678]) ).

fof(f2678,plain,
    ( spl0_258
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f908,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) )
    | ~ spl0_92
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f687]) ).

fof(f2676,plain,
    ( spl0_257
    | ~ spl0_29
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f786,f746,f296,f2674]) ).

fof(f2674,plain,
    ( spl0_257
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f786,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_29
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f297]) ).

fof(f2672,plain,
    ( spl0_256
    | ~ spl0_30
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f785,f746,f300,f2670]) ).

fof(f2670,plain,
    ( spl0_256
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f785,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_30
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f301]) ).

fof(f2650,plain,
    ( spl0_254
    | ~ spl0_248
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f2649,f2635,f2433,f2641]) ).

fof(f2641,plain,
    ( spl0_254
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f2649,plain,
    ( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_248
    | ~ spl0_253 ),
    inference(forward_demodulation,[],[f2637,f2435]) ).

fof(f2648,plain,
    ( spl0_255
    | spl0_253
    | ~ spl0_32
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f764,f742,f308,f2635,f2646]) ).

fof(f2646,plain,
    ( spl0_255
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f764,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_32
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f309]) ).

fof(f2644,plain,
    ( ~ spl0_254
    | ~ spl0_248
    | spl0_253 ),
    inference(avatar_split_clause,[],[f2639,f2635,f2433,f2641]) ).

fof(f2639,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_248
    | spl0_253 ),
    inference(forward_demodulation,[],[f2636,f2435]) ).

fof(f2638,plain,
    ( spl0_252
    | spl0_253
    | ~ spl0_31
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f763,f742,f304,f2635,f2632]) ).

fof(f2632,plain,
    ( spl0_252
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f763,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_31
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f305]) ).

fof(f2512,plain,
    ( spl0_251
    | ~ spl0_29
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f2421,f330,f296,f2509]) ).

fof(f2421,plain,
    ( member(null_class,complement(unordered_pair(u,u)))
    | ~ spl0_29
    | ~ spl0_35 ),
    inference(resolution,[],[f331,f297]) ).

fof(f2471,plain,
    ( spl0_250
    | ~ spl0_6
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1112,f1102,f197,f2469]) ).

fof(f1112,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_6
    | ~ spl0_132 ),
    inference(resolution,[],[f1103,f198]) ).

fof(f2440,plain,
    ( spl0_248
    | spl0_249
    | ~ spl0_67
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f954,f921,f533,f2437,f2433]) ).

fof(f954,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_67
    | ~ spl0_118 ),
    inference(superposition,[],[f922,f535]) ).

fof(f2431,plain,
    ( spl0_247
    | ~ spl0_20
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f788,f746,f257,f2429]) ).

fof(f788,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_20
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f258]) ).

fof(f2413,plain,
    ( spl0_246
    | spl0_158
    | ~ spl0_21
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f767,f742,f261,f1350,f2411]) ).

fof(f2411,plain,
    ( spl0_246
  <=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f767,plain,
    ( ! [X0,X1] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f262]) ).

fof(f2402,plain,
    ( spl0_245
    | ~ spl0_37
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f2391,f1350,f339,f2400]) ).

fof(f2391,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_37
    | ~ spl0_158 ),
    inference(resolution,[],[f1351,f340]) ).

fof(f2396,plain,
    ( ~ spl0_244
    | ~ spl0_101
    | spl0_243 ),
    inference(avatar_split_clause,[],[f2388,f2384,f754,f2393]) ).

fof(f2393,plain,
    ( spl0_244
  <=> member(subset_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f2388,plain,
    ( ~ member(subset_relation,subset_relation)
    | ~ spl0_101
    | spl0_243 ),
    inference(resolution,[],[f2385,f755]) ).

fof(f2387,plain,
    ( spl0_243
    | ~ spl0_158
    | spl0_200
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f2382,f2238,f1896,f1350,f2384]) ).

fof(f2382,plain,
    ( member(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_158
    | spl0_200
    | ~ spl0_229 ),
    inference(forward_demodulation,[],[f1351,f2316]) ).

fof(f2316,plain,
    ( null_class = subset_relation
    | spl0_200
    | ~ spl0_229 ),
    inference(resolution,[],[f2239,f1898]) ).

fof(f1898,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_200 ),
    inference(avatar_component_clause,[],[f1896]) ).

fof(f2371,plain,
    ( spl0_242
    | spl0_158
    | ~ spl0_22
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f759,f742,f265,f1350,f2369]) ).

fof(f759,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f266]) ).

fof(f2304,plain,
    ( spl0_241
    | ~ spl0_16
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1155,f1141,f240,f2302]) ).

fof(f2302,plain,
    ( spl0_241
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,null_class),universal_class)
        | member(not_subclass_element(X0,null_class),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(X0,null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f1155,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,null_class),universal_class)
        | member(not_subclass_element(X0,null_class),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(X0,null_class) )
    | ~ spl0_16
    | ~ spl0_136 ),
    inference(superposition,[],[f1142,f242]) ).

fof(f2285,plain,
    ( spl0_240
    | ~ spl0_107
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f986,f929,f844,f2283]) ).

fof(f986,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_107
    | ~ spl0_120 ),
    inference(duplicate_literal_removal,[],[f975]) ).

fof(f975,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_107
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f845]) ).

fof(f2281,plain,
    ( spl0_239
    | ~ spl0_37
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2171,f2110,f339,f2279]) ).

fof(f2171,plain,
    ( ! [X0] :
        ( ~ subclass(null_class,X0)
        | member(null_class,X0) )
    | ~ spl0_37
    | ~ spl0_218 ),
    inference(resolution,[],[f2112,f340]) ).

fof(f2277,plain,
    ( spl0_238
    | ~ spl0_104
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f909,f848,f813,f2275]) ).

fof(f909,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_104
    | ~ spl0_108 ),
    inference(duplicate_literal_removal,[],[f898]) ).

fof(f898,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_104
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f814]) ).

fof(f2273,plain,
    ( spl0_237
    | ~ spl0_21
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f842,f821,f261,f2271]) ).

fof(f2271,plain,
    ( spl0_237
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f842,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_106 ),
    inference(resolution,[],[f822,f262]) ).

fof(f2269,plain,
    ( ~ spl0_235
    | spl0_236
    | ~ spl0_8
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f837,f821,f206,f2266,f2262]) ).

fof(f2262,plain,
    ( spl0_235
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f2266,plain,
    ( spl0_236
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f837,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_8
    | ~ spl0_106 ),
    inference(resolution,[],[f822,f207]) ).

fof(f2260,plain,
    ( spl0_233
    | ~ spl0_234
    | ~ spl0_92
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f790,f746,f686,f2257,f2254]) ).

fof(f2254,plain,
    ( spl0_233
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f2257,plain,
    ( spl0_234
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f790,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_92
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f687]) ).

fof(f2252,plain,
    ( spl0_232
    | ~ spl0_60
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f771,f746,f488,f2250]) ).

fof(f2250,plain,
    ( spl0_232
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f771,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_60
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f489]) ).

fof(f2248,plain,
    ( spl0_231
    | ~ spl0_61
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f770,f746,f492,f2246]) ).

fof(f2246,plain,
    ( spl0_231
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f770,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_61
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f493]) ).

fof(f2244,plain,
    ( spl0_230
    | ~ spl0_25
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f696,f686,f280,f2242]) ).

fof(f696,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_25
    | ~ spl0_92 ),
    inference(resolution,[],[f687,f281]) ).

