TSTP Solution File: SET154-6 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET154-6 : 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 : n013.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 03:16:54 EDT 2024

% Result   : Unsatisfiable 13.96s 2.38s
% Output   : Refutation 14.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1071
% Syntax   : Number of formulae    : 3226 ( 136 unt;   0 def)
%            Number of atoms       : 12163 (1262 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 15842 (6905   ~;7970   |;   0   &)
%                                         ( 967 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   27 (   3 avg)
%            Number of predicates  :  979 ( 977 usr; 968 prp; 0-3 aty)
%            Number of functors    :   39 (  39 usr;  13 con; 0-3 aty)
%            Number of variables   : 4496 (4496   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f19711,plain,
    $false,
    inference(avatar_sat_refutation,[],[f208,f213,f218,f222,f227,f231,f235,f239,f243,f248,f253,f257,f261,f266,f270,f274,f278,f282,f286,f290,f294,f298,f302,f307,f312,f317,f322,f326,f330,f334,f338,f342,f346,f350,f354,f358,f362,f375,f379,f383,f388,f392,f397,f427,f431,f435,f442,f447,f451,f455,f459,f463,f467,f471,f480,f502,f506,f510,f514,f519,f527,f531,f535,f542,f546,f555,f559,f563,f567,f571,f578,f587,f591,f595,f599,f612,f616,f627,f631,f644,f648,f653,f657,f667,f672,f676,f680,f685,f689,f694,f699,f705,f721,f726,f730,f734,f738,f742,f748,f753,f760,f764,f782,f792,f805,f814,f818,f822,f826,f887,f891,f895,f918,f922,f931,f940,f950,f954,f958,f962,f966,f988,f1007,f1011,f1015,f1019,f1023,f1027,f1086,f1090,f1094,f1098,f1107,f1111,f1158,f1162,f1166,f1170,f1174,f1224,f1233,f1242,f1246,f1250,f1276,f1280,f1289,f1293,f1297,f1301,f1319,f1323,f1354,f1364,f1368,f1372,f1376,f1380,f1447,f1451,f1455,f1459,f1467,f1476,f1480,f1518,f1526,f1533,f1546,f1552,f1559,f1581,f1587,f1600,f1612,f1617,f1623,f1642,f1659,f1663,f1707,f1714,f1748,f1776,f1796,f1806,f1811,f1815,f1871,f1909,f1916,f1926,f1938,f1948,f1997,f2001,f2054,f2059,f2070,f2083,f2096,f2100,f2113,f2123,f2127,f2140,f2142,f2226,f2230,f2260,f2264,f2268,f2280,f2290,f2308,f2314,f2337,f2345,f2350,f2355,f2359,f2363,f2367,f2375,f2380,f2384,f2392,f2397,f2405,f2413,f2417,f2427,f2436,f2447,f2451,f2455,f2459,f2470,f2482,f2493,f2498,f2502,f2506,f2522,f2528,f2532,f2543,f2561,f2688,f2692,f2702,f2708,f2712,f2714,f2726,f2730,f2734,f2738,f2742,f2750,f2813,f2817,f2821,f2825,f2829,f2834,f2855,f2908,f2919,f2926,f2933,f2938,f2943,f2948,f2952,f2956,f3045,f3056,f3064,f3069,f3074,f3095,f3109,f3121,f3140,f3144,f3148,f3152,f3156,f3165,f3169,f3175,f3179,f3184,f3190,f3196,f3204,f3213,f3217,f3221,f3225,f3309,f3313,f3327,f3331,f3335,f3461,f3469,f3475,f3481,f3485,f3494,f3501,f3505,f3509,f3513,f3518,f3524,f3528,f3532,f3536,f3540,f3544,f3548,f3598,f3617,f3748,f3756,f3760,f3764,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3801,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3833,f3837,f4201,f4205,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4251,f4252,f4260,f4269,f4273,f4368,f4644,f4739,f4766,f4770,f4776,f4781,f4785,f4789,f4793,f4797,f4801,f4806,f4810,f4815,f4819,f4823,f4827,f4831,f4835,f4848,f4852,f4857,f5142,f5146,f5173,f5462,f5471,f5478,f5483,f5488,f5498,f5504,f5509,f5513,f5521,f5526,f5531,f5539,f5543,f5547,f5551,f5555,f5559,f5564,f5571,f5579,f5810,f5819,f5880,f5886,f5891,f5895,f5899,f5904,f5909,f5918,f5922,f5926,f5930,f6019,f6023,f6181,f6186,f6190,f6195,f6207,f6211,f6215,f6223,f6229,f6233,f6237,f6401,f6405,f6409,f6413,f6418,f6423,f6432,f6436,f6440,f6444,f6448,f6452,f6456,f6464,f6596,f6600,f6806,f6811,f6815,f6819,f6823,f6827,f6831,f6835,f6845,f6993,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7034,f7038,f7050,f7358,f7362,f7366,f7370,f7383,f7391,f7396,f7401,f7425,f7434,f7439,f7443,f7447,f7457,f7461,f7465,f7469,f7473,f8139,f8143,f8147,f8152,f8157,f8161,f8187,f8194,f8203,f8210,f8221,f8225,f8229,f8233,f8237,f8300,f8304,f8311,f8316,f8320,f8324,f8338,f8342,f8346,f8350,f8354,f8358,f8670,f8705,f8709,f8713,f8717,f8721,f8725,f8729,f8816,f8820,f8828,f8832,f8836,f8840,f8849,f8856,f8983,f8987,f8991,f8995,f9000,f9004,f9065,f9079,f9093,f9097,f9104,f9111,f9116,f9121,f9126,f9132,f9142,f9185,f9189,f9193,f9197,f9201,f9205,f9209,f9236,f9329,f9333,f9340,f9347,f9352,f9356,f9361,f9368,f9373,f9381,f9393,f9397,f9458,f9516,f9520,f9528,f9584,f9658,f9667,f9674,f9681,f9685,f9692,f9696,f9700,f9717,f9721,f9762,f9766,f9770,f9774,f9778,f9782,f9904,f9910,f9918,f9926,f9932,f9940,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9973,f9977,f9981,f10363,f10370,f10374,f10443,f10447,f10547,f10551,f10555,f10563,f10596,f10600,f10604,f10781,f10786,f10791,f10796,f11022,f11026,f11030,f11034,f11038,f11042,f11445,f11449,f11454,f11473,f11477,f11570,f11574,f11608,f11625,f11630,f11641,f11647,f11653,f11736,f11740,f11754,f11758,f11786,f11790,f11866,f11895,f11899,f11903,f12103,f12107,f12111,f12153,f12158,f12163,f12167,f12172,f12180,f12186,f12190,f12194,f12198,f12529,f12534,f12539,f12543,f12547,f12551,f12790,f12864,f12868,f12872,f12876,f12880,f12884,f12888,f12955,f12959,f13343,f13405,f13409,f13440,f13444,f13448,f13577,f13581,f13713,f13717,f13721,f13726,f13730,f13734,f13828,f13832,f13836,f13903,f13907,f13911,f13915,f14216,f14274,f14278,f14282,f14286,f14505,f14509,f14513,f14517,f14601,f14610,f14640,f14693,f14701,f14708,f14716,f14838,f14842,f14846,f14851,f14990,f14994,f15178,f15201,f15209,f15214,f15219,f15231,f15248,f15257,f15263,f15267,f15271,f15279,f15284,f15289,f15293,f15500,f15504,f15510,f15514,f15543,f15547,f15552,f15557,f15561,f15565,f15569,f15580,f15584,f15666,f15671,f15675,f15734,f15741,f15775,f15779,f15795,f15858,f15866,f15871,f15879,f15884,f15888,f15892,f15896,f15992,f15996,f16012,f16016,f16037,f16045,f16229,f16233,f16279,f16296,f16300,f16363,f16367,f16375,f16381,f16385,f16393,f16398,f16402,f16521,f16526,f16530,f16535,f16539,f16544,f16549,f16553,f16557,f16582,f16586,f16717,f16721,f16725,f16729,f16733,f16737,f16785,f16830,f16871,f16875,f16879,f16883,f16902,f16906,f16959,f17108,f17116,f17120,f17124,f17269,f17273,f17277,f17416,f17459,f17487,f17504,f17630,f17642,f17646,f17650,f17654,f17664,f17697,f17712,f17716,f17720,f17724,f17728,f17732,f17736,f17875,f18054,f18058,f18062,f18118,f18150,f18154,f18352,f18356,f18406,f18500,f18638,f18642,f18704,f18748,f18752,f18756,f18820,f18824,f18828,f18832,f18836,f18840,f19152,f19232,f19236,f19240,f19245,f19249,f19253,f19257,f19467,f19484,f19534,f19540,f19590,f19594,f19598,f19615,f19626,f19671,f19675,f19701,f19705,f19709,f19710]) ).

fof(f19710,plain,
    ( spl0_726
    | ~ spl0_55
    | ~ spl0_950 ),
    inference(avatar_split_clause,[],[f19472,f19242,f478,f12169]) ).

fof(f12169,plain,
    ( spl0_726
  <=> universal_class = complement(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f478,plain,
    ( spl0_55
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f19242,plain,
    ( spl0_950
  <=> subclass(universal_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f19472,plain,
    ( universal_class = complement(null_class)
    | ~ spl0_55
    | ~ spl0_950 ),
    inference(resolution,[],[f19244,f479]) ).

fof(f479,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f19244,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_950 ),
    inference(avatar_component_clause,[],[f19242]) ).

fof(f19709,plain,
    ( spl0_967
    | ~ spl0_70
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2038,f1999,f569,f19707]) ).

fof(f19707,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))),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_967])]) ).

fof(f569,plain,
    ( spl0_70
  <=> ! [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_70])]) ).

fof(f1999,plain,
    ( spl0_212
  <=> ! [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_212])]) ).

fof(f2038,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_70
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f570]) ).

fof(f570,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_70 ),
    inference(avatar_component_clause,[],[f569]) ).

fof(f2000,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_212 ),
    inference(avatar_component_clause,[],[f1999]) ).

fof(f19705,plain,
    ( spl0_966
    | ~ spl0_209
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2019,f1995,f1936,f19703]) ).

fof(f19703,plain,
    ( spl0_966
  <=> ! [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_966])]) ).