fof(f2240,plain,
    ( spl0_229
    | ~ spl0_105
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2169,f2110,f817,f2238]) ).

fof(f2169,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_105
    | ~ spl0_218 ),
    inference(resolution,[],[f2112,f818]) ).

fof(f2236,plain,
    ( spl0_228
    | ~ spl0_34
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f666,f662,f317,f2234]) ).

fof(f2234,plain,
    ( spl0_228
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f662,plain,
    ( spl0_87
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f666,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_34
    | ~ spl0_87 ),
    inference(resolution,[],[f663,f318]) ).

fof(f663,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f662]) ).

fof(f2199,plain,
    ( spl0_227
    | ~ spl0_16
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1066,f1048,f240,f2197]) ).

fof(f2197,plain,
    ( spl0_227
  <=> ! [X0,X1] :
        ( ~ subclass(null_class,X0)
        | ~ member(X1,universal_class)
        | member(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f1066,plain,
    ( ! [X0,X1] :
        ( ~ subclass(null_class,X0)
        | ~ member(X1,universal_class)
        | member(X1,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | member(X1,X0) )
    | ~ spl0_16
    | ~ spl0_127 ),
    inference(superposition,[],[f1049,f242]) ).

fof(f2195,plain,
    ( spl0_226
    | ~ spl0_37
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f739,f728,f339,f2193]) ).

fof(f2193,plain,
    ( spl0_226
  <=> ! [X0,X1] :
        ( member(X0,null_class)
        | ~ member(X0,universal_class)
        | ~ subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f739,plain,
    ( ! [X0,X1] :
        ( member(X0,null_class)
        | ~ member(X0,universal_class)
        | ~ subclass(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),X1)
        | member(X0,X1) )
    | ~ spl0_37
    | ~ spl0_96 ),
    inference(resolution,[],[f729,f340]) ).

fof(f2184,plain,
    ( spl0_225
    | ~ spl0_93
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f981,f929,f701,f2182]) ).

fof(f981,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),null_class) )
    | ~ spl0_93
    | ~ spl0_120 ),
    inference(resolution,[],[f930,f702]) ).

fof(f2168,plain,
    ( spl0_224
    | ~ spl0_219
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2164,f2159,f2119,f2166]) ).

fof(f2166,plain,
    ( spl0_224
  <=> ! [X0] :
        ( ~ member(regular(X0),identity_relation)
        | identity_relation = X0
        | ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(identity_relation))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f2164,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),identity_relation)
        | identity_relation = X0
        | ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(identity_relation))))))))) )
    | ~ spl0_219
    | ~ spl0_223 ),
    inference(forward_demodulation,[],[f2163,f2121]) ).

fof(f2163,plain,
    ( ! [X0] :
        ( identity_relation = X0
        | ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(identity_relation)))))))))
        | ~ member(regular(X0),null_class) )
    | ~ spl0_219
    | ~ spl0_223 ),
    inference(forward_demodulation,[],[f2162,f2121]) ).

fof(f2162,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(identity_relation)))))))))
        | null_class = X0
        | ~ member(regular(X0),null_class) )
    | ~ spl0_219
    | ~ spl0_223 ),
    inference(forward_demodulation,[],[f2160,f2121]) ).

fof(f2161,plain,
    ( spl0_223
    | ~ spl0_93
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f904,f848,f701,f2159]) ).

fof(f904,plain,
    ( ! [X0] :
        ( ~ subclass(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | null_class = X0
        | ~ member(regular(X0),null_class) )
    | ~ spl0_93
    | ~ spl0_108 ),
    inference(resolution,[],[f849,f702]) ).

fof(f2157,plain,
    ( ~ spl0_222
    | spl0_158
    | ~ spl0_13
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f765,f742,f227,f1350,f2154]) ).

fof(f2154,plain,
    ( spl0_222
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f765,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_13
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f229]) ).

fof(f2152,plain,
    ( ~ spl0_221
    | spl0_158
    | ~ spl0_12
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f760,f742,f222,f1350,f2149]) ).

fof(f2149,plain,
    ( spl0_221
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f222,plain,
    ( spl0_12
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f760,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(element_relation)
    | ~ spl0_12
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f224]) ).

fof(f224,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f222]) ).

fof(f2126,plain,
    ( spl0_219
    | spl0_220
    | ~ spl0_23
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f699,f686,f269,f2123,f2119]) ).

fof(f699,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_23
    | ~ spl0_92 ),
    inference(resolution,[],[f687,f270]) ).

fof(f2113,plain,
    ( ~ spl0_88
    | spl0_218
    | spl0_35
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1963,f728,f330,f2110,f668]) ).

fof(f1963,plain,
    ( member(null_class,null_class)
    | ~ member(null_class,universal_class)
    | spl0_35
    | ~ spl0_96 ),
    inference(resolution,[],[f332,f729]) ).

fof(f2108,plain,
    ( spl0_217
    | ~ spl0_16
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f890,f844,f240,f2106]) ).

fof(f2106,plain,
    ( spl0_217
  <=> ! [X0] :
        ( ~ member(not_subclass_element(null_class,X0),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f890,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(null_class,X0),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | subclass(null_class,X0) )
    | ~ spl0_16
    | ~ spl0_107 ),
    inference(superposition,[],[f845,f242]) ).

fof(f2104,plain,
    ( spl0_215
    | ~ spl0_216
    | ~ spl0_93
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f787,f746,f701,f2101,f2098]) ).

fof(f2101,plain,
    ( spl0_216
  <=> subclass(universal_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f787,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(unordered_pair(X0,X1),null_class) )
    | ~ spl0_93
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f702]) ).

fof(f2076,plain,
    ( spl0_214
    | ~ spl0_45
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f704,f701,f400,f2074]) ).

fof(f2074,plain,
    ( spl0_214
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))
        | ~ member(X0,complement(unordered_pair(u,u))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f704,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))
        | ~ member(X0,complement(unordered_pair(u,u))) )
    | ~ spl0_45
    | ~ spl0_93 ),
    inference(resolution,[],[f702,f401]) ).

fof(f1995,plain,
    ( ~ spl0_4
    | ~ spl0_206 ),
    inference(avatar_contradiction_clause,[],[f1992]) ).

fof(f1992,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_206 ),
    inference(resolution,[],[f1926,f189]) ).

fof(f1926,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_206 ),
    inference(avatar_component_clause,[],[f1925]) ).

fof(f1925,plain,
    ( spl0_206
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f1994,plain,
    ( ~ spl0_89
    | ~ spl0_206 ),
    inference(avatar_contradiction_clause,[],[f1993]) ).

fof(f1993,plain,
    ( $false
    | ~ spl0_89
    | ~ spl0_206 ),
    inference(resolution,[],[f1926,f674]) ).

fof(f674,plain,
    ( inductive(universal_class)
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f672]) ).

fof(f1991,plain,
    ( spl0_213
    | ~ spl0_37
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f1929,f668,f339,f1989]) ).

fof(f1989,plain,
    ( spl0_213
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f1929,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_37
    | ~ spl0_88 ),
    inference(resolution,[],[f669,f340]) ).

fof(f1987,plain,
    ( spl0_211
    | ~ spl0_212
    | ~ spl0_56
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f773,f746,f471,f1984,f1981]) ).

fof(f1981,plain,
    ( spl0_211
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f1984,plain,
    ( spl0_212
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f773,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_56
    | ~ spl0_99 ),
    inference(resolution,[],[f747,f472]) ).