fof(f1936,plain,
    ( spl0_209
  <=> ! [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_209])]) ).

fof(f1995,plain,
    ( spl0_211
  <=> ! [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_211])]) ).

fof(f2019,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_209
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f1937]) ).

fof(f1937,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_209 ),
    inference(avatar_component_clause,[],[f1936]) ).

fof(f1996,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_211 ),
    inference(avatar_component_clause,[],[f1995]) ).

fof(f19701,plain,
    ( spl0_965
    | ~ spl0_70
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2015,f1995,f569,f19699]) ).

fof(f19699,plain,
    ( spl0_965
  <=> ! [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_965])]) ).

fof(f2015,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_70
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f570]) ).

fof(f19675,plain,
    ( spl0_964
    | ~ spl0_198
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2047,f1999,f1712,f19673]) ).

fof(f19673,plain,
    ( spl0_964
  <=> ! [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_964])]) ).

fof(f1712,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

fof(f2047,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_198
    | ~ spl0_212 ),
    inference(superposition,[],[f2000,f1713]) ).

fof(f1713,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_198 ),
    inference(avatar_component_clause,[],[f1712]) ).

fof(f19671,plain,
    ( spl0_963
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1902,f1869,f1295,f19669]) ).

fof(f19669,plain,
    ( spl0_963
  <=> ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),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(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f1295,plain,
    ( spl0_158
  <=> ! [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_158])]) ).

fof(f1869,plain,
    ( spl0_205
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f1902,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),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(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f1296]) ).

fof(f1296,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_158 ),
    inference(avatar_component_clause,[],[f1295]) ).

fof(f1870,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
        | ~ subclass(composition_function,X2)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_205 ),
    inference(avatar_component_clause,[],[f1869]) ).

fof(f19626,plain,
    ( spl0_962
    | ~ spl0_197
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2049,f1999,f1705,f19624]) ).

fof(f19624,plain,
    ( spl0_962
  <=> ! [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_962])]) ).

fof(f1705,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

fof(f2049,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_197
    | ~ spl0_212 ),
    inference(duplicate_literal_removal,[],[f2040]) ).

fof(f2040,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_197
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f1706]) ).

fof(f1706,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_197 ),
    inference(avatar_component_clause,[],[f1705]) ).

fof(f19615,plain,
    ( spl0_961
    | ~ spl0_228
    | ~ spl0_950 ),
    inference(avatar_split_clause,[],[f19471,f19242,f2266,f19612]) ).

fof(f19612,plain,
    ( spl0_961
  <=> member(null_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f2266,plain,
    ( spl0_228
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f19471,plain,
    ( member(null_class,complement(null_class))
    | ~ spl0_228
    | ~ spl0_950 ),
    inference(resolution,[],[f19244,f2267]) ).

fof(f2267,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_228 ),
    inference(avatar_component_clause,[],[f2266]) ).

fof(f19598,plain,
    ( spl0_960
    | ~ spl0_199
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1862,f1813,f1746,f19596]) ).

fof(f19596,plain,
    ( spl0_960
  <=> ! [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_960])]) ).

fof(f1746,plain,
    ( spl0_199
  <=> ! [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_199])]) ).

fof(f1813,plain,
    ( spl0_204
  <=> ! [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_204])]) ).

fof(f1862,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_199
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1747]) ).

fof(f1747,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_199 ),
    inference(avatar_component_clause,[],[f1746]) ).

fof(f1814,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_204 ),
    inference(avatar_component_clause,[],[f1813]) ).

fof(f19594,plain,
    ( spl0_959
    | ~ spl0_199
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1836,f1804,f1746,f19592]) ).

fof(f19592,plain,
    ( spl0_959
  <=> ! [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_959])]) ).

fof(f1804,plain,
    ( spl0_202
  <=> ! [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_202])]) ).

fof(f1836,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_199
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1747]) ).

fof(f1805,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_202 ),
    inference(avatar_component_clause,[],[f1804]) ).

fof(f19590,plain,
    ( spl0_958
    | ~ spl0_93
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1767,f1746,f703,f19588]) ).

fof(f19588,plain,
    ( spl0_958
  <=> ! [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_958])]) ).

fof(f703,plain,
    ( spl0_93
  <=> ! [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_93])]) ).

fof(f1767,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_93
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f704]) ).

fof(f704,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_93 ),
    inference(avatar_component_clause,[],[f703]) ).

fof(f19540,plain,
    ( spl0_957
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_956 ),
    inference(avatar_split_clause,[],[f19536,f19532,f16735,f14710,f19538]) ).

fof(f19538,plain,
    ( spl0_957
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_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(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_957])]) ).

fof(f14710,plain,
    ( spl0_787
  <=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f16735,plain,
    ( spl0_884
  <=> ! [X0] : null_class = intersection(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f19532,plain,
    ( spl0_956
  <=> ! [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_956])]) ).

fof(f19536,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_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(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_787
    | ~ spl0_884
    | ~ spl0_956 ),
    inference(forward_demodulation,[],[f19535,f16736]) ).

fof(f16736,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_884 ),
    inference(avatar_component_clause,[],[f16735]) ).

fof(f19535,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(null_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_787
    | ~ spl0_956 ),
    inference(forward_demodulation,[],[f19533,f14712]) ).

fof(f14712,plain,
    ( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_787 ),
    inference(avatar_component_clause,[],[f14710]) ).

fof(f19533,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_956 ),
    inference(avatar_component_clause,[],[f19532]) ).

fof(f19534,plain,
    ( spl0_956
    | ~ spl0_206
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2041,f1999,f1907,f19532]) ).

fof(f1907,plain,
    ( spl0_206
  <=> ! [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_206])]) ).

fof(f2041,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_206
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f1908]) ).

fof(f1908,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_206 ),
    inference(avatar_component_clause,[],[f1907]) ).

fof(f19484,plain,
    ( spl0_955
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_954 ),
    inference(avatar_split_clause,[],[f19469,f19465,f16735,f14710,f19482]) ).

fof(f19482,plain,
    ( spl0_955
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_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(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_955])]) ).

fof(f19465,plain,
    ( spl0_954
  <=> ! [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_954])]) ).

fof(f19469,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_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(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_787
    | ~ spl0_884
    | ~ spl0_954 ),
    inference(forward_demodulation,[],[f19468,f16736]) ).

fof(f19468,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_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_787
    | ~ spl0_954 ),
    inference(forward_demodulation,[],[f19466,f14712]) ).

fof(f19466,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_954 ),
    inference(avatar_component_clause,[],[f19465]) ).

fof(f19467,plain,
    ( spl0_954
    | ~ spl0_206
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2018,f1995,f1907,f19465]) ).

fof(f2018,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_206
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f1908]) ).

fof(f19257,plain,
    ( spl0_953
    | ~ spl0_135
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1851,f1813,f1088,f19255]) ).

fof(f19255,plain,
    ( spl0_953
  <=> ! [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_953])]) ).

fof(f1088,plain,
    ( spl0_135
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1851,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_135
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1089]) ).

fof(f1089,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1088]) ).

fof(f19253,plain,
    ( spl0_952
    | ~ spl0_134
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1845,f1813,f1084,f19251]) ).

fof(f19251,plain,
    ( spl0_952
  <=> ! [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_952])]) ).

fof(f1084,plain,
    ( spl0_134
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1845,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_134
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1085]) ).

fof(f1085,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1084]) ).

fof(f19249,plain,
    ( spl0_951
    | ~ spl0_135
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1825,f1804,f1088,f19247]) ).

fof(f19247,plain,
    ( spl0_951
  <=> ! [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_951])]) ).

fof(f1825,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_135
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1089]) ).

fof(f19245,plain,
    ( spl0_950
    | ~ spl0_287
    | ~ spl0_938 ),
    inference(avatar_split_clause,[],[f18876,f18750,f2740,f19242]) ).

fof(f2740,plain,
    ( spl0_287
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f18750,plain,
    ( spl0_938
  <=> ! [X0] : ~ member(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f18876,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_287
    | ~ spl0_938 ),
    inference(resolution,[],[f18751,f2741]) ).

fof(f2741,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f2740]) ).

fof(f18751,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_938 ),
    inference(avatar_component_clause,[],[f18750]) ).

fof(f19240,plain,
    ( spl0_949
    | ~ spl0_134
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1819,f1804,f1084,f19238]) ).

fof(f19238,plain,
    ( spl0_949
  <=> ! [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_949])]) ).

fof(f1819,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_134
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1085]) ).

fof(f19236,plain,
    ( spl0_948
    | ~ spl0_93
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1138,f1088,f703,f19234]) ).

fof(f19234,plain,
    ( spl0_948
  <=> ! [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_948])]) ).

fof(f1138,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_93
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f704]) ).

fof(f19232,plain,
    ( spl0_947
    | ~ spl0_93
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1120,f1084,f703,f19230]) ).

fof(f19230,plain,
    ( spl0_947
  <=> ! [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_947])]) ).

fof(f1120,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_93
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f704]) ).

fof(f19152,plain,
    ( spl0_946
    | ~ spl0_99
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1730,f1712,f740,f19150]) ).

fof(f19150,plain,
    ( spl0_946
  <=> ! [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_946])]) ).

fof(f740,plain,
    ( spl0_99
  <=> ! [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_99])]) ).

fof(f1730,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_99
    | ~ spl0_198 ),
    inference(superposition,[],[f741,f1713]) ).

fof(f741,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_99 ),
    inference(avatar_component_clause,[],[f740]) ).

fof(f18840,plain,
    ( spl0_945
    | ~ spl0_129
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1858,f1813,f1009,f18838]) ).

fof(f18838,plain,
    ( spl0_945
  <=> ! [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_945])]) ).

fof(f1009,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f1858,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_129
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1010]) ).

fof(f1010,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1009]) ).

fof(f18836,plain,
    ( spl0_944
    | ~ spl0_128
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1850,f1813,f1005,f18834]) ).

fof(f18834,plain,
    ( spl0_944
  <=> ! [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_944])]) ).

fof(f1005,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1850,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_128
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1006]) ).

fof(f1006,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1005]) ).

fof(f18832,plain,
    ( spl0_943
    | ~ spl0_129
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1832,f1804,f1009,f18830]) ).

fof(f18830,plain,
    ( spl0_943
  <=> ! [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_943])]) ).

fof(f1832,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_129
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1010]) ).

fof(f18828,plain,
    ( spl0_942
    | ~ spl0_128
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1824,f1804,f1005,f18826]) ).

fof(f18826,plain,
    ( spl0_942
  <=> ! [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_942])]) ).

fof(f1824,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_128
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1006]) ).

fof(f18824,plain,
    ( spl0_941
    | ~ spl0_93
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1051,f1009,f703,f18822]) ).

fof(f18822,plain,
    ( spl0_941
  <=> ! [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_941])]) ).

fof(f1051,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_93
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f704]) ).

fof(f18820,plain,
    ( spl0_940
    | ~ spl0_93
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1035,f1005,f703,f18818]) ).

fof(f18818,plain,
    ( spl0_940
  <=> ! [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_940])]) ).

fof(f1035,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_93
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f704]) ).

fof(f18756,plain,
    ( spl0_939
    | ~ spl0_27
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1844,f1813,f320,f18754]) ).

fof(f18754,plain,
    ( spl0_939
  <=> ! [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_939])]) ).

fof(f320,plain,
    ( spl0_27
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f1844,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_27
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f321]) ).

fof(f321,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f320]) ).

fof(f18752,plain,
    ( spl0_938
    | ~ spl0_902
    | ~ spl0_926 ),
    inference(avatar_split_clause,[],[f18407,f18115,f17271,f18750]) ).

fof(f17271,plain,
    ( spl0_902
  <=> ! [X0] : ~ member(X0,domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f18115,plain,
    ( spl0_926
  <=> null_class = domain_of(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f18407,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_902
    | ~ spl0_926 ),
    inference(superposition,[],[f17272,f18117]) ).

fof(f18117,plain,
    ( null_class = domain_of(null_class)
    | ~ spl0_926 ),
    inference(avatar_component_clause,[],[f18115]) ).

fof(f17272,plain,
    ( ! [X0] : ~ member(X0,domain_of(null_class))
    | ~ spl0_902 ),
    inference(avatar_component_clause,[],[f17271]) ).

fof(f18748,plain,
    ( spl0_937
    | ~ spl0_27
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1818,f1804,f320,f18746]) ).

fof(f18746,plain,
    ( spl0_937
  <=> ! [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_937])]) ).

fof(f1818,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_27
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f321]) ).

fof(f18704,plain,
    ( spl0_936
    | ~ spl0_111
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2085,f2081,f824,f18702]) ).

fof(f18702,plain,
    ( spl0_936
  <=> ! [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_936])]) ).

fof(f824,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f2081,plain,
    ( spl0_216
  <=> ! [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_216])]) ).

fof(f2085,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_111
    | ~ spl0_216 ),
    inference(resolution,[],[f2082,f825]) ).

fof(f825,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f824]) ).

fof(f2082,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_216 ),
    inference(avatar_component_clause,[],[f2081]) ).

fof(f18642,plain,
    ( spl0_935
    | ~ spl0_23
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1849,f1813,f300,f18640]) ).

fof(f18640,plain,
    ( spl0_935
  <=> ! [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_935])]) ).

fof(f300,plain,
    ( spl0_23
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f1849,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_204 ),
    inference(resolution,[],[f1814,f301]) ).

fof(f301,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f18638,plain,
    ( spl0_934
    | ~ spl0_23
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1823,f1804,f300,f18636]) ).

fof(f18636,plain,
    ( spl0_934
  <=> ! [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_934])]) ).

fof(f1823,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_202 ),
    inference(resolution,[],[f1805,f301]) ).

fof(f18500,plain,
    ( spl0_933
    | ~ spl0_96
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1886,f1869,f728,f18498]) ).

fof(f18498,plain,
    ( spl0_933
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,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))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f728,plain,
    ( spl0_96
  <=> ! [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_96])]) ).

fof(f1886,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,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))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) )
    | ~ spl0_96
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f729]) ).

fof(f729,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_96 ),
    inference(avatar_component_clause,[],[f728]) ).

fof(f18406,plain,
    ( spl0_932
    | ~ spl0_111
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2072,f2068,f824,f18404]) ).

fof(f18404,plain,
    ( spl0_932
  <=> ! [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_932])]) ).

fof(f2068,plain,
    ( spl0_215
  <=> ! [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_215])]) ).

fof(f2072,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_111
    | ~ spl0_215 ),
    inference(resolution,[],[f2069,f825]) ).

fof(f2069,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_215 ),
    inference(avatar_component_clause,[],[f2068]) ).

fof(f18356,plain,
    ( spl0_931
    | ~ spl0_98
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1729,f1712,f736,f18354]) ).

fof(f18354,plain,
    ( spl0_931
  <=> ! [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_931])]) ).

fof(f736,plain,
    ( spl0_98
  <=> ! [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_98])]) ).

fof(f1729,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_98
    | ~ spl0_198 ),
    inference(superposition,[],[f737,f1713]) ).

fof(f737,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_98 ),
    inference(avatar_component_clause,[],[f736]) ).

fof(f18352,plain,
    ( spl0_929
    | ~ spl0_930
    | ~ spl0_99
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1421,f1370,f740,f18349,f18346]) ).

fof(f18346,plain,
    ( spl0_929
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),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(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2)
        | 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(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f18349,plain,
    ( spl0_930
  <=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f1370,plain,
    ( spl0_165
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f1421,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),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(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2))
        | ~ 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(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2) )
    | ~ spl0_99
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f741]) ).

fof(f1371,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
        | ~ subclass(domain_relation,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1370]) ).

fof(f18154,plain,
    ( spl0_928
    | ~ spl0_49
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2034,f1999,f449,f18152]) ).

fof(f18152,plain,
    ( spl0_928
  <=> ! [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_928])]) ).

fof(f449,plain,
    ( spl0_49
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f2034,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_49
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f450]) ).

fof(f450,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f449]) ).

fof(f18150,plain,
    ( spl0_927
    | ~ spl0_49
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2011,f1995,f449,f18148]) ).

fof(f18148,plain,
    ( spl0_927
  <=> ! [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_927])]) ).

fof(f2011,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_49
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f450]) ).

fof(f18118,plain,
    ( spl0_926
    | ~ spl0_23
    | ~ spl0_902 ),
    inference(avatar_split_clause,[],[f17521,f17271,f300,f18115]) ).

fof(f17521,plain,
    ( null_class = domain_of(null_class)
    | ~ spl0_23
    | ~ spl0_902 ),
    inference(resolution,[],[f17272,f301]) ).

fof(f18062,plain,
    ( spl0_925
    | ~ spl0_44
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2036,f1999,f425,f18060]) ).

fof(f18060,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))),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_925])]) ).

fof(f425,plain,
    ( spl0_44
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f2036,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_44
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f426]) ).

fof(f426,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f425]) ).

fof(f18058,plain,
    ( spl0_924
    | ~ spl0_44
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2013,f1995,f425,f18056]) ).

fof(f18056,plain,
    ( spl0_924
  <=> ! [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_924])]) ).

fof(f2013,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_44
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f426]) ).

fof(f18054,plain,
    ( spl0_923
    | ~ spl0_79
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1626,f1621,f629,f18052]) ).

fof(f18052,plain,
    ( spl0_923
  <=> ! [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_923])]) ).

fof(f629,plain,
    ( spl0_79
  <=> ! [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_79])]) ).

fof(f1621,plain,
    ( spl0_193
  <=> ! [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_193])]) ).

fof(f1626,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_79
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f630]) ).

fof(f630,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_79 ),
    inference(avatar_component_clause,[],[f629]) ).

fof(f1622,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_193 ),
    inference(avatar_component_clause,[],[f1621]) ).

fof(f17875,plain,
    ( spl0_922
    | ~ spl0_27
    | ~ spl0_902 ),
    inference(avatar_split_clause,[],[f17513,f17271,f320,f17873]) ).

fof(f17873,plain,
    ( spl0_922
  <=> ! [X0] : subclass(domain_of(null_class),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f17513,plain,
    ( ! [X0] : subclass(domain_of(null_class),X0)
    | ~ spl0_27
    | ~ spl0_902 ),
    inference(resolution,[],[f17272,f321]) ).

fof(f17736,plain,
    ( spl0_921
    | ~ spl0_30
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2030,f1999,f332,f17734]) ).

fof(f17734,plain,
    ( spl0_921
  <=> ! [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_921])]) ).

fof(f332,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f2030,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_30
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f333]) ).

fof(f333,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f332]) ).

fof(f17732,plain,
    ( spl0_920
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2029,f1999,f328,f17730]) ).

fof(f17730,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(f328,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f2029,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_29
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f329]) ).

fof(f329,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f328]) ).

fof(f17728,plain,
    ( spl0_919
    | ~ spl0_198
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2024,f1995,f1712,f17726]) ).

fof(f17726,plain,
    ( spl0_919
  <=> ! [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_919])]) ).

fof(f2024,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_198
    | ~ spl0_211 ),
    inference(superposition,[],[f1996,f1713]) ).

fof(f17724,plain,
    ( spl0_918
    | ~ spl0_30
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2007,f1995,f332,f17722]) ).

fof(f17722,plain,
    ( spl0_918
  <=> ! [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_918])]) ).

fof(f2007,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_30
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f333]) ).

fof(f17720,plain,
    ( spl0_917
    | ~ spl0_29
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2006,f1995,f328,f17718]) ).

fof(f17718,plain,
    ( spl0_917
  <=> ! [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_917])]) ).

fof(f2006,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_29
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f329]) ).

fof(f17716,plain,
    ( spl0_916
    | ~ spl0_158
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1769,f1746,f1295,f17714]) ).

fof(f17714,plain,
    ( spl0_916
  <=> ! [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_916])]) ).

fof(f1769,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_158
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f1296]) ).

fof(f17712,plain,
    ( spl0_915
    | ~ spl0_96
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1728,f1712,f728,f17710]) ).

fof(f17710,plain,
    ( spl0_915
  <=> ! [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_915])]) ).

fof(f1728,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_96
    | ~ spl0_198 ),
    inference(superposition,[],[f729,f1713]) ).

fof(f17697,plain,
    ( ~ spl0_914
    | ~ spl0_12
    | ~ spl0_902 ),
    inference(avatar_split_clause,[],[f17517,f17271,f255,f17694]) ).