fof(f1969,plain,
    ( spl0_210
    | ~ spl0_30
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f737,f728,f300,f1967]) ).

fof(f1967,plain,
    ( spl0_210
  <=> ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,universal_class)
        | member(X0,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f737,plain,
    ( ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,universal_class)
        | member(X0,complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))) )
    | ~ spl0_30
    | ~ spl0_96 ),
    inference(resolution,[],[f729,f301]) ).

fof(f1942,plain,
    ( spl0_209
    | ~ spl0_26
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1039,f999,f284,f1940]) ).

fof(f1039,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_26
    | ~ spl0_125 ),
    inference(duplicate_literal_removal,[],[f1023]) ).

fof(f1023,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_26
    | ~ spl0_125 ),
    inference(resolution,[],[f1000,f285]) ).

fof(f1938,plain,
    ( ~ spl0_208
    | ~ spl0_14
    | spl0_200 ),
    inference(avatar_split_clause,[],[f1900,f1896,f232,f1935]) ).

fof(f1935,plain,
    ( spl0_208
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f1900,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_14
    | spl0_200 ),
    inference(resolution,[],[f1898,f233]) ).

fof(f1933,plain,
    ( spl0_207
    | ~ spl0_26
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1022,f995,f284,f1931]) ).

fof(f1022,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_26
    | ~ spl0_124 ),
    inference(duplicate_literal_removal,[],[f1006]) ).

fof(f1006,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_26
    | ~ spl0_124 ),
    inference(resolution,[],[f996,f285]) ).

fof(f1927,plain,
    ( spl0_206
    | spl0_88
    | ~ spl0_6
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f757,f742,f197,f668,f1925]) ).

fof(f757,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_6
    | ~ spl0_98 ),
    inference(resolution,[],[f743,f198]) ).

fof(f1923,plain,
    ( ~ spl0_205
    | spl0_200
    | ~ spl0_14
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f697,f686,f232,f1896,f1920]) ).

fof(f1920,plain,
    ( spl0_205
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f697,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_14
    | ~ spl0_92 ),
    inference(resolution,[],[f687,f233]) ).

fof(f1918,plain,
    ( ~ spl0_203
    | spl0_204
    | ~ spl0_13
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f840,f821,f227,f1915,f1911]) ).

fof(f1911,plain,
    ( spl0_203
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1915,plain,
    ( spl0_204
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f840,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_13
    | ~ spl0_106 ),
    inference(resolution,[],[f822,f229]) ).

fof(f1909,plain,
    ( ~ spl0_201
    | spl0_202
    | ~ spl0_12
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f838,f821,f222,f1906,f1902]) ).

fof(f838,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_12
    | ~ spl0_106 ),
    inference(resolution,[],[f822,f224]) ).

fof(f1899,plain,
    ( ~ spl0_200
    | ~ spl0_101
    | spl0_158 ),
    inference(avatar_split_clause,[],[f1358,f1350,f754,f1896]) ).

fof(f1358,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_101
    | spl0_158 ),
    inference(resolution,[],[f1352,f755]) ).

fof(f1884,plain,
    ( spl0_199
    | ~ spl0_29
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f738,f728,f296,f1882]) ).

fof(f738,plain,
    ( ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,universal_class)
        | member(X0,complement(unordered_pair(u,u))) )
    | ~ spl0_29
    | ~ spl0_96 ),
    inference(resolution,[],[f729,f297]) ).

fof(f1879,plain,
    ( ~ spl0_198
    | ~ spl0_99
    | spl0_187 ),
    inference(avatar_split_clause,[],[f1755,f1748,f746,f1876]) ).

fof(f1876,plain,
    ( spl0_198
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f1755,plain,
    ( ~ subclass(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_99
    | spl0_187 ),
    inference(resolution,[],[f1750,f747]) ).

fof(f1865,plain,
    ( spl0_197
    | ~ spl0_77
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f604,f600,f595,f1863]) ).

fof(f604,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_77
    | ~ spl0_78 ),
    inference(resolution,[],[f601,f596]) ).

fof(f1861,plain,
    ( spl0_196
    | ~ spl0_46
    | ~ spl0_77
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f648,f643,f595,f404,f1859]) ).

fof(f1859,plain,
    ( spl0_196
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f648,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_46
    | ~ spl0_77
    | ~ spl0_84 ),
    inference(forward_demodulation,[],[f646,f405]) ).

fof(f646,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_77
    | ~ spl0_84 ),
    inference(resolution,[],[f644,f596]) ).

fof(f1853,plain,
    ( spl0_195
    | ~ spl0_63
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f647,f643,f500,f1851]) ).

fof(f647,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_63
    | ~ spl0_84 ),
    inference(resolution,[],[f644,f501]) ).

fof(f1840,plain,
    ( spl0_194
    | ~ spl0_74
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f607,f600,f575,f1838]) ).

fof(f607,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_74
    | ~ spl0_78 ),
    inference(resolution,[],[f601,f576]) ).

fof(f1836,plain,
    ( spl0_193
    | ~ spl0_71
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f580,f575,f558,f1834]) ).

fof(f580,plain,
    ( ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
    | ~ spl0_71
    | ~ spl0_74 ),
    inference(resolution,[],[f576,f559]) ).

fof(f1823,plain,
    ( spl0_192
    | ~ spl0_25
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f605,f600,f280,f1821]) ).

fof(f605,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_25
    | ~ spl0_78 ),
    inference(resolution,[],[f601,f281]) ).

fof(f1819,plain,
    ( ~ spl0_191
    | ~ spl0_99
    | spl0_186 ),
    inference(avatar_split_clause,[],[f1752,f1744,f746,f1816]) ).

fof(f1816,plain,
    ( spl0_191
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1744,plain,
    ( spl0_186
  <=> member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f1752,plain,
    ( ~ subclass(universal_class,successor_relation)
    | ~ spl0_99
    | spl0_186 ),
    inference(resolution,[],[f1745,f747]) ).

fof(f1745,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),successor_relation)
    | spl0_186 ),
    inference(avatar_component_clause,[],[f1744]) ).

fof(f1805,plain,
    ( spl0_190
    | ~ spl0_23
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f608,f600,f269,f1803]) ).

fof(f608,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_78 ),
    inference(resolution,[],[f601,f270]) ).

fof(f1763,plain,
    ( spl0_189
    | ~ spl0_68
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f641,f637,f538,f1761]) ).

fof(f641,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_68
    | ~ spl0_83 ),
    inference(resolution,[],[f638,f539]) ).

fof(f1759,plain,
    ( spl0_188
    | ~ spl0_68
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f640,f633,f538,f1757]) ).

fof(f640,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_68
    | ~ spl0_82 ),
    inference(resolution,[],[f634,f539]) ).

fof(f1751,plain,
    ( spl0_186
    | ~ spl0_187
    | ~ spl0_16
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f620,f616,f240,f1748,f1744]) ).

fof(f620,plain,
    ( ~ member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),cross_product(universal_class,universal_class))
    | member(unordered_pair(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),unordered_pair(complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))))),complement(intersection(null_class,complement(unordered_pair(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))))))))),successor_relation)
    | ~ spl0_16
    | ~ spl0_79 ),
    inference(superposition,[],[f617,f242]) ).

fof(f1696,plain,
    ( spl0_185
    | ~ spl0_5
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f665,f662,f192,f1693]) ).

fof(f1693,plain,
    ( spl0_185
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f665,plain,
    ( single_valued_class(choice)
    | ~ spl0_5
    | ~ spl0_87 ),
    inference(resolution,[],[f663,f194]) ).

fof(f1691,plain,
    ( spl0_184
    | ~ spl0_68
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f561,f558,f538,f1689]) ).

fof(f1689,plain,
    ( spl0_184
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f561,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) )
    | ~ spl0_68
    | ~ spl0_71 ),
    inference(resolution,[],[f559,f539]) ).

fof(f1681,plain,
    ( spl0_183
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f613,f600,f347,f1679]) ).

fof(f613,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(superposition,[],[f601,f348]) ).

fof(f1671,plain,
    ( spl0_182
    | ~ spl0_63
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f603,f600,f500,f1669]) ).

fof(f603,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_63
    | ~ spl0_78 ),
    inference(resolution,[],[f601,f501]) ).

fof(f1663,plain,
    ( spl0_181
    | ~ spl0_44
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f579,f575,f396,f1661]) ).

fof(f579,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_44
    | ~ spl0_74 ),
    inference(resolution,[],[f576,f397]) ).

fof(f1656,plain,
    ( spl0_180
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f610,f600,f347,f1654]) ).

fof(f610,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(superposition,[],[f601,f348]) ).

fof(f1602,plain,
    ( spl0_179
    | ~ spl0_46
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f612,f600,f404,f1600]) ).

fof(f612,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_46
    | ~ spl0_78 ),
    inference(superposition,[],[f601,f405]) ).

fof(f1598,plain,
    ( spl0_178
    | ~ spl0_46
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f609,f600,f404,f1596]) ).

fof(f609,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_46
    | ~ spl0_78 ),
    inference(superposition,[],[f601,f405]) ).

fof(f1588,plain,
    ( spl0_177
    | ~ spl0_14
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f606,f600,f232,f1586]) ).

fof(f606,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_14
    | ~ spl0_78 ),
    inference(resolution,[],[f601,f233]) ).

fof(f1572,plain,
    ( spl0_176
    | ~ spl0_25
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f564,f558,f280,f1570]) ).

fof(f564,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) )
    | ~ spl0_25
    | ~ spl0_71 ),
    inference(resolution,[],[f559,f281]) ).

fof(f1547,plain,
    ( spl0_175
    | ~ spl0_37
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f598,f595,f339,f1545]) ).

fof(f598,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
    | ~ spl0_37
    | ~ spl0_77 ),
    inference(resolution,[],[f596,f340]) ).

fof(f1519,plain,
    ( ~ spl0_174
    | spl0_144
    | ~ spl0_22
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f1046,f852,f265,f1224,f1516]) ).

fof(f1516,plain,
    ( spl0_174
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f852,plain,
    ( spl0_109
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1046,plain,
    ( member(u,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_22
    | ~ spl0_109 ),
    inference(resolution,[],[f853,f266]) ).

fof(f853,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(u,X0) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f852]) ).

fof(f1514,plain,
    ( spl0_173
    | ~ spl0_23
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f563,f558,f269,f1512]) ).

fof(f563,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_71 ),
    inference(resolution,[],[f559,f270]) ).

fof(f1507,plain,
    ( spl0_172
    | ~ spl0_68
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f619,f616,f538,f1505]) ).

fof(f619,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_79 ),
    inference(resolution,[],[f617,f539]) ).

fof(f1467,plain,
    ( spl0_171
    | ~ spl0_29
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f582,f575,f296,f1465]) ).

fof(f582,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_29
    | ~ spl0_74 ),
    inference(resolution,[],[f576,f297]) ).

fof(f1463,plain,
    ( spl0_170
    | ~ spl0_30
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f581,f575,f300,f1461]) ).

fof(f581,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_30
    | ~ spl0_74 ),
    inference(resolution,[],[f576,f301]) ).

fof(f1445,plain,
    ( spl0_169
    | ~ spl0_20
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f583,f575,f257,f1443]) ).

fof(f583,plain,
    ( ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_74 ),
    inference(resolution,[],[f576,f258]) ).

fof(f1427,plain,
    ( spl0_168
    | ~ spl0_37
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f578,f575,f339,f1425]) ).

fof(f578,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_37
    | ~ spl0_74 ),
    inference(resolution,[],[f576,f340]) ).

fof(f1421,plain,
    ( spl0_167
    | ~ spl0_38
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f486,f479,f343,f1419]) ).

fof(f486,plain,
    ( ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_38
    | ~ spl0_58 ),
    inference(resolution,[],[f480,f344]) ).

fof(f1409,plain,
    ( ~ spl0_164
    | ~ spl0_165
    | spl0_166
    | ~ spl0_64
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f541,f533,f509,f1406,f1402,f1398]) ).

fof(f1402,plain,
    ( spl0_165
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f1406,plain,
    ( spl0_166
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f509,plain,
    ( spl0_64
  <=> ! [X0,X8] :
        ( ~ function(X8)
        | ~ member(X0,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f541,plain,
    ( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(universal_class,universal_class)
    | ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_64
    | ~ spl0_67 ),
    inference(superposition,[],[f510,f535]) ).

fof(f510,plain,
    ( ! [X0,X8] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X8) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f509]) ).

fof(f1396,plain,
    ( spl0_163
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f507,f500,f404,f284,f1394]) ).

fof(f507,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_63 ),
    inference(forward_demodulation,[],[f506,f405]) ).

fof(f506,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_26
    | ~ spl0_63 ),
    inference(resolution,[],[f501,f285]) ).

fof(f1375,plain,
    ( ~ spl0_162
    | ~ spl0_101
    | spl0_144 ),
    inference(avatar_split_clause,[],[f1340,f1224,f754,f1372]) ).

fof(f1340,plain,
    ( ~ member(u,subset_relation)
    | ~ spl0_101
    | spl0_144 ),
    inference(resolution,[],[f1225,f755]) ).

fof(f1225,plain,
    ( ~ member(u,cross_product(universal_class,universal_class))
    | spl0_144 ),
    inference(avatar_component_clause,[],[f1224]) ).

fof(f1370,plain,
    ( spl0_161
    | ~ spl0_45
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f542,f533,f400,f1368]) ).

fof(f542,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_45
    | ~ spl0_67 ),
    inference(superposition,[],[f401,f535]) ).

fof(f1363,plain,
    ( spl0_160
    | ~ spl0_37
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f547,f538,f339,f1361]) ).

fof(f547,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_37
    | ~ spl0_68 ),
    inference(resolution,[],[f539,f340]) ).

fof(f1357,plain,
    ( ~ spl0_157
    | ~ spl0_158
    | spl0_159
    | ~ spl0_22
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f531,f520,f265,f1354,f1350,f1346]) ).

fof(f1354,plain,
    ( spl0_159
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f520,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f531,plain,
    ( inductive(cross_product(universal_class,universal_class))
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | ~ spl0_22
    | ~ spl0_66 ),
    inference(resolution,[],[f521,f266]) ).

fof(f521,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f520]) ).

fof(f1344,plain,
    ( spl0_156
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f461,f458,f343,f1342]) ).

fof(f1342,plain,
    ( spl0_156
  <=> ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f461,plain,
    ( ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(resolution,[],[f459,f344]) ).

fof(f1339,plain,
    ( spl0_154
    | spl0_155
    | ~ spl0_39
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f525,f509,f347,f1336,f1333]) ).