fof(f17694,plain,
    ( spl0_914
  <=> inductive(domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f255,plain,
    ( spl0_12
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f17517,plain,
    ( ~ inductive(domain_of(null_class))
    | ~ spl0_12
    | ~ spl0_902 ),
    inference(resolution,[],[f17272,f256]) ).

fof(f256,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f17664,plain,
    ( spl0_913
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_912 ),
    inference(avatar_split_clause,[],[f17660,f17652,f16735,f14710,f17662]) ).

fof(f17662,plain,
    ( spl0_913
  <=> ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(null_class,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(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,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(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))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f17652,plain,
    ( spl0_912
  <=> ! [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_912])]) ).

fof(f17660,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(null_class,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(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,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(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))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_912 ),
    inference(forward_demodulation,[],[f17659,f16736]) ).

fof(f17659,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(null_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(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,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(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))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_912 ),
    inference(forward_demodulation,[],[f17658,f14712]) ).

fof(f17658,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)))),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(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))
        | 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_787
    | ~ spl0_884
    | ~ spl0_912 ),
    inference(forward_demodulation,[],[f17657,f16736]) ).

fof(f17657,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(null_class,X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_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(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))
        | 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_787
    | ~ spl0_884
    | ~ spl0_912 ),
    inference(forward_demodulation,[],[f17656,f14712]) ).

fof(f17656,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(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_787
    | ~ spl0_884
    | ~ spl0_912 ),
    inference(forward_demodulation,[],[f17655,f16736]) ).

fof(f17655,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(null_class,X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_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_787
    | ~ spl0_912 ),
    inference(forward_demodulation,[],[f17653,f14712]) ).

fof(f17653,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_912 ),
    inference(avatar_component_clause,[],[f17652]) ).

fof(f17654,plain,
    ( spl0_912
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2088,f2081,f381,f17652]) ).

fof(f381,plain,
    ( spl0_40
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f2088,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_40
    | ~ spl0_216 ),
    inference(superposition,[],[f2082,f382]) ).

fof(f382,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f381]) ).

fof(f17650,plain,
    ( spl0_911
    | ~ spl0_193
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1855,f1813,f1621,f17648]) ).

fof(f17648,plain,
    ( spl0_911
  <=> ! [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_911])]) ).

fof(f1855,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_193
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1622]) ).

fof(f17646,plain,
    ( spl0_910
    | ~ spl0_193
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1829,f1804,f1621,f17644]) ).

fof(f17644,plain,
    ( spl0_910
  <=> ! [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_910])]) ).

fof(f1829,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_193
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1622]) ).

fof(f17642,plain,
    ( spl0_909
    | ~ spl0_93
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1633,f1621,f703,f17640]) ).

fof(f17640,plain,
    ( spl0_909
  <=> ! [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_909])]) ).

fof(f1633,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_93
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f704]) ).

fof(f17630,plain,
    ( spl0_908
    | spl0_852
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_907 ),
    inference(avatar_split_clause,[],[f17510,f17502,f16735,f14710,f16039,f17628]) ).

fof(f17628,plain,
    ( spl0_908
  <=> ! [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)))))))),compose(X1,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(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)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f16039,plain,
    ( spl0_852
  <=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f17502,plain,
    ( spl0_907
  <=> ! [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_907])]) ).

fof(f17510,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(null_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(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(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(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17509,f16736]) ).

fof(f17509,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(null_class,X1),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(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(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(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_787
    | ~ spl0_884
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17508,f14712]) ).

fof(f17508,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)))))))),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(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,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_787
    | ~ spl0_884
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17507,f16736]) ).

fof(f17507,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(null_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(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,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_787
    | ~ spl0_884
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17506,f14712]) ).

fof(f17506,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(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_787
    | ~ spl0_884
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17505,f16736]) ).

fof(f17505,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(null_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_787
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17503,f14712]) ).

fof(f17503,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_907 ),
    inference(avatar_component_clause,[],[f17502]) ).

fof(f17504,plain,
    ( spl0_907
    | ~ spl0_40
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2075,f2068,f381,f17502]) ).

fof(f2075,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_40
    | ~ spl0_215 ),
    inference(superposition,[],[f2069,f382]) ).

fof(f17487,plain,
    ( spl0_906
    | ~ spl0_24
    | ~ spl0_100
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1875,f1869,f746,f304,f17485]) ).

fof(f17485,plain,
    ( spl0_906
  <=> ! [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(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).

fof(f304,plain,
    ( spl0_24
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f746,plain,
    ( spl0_100
  <=> ! [X4,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1875,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,cross_product(universal_class,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(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_100
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f747]) ).

fof(f747,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f746]) ).

fof(f17459,plain,
    ( spl0_905
    | ~ spl0_111
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2061,f2052,f824,f17457]) ).

fof(f17457,plain,
    ( spl0_905
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f2052,plain,
    ( spl0_213
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class)))))))))),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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f2061,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_213 ),
    inference(resolution,[],[f2053,f825]) ).

fof(f2053,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class)))))))))),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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(X0,domain_of(X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f2052]) ).

fof(f17416,plain,
    ( spl0_904
    | ~ spl0_77
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2084,f2081,f614,f17414]) ).

fof(f17414,plain,
    ( spl0_904
  <=> ! [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_904])]) ).

fof(f614,plain,
    ( spl0_77
  <=> ! [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_77])]) ).

fof(f2084,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_77
    | ~ spl0_216 ),
    inference(resolution,[],[f2082,f615]) ).

fof(f615,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_77 ),
    inference(avatar_component_clause,[],[f614]) ).

fof(f17277,plain,
    ( spl0_903
    | ~ spl0_77
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2071,f2068,f614,f17275]) ).

fof(f17275,plain,
    ( spl0_903
  <=> ! [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_903])]) ).

fof(f2071,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_77
    | ~ spl0_215 ),
    inference(resolution,[],[f2069,f615]) ).

fof(f17273,plain,
    ( spl0_902
    | ~ spl0_145
    | ~ spl0_884 ),
    inference(avatar_split_clause,[],[f17082,f16735,f1172,f17271]) ).

fof(f1172,plain,
    ( spl0_145
  <=> ! [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_145])]) ).

fof(f17082,plain,
    ( ! [X0] : ~ member(X0,domain_of(null_class))
    | ~ spl0_145
    | ~ spl0_884 ),
    inference(trivial_inequality_removal,[],[f17034]) ).

fof(f17034,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(null_class)) )
    | ~ spl0_145
    | ~ spl0_884 ),
    inference(superposition,[],[f1173,f16736]) ).

fof(f1173,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1172]) ).

fof(f17269,plain,
    ( spl0_901
    | ~ spl0_95
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1727,f1712,f724,f17267]) ).

fof(f17267,plain,
    ( spl0_901
  <=> ! [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_901])]) ).

fof(f724,plain,
    ( spl0_95
  <=> ! [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_95])]) ).

fof(f1727,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_95
    | ~ spl0_198 ),
    inference(superposition,[],[f725,f1713]) ).

fof(f725,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_95 ),
    inference(avatar_component_clause,[],[f724]) ).

fof(f17124,plain,
    ( spl0_652
    | spl0_900
    | ~ spl0_77
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2060,f2052,f614,f17122,f9912]) ).

fof(f9912,plain,
    ( spl0_652
  <=> ! [X0] : ~ member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f17122,plain,
    ( spl0_900
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f2060,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_77
    | ~ spl0_213 ),
    inference(resolution,[],[f2053,f615]) ).

fof(f17120,plain,
    ( spl0_899
    | ~ spl0_95
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1419,f1370,f724,f17118]) ).

fof(f17118,plain,
    ( spl0_899
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,rotate(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f1419,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,rotate(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) )
    | ~ spl0_95
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f725]) ).

fof(f17116,plain,
    ( ~ spl0_897
    | spl0_898
    | ~ spl0_90
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1206,f1168,f687,f17114,f17110]) ).

fof(f17110,plain,
    ( spl0_897
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f17114,plain,
    ( spl0_898
  <=> ! [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_898])]) ).

fof(f687,plain,
    ( spl0_90
  <=> ! [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_90])]) ).

fof(f1168,plain,
    ( spl0_144
  <=> ! [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_144])]) ).

fof(f1206,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_90
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f688]) ).

fof(f688,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_90 ),
    inference(avatar_component_clause,[],[f687]) ).

fof(f1169,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1168]) ).

fof(f17108,plain,
    ( spl0_895
    | ~ spl0_896
    | ~ spl0_100
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f839,f803,f746,f17105,f17102]) ).

fof(f17102,plain,
    ( spl0_895
  <=> ! [X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class)))))))))),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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f17105,plain,
    ( spl0_896
  <=> subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f803,plain,
    ( spl0_106
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f839,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class)))))))))),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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) )
    | ~ spl0_100
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f747]) ).

fof(f804,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f803]) ).

fof(f16959,plain,
    ( spl0_893
    | ~ spl0_894
    | ~ spl0_185
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1894,f1869,f1557,f16956,f16953]) ).

fof(f16953,plain,
    ( spl0_893
  <=> ! [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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f16956,plain,
    ( spl0_894
  <=> subclass(composition_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_894])]) ).

fof(f1557,plain,
    ( spl0_185
  <=> ! [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_185])]) ).

fof(f1894,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,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(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_185
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f1558]) ).

fof(f1558,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_185 ),
    inference(avatar_component_clause,[],[f1557]) ).

fof(f16906,plain,
    ( spl0_892
    | ~ spl0_162
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2035,f1999,f1352,f16904]) ).

fof(f16904,plain,
    ( spl0_892
  <=> ! [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_892])]) ).

fof(f1352,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

fof(f2035,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_162
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f1353]) ).

fof(f1353,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_162 ),
    inference(avatar_component_clause,[],[f1352]) ).

fof(f16902,plain,
    ( spl0_891
    | ~ spl0_162
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2012,f1995,f1352,f16900]) ).

fof(f16900,plain,
    ( spl0_891
  <=> ! [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_891])]) ).

fof(f2012,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_162
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f1353]) ).

fof(f16883,plain,
    ( spl0_890
    | ~ spl0_171
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1853,f1813,f1457,f16881]) ).

fof(f16881,plain,
    ( spl0_890
  <=> ! [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_890])]) ).