fof(f1333,plain,
    ( spl0_154
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | null_class = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f525,plain,
    ( ! [X0] :
        ( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | null_class = cross_product(X0,universal_class) )
    | ~ spl0_39
    | ~ spl0_64 ),
    inference(superposition,[],[f510,f348]) ).

fof(f1298,plain,
    ( spl0_153
    | ~ spl0_68
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f589,f585,f538,f1296]) ).

fof(f589,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_75 ),
    inference(resolution,[],[f586,f539]) ).

fof(f1294,plain,
    ( spl0_151
    | spl0_152
    | ~ spl0_14
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f562,f558,f232,f1291,f1288]) ).

fof(f1288,plain,
    ( spl0_151
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f562,plain,
    ( ! [X0,X1] :
        ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_14
    | ~ spl0_71 ),
    inference(resolution,[],[f559,f233]) ).

fof(f1286,plain,
    ( spl0_150
    | ~ spl0_37
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f527,f516,f339,f1284]) ).

fof(f516,plain,
    ( spl0_65
  <=> ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f527,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
    | ~ spl0_37
    | ~ spl0_65 ),
    inference(resolution,[],[f517,f340]) ).

fof(f517,plain,
    ( ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f516]) ).

fof(f1282,plain,
    ( spl0_149
    | ~ spl0_37
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f523,f509,f339,f1280]) ).

fof(f523,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
    | ~ spl0_37
    | ~ spl0_64 ),
    inference(resolution,[],[f510,f340]) ).

fof(f1278,plain,
    ( spl0_148
    | ~ spl0_38
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f445,f412,f343,f1276]) ).

fof(f1276,plain,
    ( spl0_148
  <=> ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f445,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_38
    | ~ spl0_48 ),
    inference(resolution,[],[f413,f344]) ).

fof(f1274,plain,
    ( spl0_147
    | ~ spl0_38
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f444,f408,f343,f1272]) ).

fof(f1272,plain,
    ( spl0_147
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f444,plain,
    ( ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_38
    | ~ spl0_47 ),
    inference(resolution,[],[f409,f344]) ).

fof(f1235,plain,
    ( spl0_146
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f569,f566,f1233]) ).

fof(f566,plain,
    ( spl0_72
  <=> ! [X9,X11,X10] :
        ( ~ function(X9)
        | compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) != domain_of(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f569,plain,
    ( ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
    | ~ spl0_72 ),
    inference(equality_resolution,[],[f567]) ).

fof(f567,plain,
    ( ! [X10,X11,X9] :
        ( domain_of(domain_of(X10)) != domain_of(X9)
        | compatible(X9,X10,X11)
        | ~ function(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f566]) ).

fof(f1231,plain,
    ( spl0_145
    | ~ spl0_37
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f505,f500,f339,f1229]) ).

fof(f505,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) )
    | ~ spl0_37
    | ~ spl0_63 ),
    inference(resolution,[],[f501,f340]) ).

fof(f1227,plain,
    ( ~ spl0_143
    | spl0_144
    | ~ spl0_22
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f514,f416,f265,f1224,f1220]) ).

fof(f1220,plain,
    ( spl0_143
  <=> function(x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f416,plain,
    ( spl0_49
  <=> ! [X0] :
        ( ~ subclass(x,X0)
        | member(u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f514,plain,
    ( member(u,cross_product(universal_class,universal_class))
    | ~ function(x)
    | ~ spl0_22
    | ~ spl0_49 ),
    inference(resolution,[],[f417,f266]) ).

fof(f417,plain,
    ( ! [X0] :
        ( ~ subclass(x,X0)
        | member(u,X0) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f416]) ).

fof(f1218,plain,
    ( spl0_142
    | ~ spl0_26
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f435,f400,f284,f1216]) ).

fof(f435,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_26
    | ~ spl0_45 ),
    inference(resolution,[],[f401,f285]) ).

fof(f1214,plain,
    ( spl0_141
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f431,f396,f280,f1212]) ).

fof(f431,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) )
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(resolution,[],[f397,f281]) ).

fof(f1204,plain,
    ( spl0_140
    | ~ spl0_30
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f543,f533,f300,f1202]) ).

fof(f543,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_30
    | ~ spl0_67 ),
    inference(superposition,[],[f301,f535]) ).

fof(f1173,plain,
    ( spl0_139
    | ~ spl0_46
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f524,f509,f404,f1171]) ).

fof(f524,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_46
    | ~ spl0_64 ),
    inference(superposition,[],[f510,f405]) ).

fof(f1169,plain,
    ( spl0_138
    | ~ spl0_23
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f430,f396,f269,f1167]) ).

fof(f430,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_44 ),
    inference(resolution,[],[f397,f270]) ).

fof(f1147,plain,
    ( spl0_137
    | ~ spl0_39
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f469,f463,f347,f1145]) ).

fof(f463,plain,
    ( spl0_55
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f469,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_55 ),
    inference(trivial_inequality_removal,[],[f467]) ).

fof(f467,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_39
    | ~ spl0_55 ),
    inference(superposition,[],[f464,f348]) ).

fof(f464,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f463]) ).

fof(f1143,plain,
    ( spl0_136
    | ~ spl0_26
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f392,f379,f284,f1141]) ).

fof(f392,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_26
    | ~ spl0_41 ),
    inference(resolution,[],[f380,f285]) ).

fof(f1139,plain,
    ( spl0_135
    | ~ spl0_32
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f370,f343,f308,f1137]) ).

fof(f370,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_32
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f309]) ).

fof(f1135,plain,
    ( spl0_134
    | ~ spl0_31
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f369,f343,f304,f1133]) ).

fof(f369,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_31
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f305]) ).

fof(f1111,plain,
    ( spl0_133
    | ~ spl0_37
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f448,f424,f339,f1109]) ).

fof(f424,plain,
    ( spl0_51
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f448,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_37
    | ~ spl0_51 ),
    inference(resolution,[],[f425,f340]) ).

fof(f425,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f424]) ).

fof(f1104,plain,
    ( spl0_132
    | ~ spl0_37
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f434,f400,f339,f1102]) ).

fof(f434,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_37
    | ~ spl0_45 ),
    inference(resolution,[],[f401,f340]) ).

fof(f1100,plain,
    ( spl0_131
    | ~ spl0_21
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f373,f343,f261,f1098]) ).

fof(f373,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_21
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f262]) ).

fof(f1062,plain,
    ( spl0_130
    | ~ spl0_46
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f466,f463,f404,f1060]) ).

fof(f1060,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f466,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_46
    | ~ spl0_55 ),
    inference(superposition,[],[f464,f405]) ).

fof(f1058,plain,
    ( spl0_129
    | ~ spl0_40
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f437,f400,f351,f1056]) ).

fof(f437,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_40
    | ~ spl0_45 ),
    inference(superposition,[],[f401,f353]) ).

fof(f1054,plain,
    ( spl0_128
    | ~ spl0_39
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f436,f400,f347,f1052]) ).

fof(f436,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_39
    | ~ spl0_45 ),
    inference(superposition,[],[f401,f348]) ).

fof(f1050,plain,
    ( spl0_127
    | ~ spl0_37
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f391,f379,f339,f1048]) ).

fof(f391,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_37
    | ~ spl0_41 ),
    inference(resolution,[],[f380,f340]) ).

fof(f1005,plain,
    ( spl0_126
    | ~ spl0_22
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f367,f343,f265,f1003]) ).

fof(f367,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f266]) ).

fof(f1001,plain,
    ( spl0_125
    | ~ spl0_25
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f328,f300,f280,f999]) ).