fof(f1457,plain,
    ( spl0_171
  <=> ! [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_171])]) ).

fof(f1853,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_171
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1458]) ).

fof(f1458,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_171 ),
    inference(avatar_component_clause,[],[f1457]) ).

fof(f16879,plain,
    ( spl0_889
    | ~ spl0_171
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1827,f1804,f1457,f16877]) ).

fof(f16877,plain,
    ( spl0_889
  <=> ! [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_889])]) ).

fof(f1827,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_171
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1458]) ).

fof(f16875,plain,
    ( spl0_888
    | ~ spl0_224
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f16591,f16010,f2228,f16873]) ).

fof(f16873,plain,
    ( spl0_888
  <=> ! [X0] : null_class = intersection(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f2228,plain,
    ( spl0_224
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f16010,plain,
    ( spl0_849
  <=> ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f16591,plain,
    ( ! [X0] : null_class = intersection(X0,null_class)
    | ~ spl0_224
    | ~ spl0_849 ),
    inference(resolution,[],[f16011,f2229]) ).

fof(f2229,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f2228]) ).

fof(f16011,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 )
    | ~ spl0_849 ),
    inference(avatar_component_clause,[],[f16010]) ).

fof(f16871,plain,
    ( spl0_887
    | ~ spl0_93
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1507,f1457,f703,f16869]) ).

fof(f16869,plain,
    ( spl0_887
  <=> ! [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_887])]) ).

fof(f1507,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_93
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f704]) ).

fof(f16830,plain,
    ( spl0_886
    | ~ spl0_186
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2048,f1999,f1579,f16828]) ).

fof(f16828,plain,
    ( spl0_886
  <=> ! [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(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,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_886])]) ).

fof(f1579,plain,
    ( spl0_186
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f2048,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(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,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_186
    | ~ spl0_212 ),
    inference(duplicate_literal_removal,[],[f2044]) ).

fof(f2044,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(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,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(compose(X2,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_186
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f1580]) ).

fof(f1580,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1579]) ).

fof(f16785,plain,
    ( spl0_885
    | ~ spl0_165
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2025,f1999,f1370,f16783]) ).

fof(f16783,plain,
    ( spl0_885
  <=> ! [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(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
        | ~ member(domain_of(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))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f2025,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(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
        | ~ member(domain_of(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))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_165
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f1371]) ).

fof(f16737,plain,
    ( spl0_884
    | ~ spl0_223
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f16590,f16010,f2224,f16735]) ).

fof(f2224,plain,
    ( spl0_223
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f16590,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_223
    | ~ spl0_849 ),
    inference(resolution,[],[f16011,f2225]) ).

fof(f2225,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2224]) ).

fof(f16733,plain,
    ( spl0_883
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2091,f2081,f381,f16731]) ).

fof(f16731,plain,
    ( spl0_883
  <=> ! [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_883])]) ).

fof(f2091,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_40
    | ~ spl0_216 ),
    inference(superposition,[],[f2082,f382]) ).

fof(f16729,plain,
    ( spl0_882
    | ~ spl0_199
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1932,f1924,f1746,f16727]) ).

fof(f16727,plain,
    ( spl0_882
  <=> ! [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_882])]) ).

fof(f1924,plain,
    ( spl0_208
  <=> ! [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_208])]) ).

fof(f1932,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_199
    | ~ spl0_208 ),
    inference(resolution,[],[f1925,f1747]) ).

fof(f1925,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_208 ),
    inference(avatar_component_clause,[],[f1924]) ).

fof(f16725,plain,
    ( spl0_881
    | ~ spl0_165
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1852,f1813,f1370,f16723]) ).

fof(f16723,plain,
    ( spl0_881
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,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_881])]) ).

fof(f1852,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,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_165
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1371]) ).

fof(f16721,plain,
    ( spl0_880
    | ~ spl0_165
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1826,f1804,f1370,f16719]) ).

fof(f16719,plain,
    ( spl0_880
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,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_880])]) ).

fof(f1826,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,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_165
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1371]) ).

fof(f16717,plain,
    ( spl0_879
    | ~ spl0_93
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1431,f1370,f703,f16715]) ).

fof(f16715,plain,
    ( spl0_879
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(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(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f1431,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(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(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f704]) ).

fof(f16586,plain,
    ( spl0_878
    | ~ spl0_235
    | ~ spl0_873 ),
    inference(avatar_split_clause,[],[f16545,f16542,f2311,f16584]) ).

fof(f16584,plain,
    ( spl0_878
  <=> ! [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))),singleton_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(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f2311,plain,
    ( spl0_235
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f16542,plain,
    ( spl0_873
  <=> ! [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_873])]) ).

fof(f16545,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))),singleton_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(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_235
    | ~ spl0_873 ),
    inference(forward_demodulation,[],[f16543,f2313]) ).

fof(f2313,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2311]) ).

fof(f16543,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_873 ),
    inference(avatar_component_clause,[],[f16542]) ).

fof(f16582,plain,
    ( spl0_877
    | ~ spl0_235
    | ~ spl0_872 ),
    inference(avatar_split_clause,[],[f16540,f16537,f2311,f16580]) ).

fof(f16580,plain,
    ( spl0_877
  <=> ! [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(complement(compose(element_relation,complement(singleton_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))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f16537,plain,
    ( spl0_872
  <=> ! [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(complement(compose(element_relation,complement(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(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))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f16540,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(complement(compose(element_relation,complement(singleton_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))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_872 ),
    inference(forward_demodulation,[],[f16538,f2313]) ).

fof(f16538,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(complement(compose(element_relation,complement(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(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))),singleton_relation) )
    | ~ spl0_872 ),
    inference(avatar_component_clause,[],[f16537]) ).

fof(f16557,plain,
    ( spl0_876
    | ~ spl0_235
    | ~ spl0_870 ),
    inference(avatar_split_clause,[],[f16531,f16528,f2311,f16555]) ).

fof(f16555,plain,
    ( spl0_876
  <=> ! [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))),singleton_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(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f16528,plain,
    ( spl0_870
  <=> ! [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_870])]) ).

fof(f16531,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))),singleton_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(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_235
    | ~ spl0_870 ),
    inference(forward_demodulation,[],[f16529,f2313]) ).

fof(f16529,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_870 ),
    inference(avatar_component_clause,[],[f16528]) ).

fof(f16553,plain,
    ( spl0_875
    | ~ spl0_235
    | ~ spl0_868 ),
    inference(avatar_split_clause,[],[f16522,f16519,f2311,f16551]) ).

fof(f16551,plain,
    ( spl0_875
  <=> ! [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(complement(compose(element_relation,complement(singleton_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))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f16519,plain,
    ( spl0_868
  <=> ! [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(complement(compose(element_relation,complement(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(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))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f16522,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(complement(compose(element_relation,complement(singleton_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))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_868 ),
    inference(forward_demodulation,[],[f16520,f2313]) ).

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(complement(compose(element_relation,complement(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(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))),singleton_relation) )
    | ~ spl0_868 ),
    inference(avatar_component_clause,[],[f16519]) ).

fof(f16549,plain,
    ( spl0_874
    | ~ spl0_123
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2043,f1999,f952,f16547]) ).

fof(f16547,plain,
    ( spl0_874
  <=> ! [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_874])]) ).

fof(f952,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f2043,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_123
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f953]) ).

fof(f953,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,null_class)
        | null_class = X0 )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f952]) ).

fof(f16544,plain,
    ( spl0_873
    | ~ spl0_125
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2039,f1999,f960,f16542]) ).

fof(f960,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f2039,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_125
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f961]) ).

fof(f961,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f960]) ).

fof(f16539,plain,
    ( spl0_872
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2037,f1999,f956,f16537]) ).

fof(f956,plain,
    ( spl0_124
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f2037,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(complement(compose(element_relation,complement(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(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))),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f957]) ).

fof(f957,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f956]) ).

fof(f16535,plain,
    ( spl0_871
    | ~ spl0_123
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2020,f1995,f952,f16533]) ).

fof(f16533,plain,
    ( spl0_871
  <=> ! [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_871])]) ).

fof(f2020,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_123
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f953]) ).

fof(f16530,plain,
    ( spl0_870
    | ~ spl0_125
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2016,f1995,f960,f16528]) ).

fof(f2016,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_125
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f961]) ).

fof(f16526,plain,
    ( spl0_869
    | ~ spl0_32
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f11995,f9140,f340,f16524]) ).

fof(f16524,plain,
    ( spl0_869
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f340,plain,
    ( spl0_32
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f9140,plain,
    ( spl0_603
  <=> ! [X0] : null_class = intersection(complement(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f11995,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0) )
    | ~ spl0_32
    | ~ spl0_603 ),
    inference(superposition,[],[f341,f9141]) ).

fof(f9141,plain,
    ( ! [X0] : null_class = intersection(complement(X0),X0)
    | ~ spl0_603 ),
    inference(avatar_component_clause,[],[f9140]) ).

fof(f341,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f340]) ).

fof(f16521,plain,
    ( spl0_868
    | ~ spl0_124
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2014,f1995,f956,f16519]) ).

fof(f2014,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(complement(compose(element_relation,complement(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(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))),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f957]) ).

fof(f16402,plain,
    ( spl0_867
    | ~ spl0_66
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2046,f1999,f553,f16400]) ).

fof(f16400,plain,
    ( spl0_867
  <=> ! [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(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
        | ~ member(domain_of(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_867])]) ).

fof(f553,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f2046,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(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
        | ~ member(domain_of(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_66
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f554]) ).

fof(f554,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f553]) ).

fof(f16398,plain,
    ( spl0_866
    | ~ spl0_142
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1904,f1869,f1160,f16396]) ).

fof(f16396,plain,
    ( spl0_866
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,regular(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f1160,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1904,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,regular(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f1161]) ).

fof(f1161,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,null_class)
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1160]) ).

fof(f16393,plain,
    ( spl0_864
    | ~ spl0_865
    | ~ spl0_144
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1901,f1869,f1168,f16390,f16387]) ).

fof(f16387,plain,
    ( spl0_864
  <=> ! [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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f16390,plain,
    ( spl0_865
  <=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f1901,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(flip(cross_product(subset_relation,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(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f1169]) ).

fof(f16385,plain,
    ( spl0_863
    | ~ spl0_20
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f3599,f3478,f288,f16383]) ).