fof(f328,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_25
    | ~ spl0_30 ),
    inference(resolution,[],[f301,f281]) ).

fof(f997,plain,
    ( spl0_124
    | ~ spl0_25
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f325,f296,f280,f995]) ).

fof(f325,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_25
    | ~ spl0_29 ),
    inference(resolution,[],[f297,f281]) ).

fof(f958,plain,
    ( spl0_123
    | ~ spl0_37
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f811,f732,f339,f956]) ).

fof(f956,plain,
    ( spl0_123
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(w,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f811,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(w,X0) )
    | ~ spl0_37
    | ~ spl0_97 ),
    inference(resolution,[],[f734,f340]) ).

fof(f939,plain,
    ( spl0_122
    | ~ spl0_28
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f361,f339,f292,f937]) ).

fof(f361,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_28
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f293]) ).

fof(f935,plain,
    ( spl0_121
    | ~ spl0_27
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f360,f339,f288,f933]) ).

fof(f360,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_27
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f289]) ).

fof(f931,plain,
    ( spl0_120
    | ~ spl0_25
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f357,f339,f280,f929]) ).

fof(f357,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_25
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f281]) ).

fof(f927,plain,
    ( spl0_119
    | ~ spl0_23
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f327,f300,f269,f925]) ).

fof(f327,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_30 ),
    inference(resolution,[],[f301,f270]) ).

fof(f923,plain,
    ( spl0_118
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f324,f296,f269,f921]) ).

fof(f324,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(resolution,[],[f297,f270]) ).

fof(f897,plain,
    ( spl0_117
    | ~ spl0_37
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f689,f654,f339,f895]) ).

fof(f895,plain,
    ( spl0_117
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(v,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f689,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(v,X0) )
    | ~ spl0_37
    | ~ spl0_86 ),
    inference(resolution,[],[f656,f340]) ).

fof(f884,plain,
    ( spl0_116
    | ~ spl0_14
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f429,f396,f232,f882]) ).

fof(f429,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_14
    | ~ spl0_44 ),
    inference(resolution,[],[f397,f233]) ).

fof(f880,plain,
    ( spl0_115
    | ~ spl0_29
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f377,f351,f296,f878]) ).

fof(f377,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_29
    | ~ spl0_40 ),
    inference(superposition,[],[f297,f353]) ).

fof(f876,plain,
    ( spl0_114
    | ~ spl0_30
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f374,f347,f300,f874]) ).

fof(f374,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_30
    | ~ spl0_39 ),
    inference(superposition,[],[f301,f348]) ).

fof(f872,plain,
    ( spl0_112
    | ~ spl0_113
    | ~ spl0_13
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f371,f343,f227,f869,f865]) ).

fof(f371,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_13
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f229]) ).

fof(f863,plain,
    ( spl0_110
    | ~ spl0_111
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f368,f343,f222,f860,f856]) ).

fof(f368,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f224]) ).

fof(f854,plain,
    ( spl0_109
    | ~ spl0_37
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f588,f553,f339,f852]) ).

fof(f588,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(u,X0) )
    | ~ spl0_37
    | ~ spl0_70 ),
    inference(resolution,[],[f555,f340]) ).

fof(f850,plain,
    ( spl0_108
    | ~ spl0_23
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f356,f339,f269,f848]) ).

fof(f356,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f270]) ).

fof(f846,plain,
    ( spl0_107
    | ~ spl0_20
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f320,f280,f257,f844]) ).

fof(f320,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_20
    | ~ spl0_25 ),
    inference(resolution,[],[f281,f258]) ).

fof(f823,plain,
    ( spl0_106
    | ~ spl0_47
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f504,f496,f408,f821]) ).

fof(f496,plain,
    ( spl0_62
  <=> ! [X8] :
        ( function(X8)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f504,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_47
    | ~ spl0_62 ),
    inference(resolution,[],[f497,f409]) ).

fof(f497,plain,
    ( ! [X8] :
        ( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | function(X8) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f496]) ).

fof(f819,plain,
    ( spl0_105
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f375,f347,f296,f817]) ).

fof(f375,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(superposition,[],[f297,f348]) ).

fof(f815,plain,
    ( spl0_104
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f278,f269,f257,f813]) ).

fof(f278,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(resolution,[],[f270,f258]) ).

fof(f810,plain,
    ( ~ spl0_102
    | spl0_103
    | ~ spl0_16
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f528,f516,f240,f807,f803]) ).

fof(f803,plain,
    ( spl0_102
  <=> member(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f807,plain,
    ( spl0_103
  <=> member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(null_class,universal_class)),universal_class))))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f528,plain,
    ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(null_class,universal_class)),universal_class))))),universal_class)
    | ~ member(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))),universal_class)
    | ~ spl0_16
    | ~ spl0_65 ),
    inference(superposition,[],[f517,f242]) ).

fof(f756,plain,
    ( spl0_101
    | ~ spl0_29
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f544,f533,f296,f754]) ).

fof(f544,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_29
    | ~ spl0_67 ),
    inference(superposition,[],[f297,f535]) ).

fof(f752,plain,
    ( spl0_100
    | ~ spl0_15
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f372,f343,f236,f750]) ).

fof(f236,plain,
    ( spl0_15
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f372,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_15
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f237]) ).

fof(f237,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f748,plain,
    ( spl0_99
    | ~ spl0_11
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f359,f339,f218,f746]) ).

fof(f359,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_11
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f219]) ).

fof(f744,plain,
    ( spl0_98
    | ~ spl0_14
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f355,f339,f232,f742]) ).

fof(f355,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_14
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f233]) ).

fof(f735,plain,
    ( spl0_97
    | ~ spl0_6
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f658,f483,f197,f732]) ).

fof(f483,plain,
    ( spl0_59
  <=> ! [X0] :
        ( ~ subclass(x,X0)
        | member(w,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f658,plain,
    ( member(w,universal_class)
    | ~ spl0_6
    | ~ spl0_59 ),
    inference(resolution,[],[f484,f198]) ).

fof(f484,plain,
    ( ! [X0] :
        ( ~ subclass(x,X0)
        | member(w,X0) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f483]) ).

fof(f730,plain,
    ( spl0_96
    | ~ spl0_16
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f393,f379,f240,f728]) ).

fof(f393,plain,
    ( ! [X0] :
        ( member(X0,null_class)
        | member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
        | ~ member(X0,universal_class) )
    | ~ spl0_16
    | ~ spl0_41 ),
    inference(superposition,[],[f380,f242]) ).

fof(f716,plain,
    ( spl0_95
    | ~ spl0_14
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f326,f300,f232,f714]) ).

fof(f714,plain,
    ( spl0_95
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f326,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_14
    | ~ spl0_30 ),
    inference(resolution,[],[f301,f233]) ).

fof(f712,plain,
    ( spl0_94
    | ~ spl0_14
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f323,f296,f232,f710]) ).

fof(f710,plain,
    ( spl0_94
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f323,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_14
    | ~ spl0_29 ),
    inference(resolution,[],[f297,f233]) ).

fof(f703,plain,
    ( spl0_93
    | ~ spl0_16
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f273,f257,f240,f701]) ).

fof(f273,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) )
    | ~ spl0_16
    | ~ spl0_20 ),
    inference(superposition,[],[f258,f242]) ).

fof(f688,plain,
    ( spl0_92
    | ~ spl0_30
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f376,f351,f300,f686]) ).

fof(f376,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_30
    | ~ spl0_40 ),
    inference(superposition,[],[f301,f353]) ).

fof(f684,plain,
    ( spl0_91
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f365,f343,f197,f682]) ).

fof(f365,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(resolution,[],[f344,f198]) ).

fof(f680,plain,
    ( spl0_90
    | ~ spl0_7
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f358,f339,f201,f678]) ).

fof(f201,plain,
    ( spl0_7
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f358,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_7
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f203]) ).

fof(f203,plain,
    ( member(omega,universal_class)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f201]) ).

fof(f675,plain,
    ( ~ spl0_88
    | spl0_89
    | ~ spl0_6
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f530,f520,f197,f672,f668]) ).

fof(f530,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_6
    | ~ spl0_66 ),
    inference(resolution,[],[f521,f198]) ).

fof(f664,plain,
    ( spl0_87
    | ~ spl0_48
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f446,f420,f412,f662]) ).

fof(f420,plain,
    ( spl0_50
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f446,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_48
    | ~ spl0_50 ),
    inference(resolution,[],[f421,f413]) ).

fof(f421,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f420]) ).

fof(f657,plain,
    ( spl0_86
    | ~ spl0_6
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f625,f454,f197,f654]) ).

fof(f454,plain,
    ( spl0_53
  <=> ! [X0] :
        ( ~ subclass(x,X0)
        | member(v,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f625,plain,
    ( member(v,universal_class)
    | ~ spl0_6
    | ~ spl0_53 ),
    inference(resolution,[],[f455,f198]) ).

fof(f455,plain,
    ( ! [X0] :
        ( ~ subclass(x,X0)
        | member(v,X0) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f454]) ).

fof(f652,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f170,f650]) ).

fof(f650,plain,
    ( spl0_85
  <=> ! [X9,X11,X10] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
        | ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f170,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f169,f110]) ).

fof(f110,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).

fof(f169,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f168,f110]) ).

fof(f168,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f167,f110]) ).

fof(f167,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f166,f110]) ).

fof(f166,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f165,f110]) ).

fof(f165,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f164,f110]) ).

fof(f164,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f163,f110]) ).

fof(f163,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f162,f110]) ).

fof(f162,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f161,f110]) ).

fof(f161,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f146,f110]) ).

fof(f146,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f91,f100,f101,f100,f100,f100,f100,f101]) ).

fof(f101,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

fof(f100,plain,
    ! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
    inference(definition_unfolding,[],[f68,f97,f99,f12]) ).

fof(f99,plain,
    ! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
    inference(definition_unfolding,[],[f42,f98,f29]) ).

fof(f98,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).

fof(f42,axiom,
    ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).

fof(f97,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f68,axiom,
    ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).

fof(f91,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).

fof(f645,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f160,f643]) ).

fof(f160,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f159,f110]) ).

fof(f159,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f158,f110]) ).

fof(f158,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f157,f110]) ).

fof(f157,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f156,f110]) ).

fof(f156,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f139,f110]) ).

fof(f139,plain,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f89,f101,f100,f101,f100,f100,f100,f100,f101]) ).

fof(f89,axiom,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(ordered_pair(X0,X1),domain_of(X10))
      | apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).

fof(f639,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f142,f637]) ).

fof(f142,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f37,f101,f101,f101,f101,f101,f101]) ).

fof(f37,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).

fof(f635,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f141,f633]) ).

fof(f141,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f34,f101,f101,f101,f101,f101,f101]) ).

fof(f34,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).

fof(f631,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f129,f629]) ).

fof(f129,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
    inference(definition_unfolding,[],[f36,f101,f101,f101,f101]) ).

fof(f36,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).

fof(f624,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f128,f622]) ).

fof(f128,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
    inference(definition_unfolding,[],[f33,f101,f101,f101,f101]) ).

fof(f33,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).

fof(f618,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f149,f616]) ).

fof(f149,plain,
    ! [X0] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f46,f105,f101,f101]) ).

fof(f105,plain,
    ! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
    inference(definition_unfolding,[],[f43,f26,f12]) ).

fof(f26,axiom,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).

fof(f43,axiom,
    ! [X0] : union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).

fof(f46,axiom,
    ! [X0,X1] :
      ( successor(X0) != X1
      | member(ordered_pair(X0,X1),successor_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).

fof(f602,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f140,f600]) ).

fof(f140,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f59,f101,f101,f99,f99,f12]) ).

fof(f59,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X1,X4),compose(X7,X5))
      | ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).

fof(f597,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f145,f595]) ).

fof(f145,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
    inference(definition_unfolding,[],[f90,f101]) ).

fof(f90,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).

fof(f593,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f127,f591]) ).

fof(f127,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f58,f101,f99,f99,f12]) ).

fof(f58,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),compose(X7,X5))
      | member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).

fof(f587,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f135,f585]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f20,f101,f101]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(ordered_pair(X0,X1),element_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).

fof(f577,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f155,f575]) ).

fof(f155,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f154,f110]) ).

fof(f154,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f136,f110]) ).

fof(f136,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
    inference(definition_unfolding,[],[f70,f100]) ).

fof(f70,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(apply(choice,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).

fof(f573,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f143,f571]) ).

fof(f571,plain,
    ( spl0_73
  <=> ! [X8] :
        ( ~ function(X8)
        | operation(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f143,plain,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f81,f98]) ).

fof(f81,axiom,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(range_of(X8),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).

fof(f568,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f144,f566]) ).

fof(f144,plain,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f85,f98]) ).

fof(f85,axiom,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).

fof(f560,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f126,f558]) ).

fof(f126,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
    inference(definition_unfolding,[],[f17,f101]) ).

fof(f17,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).

fof(f556,plain,
    ( spl0_70
    | ~ spl0_6
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f512,f416,f197,f553]) ).

fof(f512,plain,
    ( member(u,universal_class)
    | ~ spl0_6
    | ~ spl0_49 ),
    inference(resolution,[],[f417,f198]) ).

fof(f551,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f125,f549]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
    inference(definition_unfolding,[],[f45,f105,f101]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( successor(X0) = X1
      | ~ member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).

fof(f540,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f134,f538]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f16,f101]) ).

fof(f16,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f536,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f111,f533]) ).

fof(f111,plain,
    subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
    inference(definition_unfolding,[],[f74,f38]) ).

fof(f74,axiom,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).

fof(f522,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f153,f520]) ).

fof(f153,plain,
    ! [X0] :
      ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | inductive(X0)
      | ~ member(null_class,X0) ),
    inference(forward_demodulation,[],[f132,f110]) ).

fof(f132,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f99]) ).

fof(f49,axiom,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).

fof(f518,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f151,f516]) ).

fof(f151,plain,
    ! [X2] :
      ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
      | ~ member(X2,universal_class) ),
    inference(forward_demodulation,[],[f118,f110]) ).

fof(f118,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
    inference(definition_unfolding,[],[f56,f106]) ).

fof(f106,plain,
    ! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
    inference(definition_unfolding,[],[f55,f99]) ).

fof(f55,axiom,
    ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).

fof(f56,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).

fof(f511,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f131,f509]) ).

fof(f131,plain,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
    inference(definition_unfolding,[],[f65,f99]) ).

fof(f65,axiom,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(image(X8,X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).

fof(f502,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f137,f500]) ).

fof(f137,plain,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12]) ).

fof(f31,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

fof(f498,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f133,f496]) ).

fof(f133,plain,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f64,f38]) ).

fof(f64,axiom,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).