fof(f16383,plain,
    ( spl0_863
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f288,plain,
    ( spl0_20
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f3478,plain,
    ( spl0_341
  <=> null_class = complement(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f3599,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_20
    | ~ spl0_341 ),
    inference(superposition,[],[f289,f3480]) ).

fof(f3480,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f3478]) ).

fof(f289,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f288]) ).

fof(f16381,plain,
    ( ~ spl0_862
    | ~ spl0_235
    | spl0_861 ),
    inference(avatar_split_clause,[],[f16376,f16372,f2311,f16378]) ).

fof(f16378,plain,
    ( spl0_862
  <=> subclass(composition_function,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f16372,plain,
    ( spl0_861
  <=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f16376,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_861 ),
    inference(forward_demodulation,[],[f16374,f2313]) ).

fof(f16374,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
    | spl0_861 ),
    inference(avatar_component_clause,[],[f16372]) ).

fof(f16375,plain,
    ( spl0_860
    | ~ spl0_861
    | ~ spl0_143
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1896,f1869,f1164,f16372,f16369]) ).

fof(f16369,plain,
    ( spl0_860
  <=> ! [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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f1164,plain,
    ( spl0_143
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1896,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
        | ~ 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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f1165]) ).

fof(f1165,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1164]) ).

fof(f16367,plain,
    ( spl0_859
    | ~ spl0_170
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1861,f1813,f1453,f16365]) ).

fof(f16365,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))))))),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_859])]) ).

fof(f1453,plain,
    ( spl0_170
  <=> ! [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_170])]) ).

fof(f1861,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_170
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1454]) ).

fof(f1454,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_170 ),
    inference(avatar_component_clause,[],[f1453]) ).

fof(f16363,plain,
    ( spl0_858
    | ~ spl0_170
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1835,f1804,f1453,f16361]) ).

fof(f16361,plain,
    ( spl0_858
  <=> ! [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_858])]) ).

fof(f1835,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_170
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1454]) ).

fof(f16300,plain,
    ( spl0_857
    | spl0_631
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1501,f1457,f629,f9582,f16298]) ).

fof(f16298,plain,
    ( spl0_857
  <=> ! [X2] :
        ( ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f9582,plain,
    ( spl0_631
  <=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f1501,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(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))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) )
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f630]) ).

fof(f16296,plain,
    ( spl0_856
    | ~ spl0_93
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1489,f1453,f703,f16294]) ).

fof(f16294,plain,
    ( spl0_856
  <=> ! [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_856])]) ).

fof(f1489,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_93
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f704]) ).

fof(f16279,plain,
    ( ~ spl0_80
    | spl0_179
    | ~ spl0_852 ),
    inference(avatar_split_clause,[],[f16049,f16039,f1523,f637]) ).

fof(f637,plain,
    ( spl0_80
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f1523,plain,
    ( spl0_179
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f16049,plain,
    ( ~ member(null_class,universal_class)
    | spl0_179
    | ~ spl0_852 ),
    inference(superposition,[],[f1524,f16041]) ).

fof(f16041,plain,
    ( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
    | ~ spl0_852 ),
    inference(avatar_component_clause,[],[f16039]) ).

fof(f1524,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | spl0_179 ),
    inference(avatar_component_clause,[],[f1523]) ).

fof(f16233,plain,
    ( spl0_855
    | ~ spl0_111
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2032,f1999,f824,f16231]) ).

fof(f16231,plain,
    ( spl0_855
  <=> ! [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_855])]) ).

fof(f2032,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_111
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f825]) ).

fof(f16229,plain,
    ( spl0_854
    | ~ spl0_111
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2009,f1995,f824,f16227]) ).

fof(f16227,plain,
    ( spl0_854
  <=> ! [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_854])]) ).

fof(f2009,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_111
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f825]) ).

fof(f16045,plain,
    ( spl0_852
    | spl0_853
    | ~ spl0_40
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2078,f2068,f381,f16043,f16039]) ).

fof(f16043,plain,
    ( spl0_853
  <=> ! [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_853])]) ).

fof(f2078,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_40
    | ~ spl0_215 ),
    inference(superposition,[],[f2069,f382]) ).

fof(f16037,plain,
    ( spl0_851
    | ~ spl0_48
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1890,f1869,f445,f16035]) ).

fof(f16035,plain,
    ( spl0_851
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,unordered_pair(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f445,plain,
    ( spl0_48
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1890,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,unordered_pair(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f446]) ).

fof(f446,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f445]) ).

fof(f16016,plain,
    ( spl0_850
    | ~ spl0_158
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1635,f1621,f1295,f16014]) ).

fof(f16014,plain,
    ( spl0_850
  <=> ! [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_850])]) ).

fof(f1635,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_158
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1296]) ).

fof(f16012,plain,
    ( spl0_849
    | ~ spl0_39
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f3158,f2728,f377,f16010]) ).

fof(f377,plain,
    ( spl0_39
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f2728,plain,
    ( spl0_284
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f3158,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 )
    | ~ spl0_39
    | ~ spl0_284 ),
    inference(resolution,[],[f2729,f378]) ).

fof(f378,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f377]) ).

fof(f2729,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f2728]) ).

fof(f15996,plain,
    ( spl0_848
    | ~ spl0_185
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1763,f1746,f1557,f15994]) ).

fof(f15994,plain,
    ( spl0_848
  <=> ! [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_848])]) ).

fof(f1763,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_185
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f1558]) ).

fof(f15992,plain,
    ( spl0_847
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1655,f1640,f569,f453,f15990]) ).

fof(f15990,plain,
    ( spl0_847
  <=> ! [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_847])]) ).

fof(f453,plain,
    ( spl0_50
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f1640,plain,
    ( spl0_194
  <=> ! [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_194])]) ).

fof(f1655,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_50
    | ~ spl0_70
    | ~ spl0_194 ),
    inference(forward_demodulation,[],[f1651,f454]) ).

fof(f454,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f453]) ).

fof(f1651,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_70
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f570]) ).

fof(f1641,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_194 ),
    inference(avatar_component_clause,[],[f1640]) ).

fof(f15896,plain,
    ( spl0_846
    | ~ spl0_235
    | ~ spl0_842 ),
    inference(avatar_split_clause,[],[f15880,f15877,f2311,f15894]) ).

fof(f15894,plain,
    ( spl0_846
  <=> ! [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(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))))))),singleton_relation)
        | 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f15877,plain,
    ( spl0_842
  <=> ! [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_842])]) ).

fof(f15880,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(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))))))),singleton_relation)
        | 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) )
    | ~ spl0_235
    | ~ spl0_842 ),
    inference(forward_demodulation,[],[f15878,f2313]) ).

fof(f15878,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_842 ),
    inference(avatar_component_clause,[],[f15877]) ).

fof(f15892,plain,
    ( spl0_845
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(avatar_split_clause,[],[f15875,f15869,f2311,f15890]) ).

fof(f15890,plain,
    ( spl0_845
  <=> ! [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(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_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(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f15869,plain,
    ( spl0_841
  <=> ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(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(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),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(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f15875,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(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_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(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15874,f2313]) ).

fof(f15874,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(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),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(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15873,f2313]) ).

fof(f15873,plain,
    ( ! [X0] :
        ( ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),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(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),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(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15872,f2313]) ).

fof(f15872,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(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(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),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(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15870,f2313]) ).

fof(f15870,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(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(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),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(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_841 ),
    inference(avatar_component_clause,[],[f15869]) ).

fof(f15888,plain,
    ( spl0_844
    | ~ spl0_235
    | ~ spl0_840 ),
    inference(avatar_split_clause,[],[f15867,f15864,f2311,f15886]) ).

fof(f15886,plain,
    ( spl0_844
  <=> ! [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,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
        | 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f15864,plain,
    ( spl0_840
  <=> ! [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_840])]) ).

fof(f15867,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,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
        | 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) )
    | ~ spl0_235
    | ~ spl0_840 ),
    inference(forward_demodulation,[],[f15865,f2313]) ).

fof(f15865,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_840 ),
    inference(avatar_component_clause,[],[f15864]) ).

fof(f15884,plain,
    ( spl0_843
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(avatar_split_clause,[],[f15862,f15856,f2311,f15882]) ).

fof(f15882,plain,
    ( spl0_843
  <=> ! [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,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_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,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f15856,plain,
    ( spl0_839
  <=> ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(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,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),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(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f15862,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,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_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,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15861,f2313]) ).

fof(f15861,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,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_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,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15860,f2313]) ).

fof(f15860,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_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,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),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(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15859,f2313]) ).

fof(f15859,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(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,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),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(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15857,f2313]) ).

fof(f15857,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(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,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),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(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_839 ),
    inference(avatar_component_clause,[],[f15856]) ).

fof(f15879,plain,
    ( spl0_842
    | ~ spl0_144
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1694,f1661,f1168,f15877]) ).

fof(f1661,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

fof(f1694,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_144
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f1169]) ).

fof(f1662,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_196 ),
    inference(avatar_component_clause,[],[f1661]) ).

fof(f15871,plain,
    ( spl0_841
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1691,f1661,f1164,f15869]) ).

fof(f1691,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(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(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),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(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f1165]) ).

fof(f15866,plain,
    ( spl0_840
    | ~ spl0_144
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1674,f1657,f1168,f15864]) ).

fof(f1657,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

fof(f1674,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_144
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f1169]) ).

fof(f1658,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_195 ),
    inference(avatar_component_clause,[],[f1657]) ).

fof(f15858,plain,
    ( spl0_839
    | ~ spl0_143
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1671,f1657,f1164,f15856]) ).

fof(f1671,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(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,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),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(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f1165]) ).

fof(f15795,plain,
    ( spl0_631
    | spl0_838
    | ~ spl0_79
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1483,f1453,f629,f15793,f9582]) ).

fof(f15793,plain,
    ( spl0_838
  <=> ! [X0,X3] :
        ( ~ function(X0)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))))))
        | ~ member(X3,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f1483,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,cross_product(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))))) )
    | ~ spl0_79
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f630]) ).

fof(f15779,plain,
    ( spl0_837
    | ~ spl0_198
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1941,f1936,f1712,f15777]) ).

fof(f15777,plain,
    ( spl0_837
  <=> ! [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_837])]) ).

fof(f1941,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_198
    | ~ spl0_209 ),
    inference(superposition,[],[f1937,f1713]) ).

fof(f15775,plain,
    ( spl0_835
    | ~ spl0_836
    | ~ spl0_99
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f844,f803,f740,f15772,f15769]) ).

fof(f15769,plain,
    ( spl0_835
  <=> ! [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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f15772,plain,
    ( spl0_836
  <=> subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f844,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(cross_product(universal_class,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(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_99
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f741]) ).

fof(f15741,plain,
    ( spl0_834
    | ~ spl0_176
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2010,f1995,f1478,f15739]) ).

fof(f15739,plain,
    ( spl0_834
  <=> ! [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_834])]) ).

fof(f1478,plain,
    ( spl0_176
  <=> ! [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_176])]) ).

fof(f2010,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_176
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f1479]) ).

fof(f1479,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_176 ),
    inference(avatar_component_clause,[],[f1478]) ).

fof(f15734,plain,
    ( ~ spl0_832
    | ~ spl0_833
    | spl0_633
    | ~ spl0_162
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1648,f1640,f1352,f9660,f15731,f15727]) ).

fof(f15727,plain,
    ( spl0_832
  <=> 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_832])]) ).

fof(f15731,plain,
    ( spl0_833
  <=> 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_833])]) ).

fof(f9660,plain,
    ( spl0_633
  <=> 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_633])]) ).

fof(f1648,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_162
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f1353]) ).

fof(f15675,plain,
    ( spl0_831
    | ~ spl0_176
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2050,f1999,f1478,f15673]) ).

fof(f15673,plain,
    ( spl0_831
  <=> ! [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_831])]) ).

fof(f2050,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_176
    | ~ spl0_212 ),
    inference(duplicate_literal_removal,[],[f2033]) ).

fof(f2033,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_176
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f1479]) ).

fof(f15671,plain,
    ( ~ spl0_830
    | ~ spl0_235
    | spl0_802 ),
    inference(avatar_split_clause,[],[f15233,f15224,f2311,f15668]) ).

fof(f15668,plain,
    ( spl0_830
  <=> subset_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f15224,plain,
    ( spl0_802
  <=> identity_relation = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f15233,plain,
    ( subset_relation != singleton_relation
    | ~ spl0_235
    | spl0_802 ),
    inference(forward_demodulation,[],[f15225,f2313]) ).

fof(f15225,plain,
    ( identity_relation != subset_relation
    | spl0_802 ),
    inference(avatar_component_clause,[],[f15224]) ).

fof(f15666,plain,
    ( spl0_829
    | ~ spl0_89
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1939,f1936,f683,f15664]) ).

fof(f15664,plain,
    ( spl0_829
  <=> ! [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_829])]) ).

fof(f683,plain,
    ( spl0_89
  <=> ! [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_89])]) ).

fof(f1939,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_89
    | ~ spl0_209 ),
    inference(resolution,[],[f1937,f684]) ).

fof(f684,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_89 ),
    inference(avatar_component_clause,[],[f683]) ).

fof(f15584,plain,
    ( spl0_828
    | ~ spl0_235
    | ~ spl0_822 ),
    inference(avatar_split_clause,[],[f15553,f15550,f2311,f15582]) ).

fof(f15582,plain,
    ( spl0_828
  <=> ! [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)))),singleton_relation)
        | ~ 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f15550,plain,
    ( spl0_822
  <=> ! [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_822])]) ).

fof(f15553,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)))),singleton_relation)
        | ~ 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) )
    | ~ spl0_235
    | ~ spl0_822 ),
    inference(forward_demodulation,[],[f15551,f2313]) ).

fof(f15551,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_822 ),
    inference(avatar_component_clause,[],[f15550]) ).

fof(f15580,plain,
    ( spl0_827
    | ~ spl0_235
    | ~ spl0_821 ),
    inference(avatar_split_clause,[],[f15548,f15545,f2311,f15578]) ).

fof(f15578,plain,
    ( spl0_827
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ 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)))),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)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f15545,plain,
    ( spl0_821
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(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)))),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)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f15548,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ 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)))),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)))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_821 ),
    inference(forward_demodulation,[],[f15546,f2313]) ).

fof(f15546,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(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)))),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)))),singleton_relation) )
    | ~ spl0_821 ),
    inference(avatar_component_clause,[],[f15545]) ).

fof(f15569,plain,
    ( spl0_826
    | ~ spl0_198
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1933,f1924,f1712,f15567]) ).

fof(f15567,plain,
    ( spl0_826
  <=> ! [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_826])]) ).

fof(f1933,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_198
    | ~ spl0_208 ),
    inference(superposition,[],[f1925,f1713]) ).

fof(f15565,plain,
    ( spl0_825
    | ~ spl0_152
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1854,f1813,f1248,f15563]) ).

fof(f15563,plain,
    ( spl0_825
  <=> ! [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_825])]) ).

fof(f1248,plain,
    ( spl0_152
  <=> ! [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_152])]) ).

fof(f1854,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_152
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1249]) ).

fof(f1249,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1248]) ).

fof(f15561,plain,
    ( spl0_824
    | ~ spl0_152
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1828,f1804,f1248,f15559]) ).

fof(f15559,plain,
    ( spl0_824
  <=> ! [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_824])]) ).

fof(f1828,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_152
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1249]) ).

fof(f15557,plain,
    ( spl0_823
    | ~ spl0_142
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1771,f1746,f1160,f15555]) ).

fof(f15555,plain,
    ( spl0_823
  <=> ! [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_823])]) ).

fof(f1771,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_142
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f1161]) ).

fof(f15552,plain,
    ( spl0_822
    | ~ spl0_144
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1768,f1746,f1168,f15550]) ).

fof(f1768,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_144
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f1169]) ).

fof(f15547,plain,
    ( spl0_821
    | ~ spl0_143
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1765,f1746,f1164,f15545]) ).

fof(f1765,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(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)))),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)))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f1165]) ).

fof(f15543,plain,
    ( spl0_820
    | ~ spl0_93
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1268,f1248,f703,f15541]) ).

fof(f15541,plain,
    ( spl0_820
  <=> ! [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_820])]) ).

fof(f1268,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_93
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f704]) ).

fof(f15514,plain,
    ( spl0_819
    | ~ spl0_787
    | ~ spl0_817 ),
    inference(avatar_split_clause,[],[f15505,f15502,f14710,f15512]) ).

fof(f15512,plain,
    ( spl0_819
  <=> ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(null_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_819])]) ).

fof(f15502,plain,
    ( spl0_817
  <=> ! [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_817])]) ).

fof(f15505,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(null_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_787
    | ~ spl0_817 ),
    inference(forward_demodulation,[],[f15503,f14712]) ).

fof(f15503,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_817 ),
    inference(avatar_component_clause,[],[f15502]) ).

fof(f15510,plain,
    ( ~ spl0_818
    | ~ spl0_22
    | spl0_812 ),
    inference(avatar_split_clause,[],[f15285,f15276,f296,f15507]) ).

fof(f15507,plain,
    ( spl0_818
  <=> function(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f296,plain,
    ( spl0_22
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f15276,plain,
    ( spl0_812
  <=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f15285,plain,
    ( ~ function(composition_function)
    | ~ spl0_22
    | spl0_812 ),
    inference(resolution,[],[f15278,f297]) ).

fof(f297,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f15278,plain,
    ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
    | spl0_812 ),
    inference(avatar_component_clause,[],[f15276]) ).

fof(f15504,plain,
    ( spl0_817
    | ~ spl0_198
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1912,f1907,f1712,f15502]) ).

fof(f1912,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_198
    | ~ spl0_206 ),
    inference(superposition,[],[f1908,f1713]) ).

fof(f15500,plain,
    ( spl0_816
    | ~ spl0_48
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1759,f1746,f445,f15498]) ).

fof(f15498,plain,
    ( spl0_816
  <=> ! [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_816])]) ).

fof(f1759,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_48
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f446]) ).

fof(f15293,plain,
    ( spl0_815
    | ~ spl0_77
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2031,f1999,f614,f15291]) ).

fof(f15291,plain,
    ( spl0_815
  <=> ! [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_815])]) ).

fof(f2031,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_77
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f615]) ).

fof(f15289,plain,
    ( spl0_814
    | ~ spl0_77
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2008,f1995,f614,f15287]) ).

fof(f15287,plain,
    ( spl0_814
  <=> ! [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_814])]) ).

fof(f2008,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_77
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f615]) ).

fof(f15284,plain,
    ( ~ spl0_813
    | ~ spl0_235
    | spl0_803 ),
    inference(avatar_split_clause,[],[f15232,f15228,f2311,f15281]) ).

fof(f15281,plain,
    ( spl0_813
  <=> subclass(subset_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f15228,plain,
    ( spl0_803
  <=> subclass(subset_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f15232,plain,
    ( ~ subclass(subset_relation,singleton_relation)
    | ~ spl0_235
    | spl0_803 ),
    inference(forward_demodulation,[],[f15230,f2313]) ).

fof(f15230,plain,
    ( ~ subclass(subset_relation,identity_relation)
    | spl0_803 ),
    inference(avatar_component_clause,[],[f15228]) ).

fof(f15279,plain,
    ( spl0_811
    | ~ spl0_812
    | ~ spl0_85
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1878,f1869,f665,f15276,f15273]) ).

fof(f15273,plain,
    ( spl0_811
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f665,plain,
    ( spl0_85
  <=> ! [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_85])]) ).

fof(f1878,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,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(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_85
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f666]) ).

fof(f666,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_85 ),
    inference(avatar_component_clause,[],[f665]) ).

fof(f15271,plain,
    ( spl0_810
    | ~ spl0_48
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1685,f1661,f445,f15269]) ).

fof(f15269,plain,
    ( spl0_810
  <=> ! [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_810])]) ).

fof(f1685,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_48
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f446]) ).

fof(f15267,plain,
    ( spl0_809
    | ~ spl0_48
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1665,f1657,f445,f15265]) ).

fof(f15265,plain,
    ( spl0_809
  <=> ! [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_809])]) ).

fof(f1665,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_48
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f446]) ).

fof(f15263,plain,
    ( spl0_808
    | ~ spl0_96
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1420,f1370,f728,f15261]) ).