fof(f494,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f122,f492]) ).

fof(f122,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f15,f101]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f490,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f121,f488]) ).

fof(f121,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f14,f101]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f485,plain,
    ( spl0_59
    | ~ spl0_3
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f364,f339,f182,f483]) ).

fof(f364,plain,
    ( ! [X0] :
        ( ~ subclass(x,X0)
        | member(w,X0) )
    | ~ spl0_3
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f184]) ).

fof(f481,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f150,f479]) ).

fof(f150,plain,
    ! [X0] :
      ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | ~ inductive(X0) ),
    inference(forward_demodulation,[],[f114,f110]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f48,f99]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).

fof(f477,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f124,f475]) ).

fof(f475,plain,
    ( spl0_57
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f124,plain,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f84,f98]) ).

fof(f84,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).

fof(f473,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f120,f471]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
    inference(definition_unfolding,[],[f19,f101]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).

fof(f465,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f123,f463]) ).

fof(f123,plain,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f30,f29,f12]) ).

fof(f30,axiom,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) != null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f460,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f115,f458]) ).

fof(f115,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f98]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).

fof(f456,plain,
    ( spl0_53
    | ~ spl0_2
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f363,f339,f177,f454]) ).

fof(f363,plain,
    ( ! [X0] :
        ( ~ subclass(x,X0)
        | member(v,X0) )
    | ~ spl0_2
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f179]) ).

fof(f452,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f79,f450]) ).

fof(f450,plain,
    ( spl0_52
  <=> ! [X8] :
        ( ~ operation(X8)
        | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).

fof(f426,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f152,f424]) ).

fof(f152,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f119,f110]) ).

fof(f119,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f97]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).

fof(f422,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f117,f420]) ).

fof(f117,plain,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f61,f38]) ).

fof(f61,axiom,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f418,plain,
    ( spl0_49
    | ~ spl0_1
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f362,f339,f172,f416]) ).

fof(f362,plain,
    ( ! [X0] :
        ( ~ subclass(x,X0)
        | member(u,X0) )
    | ~ spl0_1
    | ~ spl0_37 ),
    inference(resolution,[],[f340,f174]) ).

fof(f414,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f116,f412]) ).

fof(f116,plain,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f63,f38]) ).

fof(f63,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).

fof(f410,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f112,f408]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f406,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f110,f404]) ).

fof(f402,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f23,f400]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).

fof(f398,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f8,f396]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f389,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f130,f387]) ).

fof(f387,plain,
    ( spl0_43
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f130,plain,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f73,f38]) ).

fof(f73,axiom,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).

fof(f385,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f83,f383]) ).

fof(f383,plain,
    ( spl0_42
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).

fof(f381,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f25,f379]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).

fof(f354,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f109,f351]) ).

fof(f109,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).

fof(f349,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f67,f347]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f345,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f7,f343]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f341,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f1,f339]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).

fof(f337,plain,
    ( ~ spl0_35
    | ~ spl0_36
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f315,f275,f240,f334,f330]) ).

fof(f334,plain,
    ( spl0_36
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f275,plain,
    ( spl0_24
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f315,plain,
    ( ~ inductive(null_class)
    | ~ member(null_class,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(superposition,[],[f276,f242]) ).

fof(f276,plain,
    ( ! [X0] :
        ( ~ inductive(complement(X0))
        | ~ member(null_class,X0) )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f319,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f113,f317]) ).

fof(f113,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).

fof(f314,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f88,f312]) ).

fof(f312,plain,
    ( spl0_33
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f310,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f35,f308]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).

fof(f306,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f32,f304]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).

fof(f302,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f22,f300]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f298,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f21,f296]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f294,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f10,f292]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f290,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f9,f288]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f286,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f3,f284]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f282,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f2,f280]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f277,plain,
    ( spl0_24
    | ~ spl0_14
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f272,f257,f232,f275]) ).

fof(f272,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_14
    | ~ spl0_20 ),
    inference(resolution,[],[f258,f233]) ).

fof(f271,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f66,f269]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f267,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f62,f265]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f263,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f57,f261]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f259,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f24,f257]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f255,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f87,f253]) ).

fof(f253,plain,
    ( spl0_19
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f251,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f86,f249]) ).

fof(f249,plain,
    ( spl0_18
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f247,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f82,f245]) ).

fof(f245,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f243,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f108,f240]) ).

fof(f108,plain,
    null_class = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),
    inference(definition_unfolding,[],[f96,f102,f102,f102]) ).

fof(f102,plain,
    ! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
    inference(definition_unfolding,[],[f92,f26,f12]) ).

fof(f92,axiom,
    ! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).

fof(f96,axiom,
    null_class = set_builder(u,set_builder(v,set_builder(w,null_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple_kludge1_4) ).

fof(f238,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f51,f236]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f234,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f47,f232]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

fof(f230,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f44,f227]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f225,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f18,f222]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f220,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f11,f218]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f216,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f78,f214]) ).

fof(f214,plain,
    ( spl0_10
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f212,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f71,f210]) ).

fof(f210,plain,
    ( spl0_9
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f208,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f147,f206]) ).

fof(f147,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).

fof(f204,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f52,f201]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f199,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f4,f197]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f195,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f69,f192]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f190,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f50,f187]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f185,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f95,f182]) ).

fof(f95,axiom,
    member(w,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple_kludge1_3) ).

fof(f180,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f94,f177]) ).

fof(f94,axiom,
    member(v,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple_kludge1_2) ).

fof(f175,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f93,f172]) ).

fof(f93,axiom,
    member(u,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple_kludge1_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET137-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 11:38:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (3794)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (3795)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (3796)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (3798)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (3799)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)
% 0.13/0.37  % (3801)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)
% 0.13/0.37  % (3797)WARNING: value z3 for option sas not known
% 0.13/0.38  % (3800)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)
% 0.13/0.39  % (3797)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)
% 0.20/0.41  TRYING [1]
% 0.20/0.41  TRYING [2]
% 0.20/0.47  TRYING [3]
% 0.20/0.51  TRYING [1]
% 0.20/0.51  TRYING [2]
% 0.20/0.56  TRYING [4]
% 0.20/0.58  TRYING [3]
% 2.97/0.83  TRYING [5]
% 6.06/1.21  TRYING [4]
% 7.87/1.47  TRYING [1]
% 7.87/1.47  TRYING [2]
% 7.87/1.48  TRYING [3]
% 8.17/1.53  TRYING [4]
% 9.05/1.67  TRYING [5]
% 12.61/2.14  TRYING [6]
% 12.61/2.21  TRYING [6]
% 23.69/3.76  TRYING [7]
% 24.25/3.83  % (3799)First to succeed.
% 24.73/3.92  % (3799)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3794"
% 24.73/3.92  % (3799)Refutation found. Thanks to Tanya!
% 24.73/3.92  % SZS status Unsatisfiable for theBenchmark
% 24.73/3.92  % SZS output start Proof for theBenchmark
% See solution above
% 24.73/3.95  % (3799)------------------------------
% 24.73/3.95  % (3799)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 24.73/3.95  % (3799)Termination reason: Refutation
% 24.73/3.95  
% 24.73/3.95  % (3799)Memory used [KB]: 27719
% 24.73/3.95  % (3799)Time elapsed: 3.551 s
% 24.73/3.95  % (3799)Instructions burned: 9693 (million)
% 24.73/3.95  % (3794)Success in time 3.546 s
%------------------------------------------------------------------------------