fof(f15261,plain,
    ( spl0_808
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,flip(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f1420,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,flip(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) )
    | ~ spl0_96
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f729]) ).

fof(f15257,plain,
    ( ~ spl0_807
    | ~ spl0_235
    | spl0_805 ),
    inference(avatar_split_clause,[],[f15249,f15241,f2311,f15254]) ).

fof(f15254,plain,
    ( spl0_807
  <=> 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))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f15241,plain,
    ( spl0_805
  <=> 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_805])]) ).

fof(f15249,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))))))),singleton_relation)
    | ~ spl0_235
    | spl0_805 ),
    inference(forward_demodulation,[],[f15242,f2313]) ).

fof(f15242,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))))))),identity_relation)
    | spl0_805 ),
    inference(avatar_component_clause,[],[f15241]) ).

fof(f15248,plain,
    ( spl0_527
    | ~ spl0_804
    | spl0_805
    | ~ spl0_806
    | ~ spl0_84
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1210,f1168,f655,f15245,f15241,f15237,f7414]) ).

fof(f7414,plain,
    ( spl0_527
  <=> null_class = domain_of(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f15237,plain,
    ( spl0_804
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f15245,plain,
    ( spl0_806
  <=> 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_806])]) ).

fof(f655,plain,
    ( spl0_84
  <=> ! [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_84])]) ).

fof(f1210,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_84
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f656]) ).

fof(f656,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_84 ),
    inference(avatar_component_clause,[],[f655]) ).

fof(f15231,plain,
    ( spl0_802
    | ~ spl0_803
    | ~ spl0_39
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2694,f2467,f377,f15228,f15224]) ).

fof(f2467,plain,
    ( spl0_264
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2694,plain,
    ( ~ subclass(subset_relation,identity_relation)
    | identity_relation = subset_relation
    | ~ spl0_39
    | ~ spl0_264 ),
    inference(resolution,[],[f2469,f378]) ).

fof(f2469,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f2467]) ).

fof(f15219,plain,
    ( ~ spl0_801
    | ~ spl0_235
    | spl0_797 ),
    inference(avatar_split_clause,[],[f15203,f15194,f2311,f15216]) ).

fof(f15216,plain,
    ( spl0_801
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f15194,plain,
    ( spl0_797
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f15203,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(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_797 ),
    inference(forward_demodulation,[],[f15195,f2313]) ).

fof(f15195,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(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | spl0_797 ),
    inference(avatar_component_clause,[],[f15194]) ).

fof(f15214,plain,
    ( ~ spl0_800
    | ~ spl0_235
    | spl0_798 ),
    inference(avatar_split_clause,[],[f15202,f15198,f2311,f15211]) ).

fof(f15211,plain,
    ( spl0_800
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f15198,plain,
    ( spl0_798
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f15202,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(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation)
    | ~ spl0_235
    | spl0_798 ),
    inference(forward_demodulation,[],[f15200,f2313]) ).

fof(f15200,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(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
    | spl0_798 ),
    inference(avatar_component_clause,[],[f15198]) ).

fof(f15209,plain,
    ( ~ spl0_799
    | ~ spl0_235
    | spl0_796 ),
    inference(avatar_split_clause,[],[f15204,f15190,f2311,f15206]) ).

fof(f15206,plain,
    ( spl0_799
  <=> member(complement(compose(element_relation,complement(singleton_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f15190,plain,
    ( spl0_796
  <=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f15204,plain,
    ( ~ member(complement(compose(element_relation,complement(singleton_relation))),universal_class)
    | ~ spl0_235
    | spl0_796 ),
    inference(forward_demodulation,[],[f15192,f2313]) ).

fof(f15192,plain,
    ( ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | spl0_796 ),
    inference(avatar_component_clause,[],[f15190]) ).

fof(f15201,plain,
    ( spl0_521
    | ~ spl0_796
    | spl0_797
    | ~ spl0_798
    | ~ spl0_84
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1196,f1164,f655,f15198,f15194,f15190,f7372]) ).

fof(f7372,plain,
    ( spl0_521
  <=> null_class = complement(compose(element_relation,complement(identity_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f1196,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(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),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(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_84
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f656]) ).

fof(f15178,plain,
    ( spl0_795
    | ~ spl0_38
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1940,f1936,f373,f15176]) ).

fof(f15176,plain,
    ( spl0_795
  <=> ! [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_795])]) ).

fof(f373,plain,
    ( spl0_38
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1940,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_38
    | ~ spl0_209 ),
    inference(resolution,[],[f1937,f374]) ).

fof(f374,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f373]) ).

fof(f14994,plain,
    ( spl0_794
    | ~ spl0_154
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1786,f1774,f1278,f14992]) ).

fof(f14992,plain,
    ( spl0_794
  <=> ! [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_794])]) ).

fof(f1278,plain,
    ( spl0_154
  <=> ! [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_154])]) ).

fof(f1774,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

fof(f1786,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_154
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1279]) ).

fof(f1279,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_154 ),
    inference(avatar_component_clause,[],[f1278]) ).

fof(f1775,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_200 ),
    inference(avatar_component_clause,[],[f1774]) ).

fof(f14990,plain,
    ( spl0_793
    | ~ spl0_153
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1785,f1774,f1274,f14988]) ).

fof(f14988,plain,
    ( spl0_793
  <=> ! [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_793])]) ).

fof(f1274,plain,
    ( spl0_153
  <=> ! [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_153])]) ).

fof(f1785,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_153
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1275]) ).

fof(f1275,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_153 ),
    inference(avatar_component_clause,[],[f1274]) ).

fof(f14851,plain,
    ( spl0_792
    | ~ spl0_787
    | ~ spl0_791 ),
    inference(avatar_split_clause,[],[f14847,f14844,f14710,f14849]) ).

fof(f14849,plain,
    ( spl0_792
  <=> ! [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))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f14844,plain,
    ( spl0_791
  <=> ! [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_791])]) ).

fof(f14847,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_787
    | ~ spl0_791 ),
    inference(forward_demodulation,[],[f14845,f14712]) ).

fof(f14845,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_791 ),
    inference(avatar_component_clause,[],[f14844]) ).

fof(f14846,plain,
    ( spl0_791
    | ~ spl0_89
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1910,f1907,f683,f14844]) ).

fof(f1910,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_89
    | ~ spl0_206 ),
    inference(resolution,[],[f1908,f684]) ).

fof(f14842,plain,
    ( spl0_790
    | ~ spl0_142
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1696,f1661,f1160,f14840]) ).

fof(f14840,plain,
    ( spl0_790
  <=> ! [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_790])]) ).

fof(f1696,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_142
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f1161]) ).

fof(f14838,plain,
    ( spl0_789
    | ~ spl0_142
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1676,f1657,f1160,f14836]) ).

fof(f14836,plain,
    ( spl0_789
  <=> ! [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_789])]) ).

fof(f1676,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_142
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f1161]) ).

fof(f14716,plain,
    ( spl0_787
    | spl0_788
    | ~ spl0_40
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1943,f1936,f381,f14714,f14710]) ).

fof(f14714,plain,
    ( spl0_788
  <=> ! [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_788])]) ).

fof(f1943,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_40
    | ~ spl0_209 ),
    inference(superposition,[],[f1937,f382]) ).

fof(f14708,plain,
    ( spl0_786
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1840,f1804,f381,f14706]) ).

fof(f14706,plain,
    ( spl0_786
  <=> ! [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_786])]) ).

fof(f1840,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_40
    | ~ spl0_202 ),
    inference(superposition,[],[f1805,f382]) ).

fof(f14701,plain,
    ( spl0_784
    | ~ spl0_785
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1801,f1794,f381,f14698,f14695]) ).

fof(f14695,plain,
    ( spl0_784
  <=> ! [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_784])]) ).

fof(f14698,plain,
    ( spl0_785
  <=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f1794,plain,
    ( spl0_201
  <=> ! [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_201])]) ).

fof(f1801,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_40
    | ~ spl0_201 ),
    inference(superposition,[],[f1795,f382]) ).

fof(f1795,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_201 ),
    inference(avatar_component_clause,[],[f1794]) ).

fof(f14693,plain,
    ( spl0_783
    | ~ spl0_158
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1509,f1457,f1295,f14691]) ).

fof(f14691,plain,
    ( spl0_783
  <=> ! [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_783])]) ).

fof(f1509,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_158
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f1296]) ).

fof(f14640,plain,
    ( spl0_782
    | ~ spl0_49
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1647,f1640,f449,f14638]) ).

fof(f14638,plain,
    ( spl0_782
  <=> ! [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_782])]) ).

fof(f1647,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_49
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f450]) ).

fof(f14610,plain,
    ( spl0_780
    | ~ spl0_781
    | ~ spl0_39
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f2534,f2394,f377,f14607,f14603]) ).

fof(f14603,plain,
    ( spl0_780
  <=> element_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f14607,plain,
    ( spl0_781
  <=> subclass(element_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f2394,plain,
    ( spl0_251
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f2534,plain,
    ( ~ subclass(element_relation,singleton_relation)
    | element_relation = singleton_relation
    | ~ spl0_39
    | ~ spl0_251 ),
    inference(resolution,[],[f2396,f378]) ).

fof(f2396,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f2394]) ).

fof(f14601,plain,
    ( spl0_779
    | ~ spl0_185
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1629,f1621,f1557,f14599]) ).

fof(f14599,plain,
    ( spl0_779
  <=> ! [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_779])]) ).

fof(f1629,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_185
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1558]) ).

fof(f14517,plain,
    ( spl0_778
    | ~ spl0_130
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1860,f1813,f1013,f14515]) ).

fof(f14515,plain,
    ( spl0_778
  <=> ! [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_778])]) ).

fof(f1013,plain,
    ( spl0_130
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f1860,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_130
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f1014]) ).

fof(f1014,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1013]) ).

fof(f14513,plain,
    ( spl0_777
    | ~ spl0_130
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1834,f1804,f1013,f14511]) ).

fof(f14511,plain,
    ( spl0_777
  <=> ! [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_777])]) ).

fof(f1834,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_130
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f1014]) ).

fof(f14509,plain,
    ( spl0_776
    | ~ spl0_114
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1790,f1774,f893,f14507]) ).

fof(f14507,plain,
    ( spl0_776
  <=> ! [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_776])]) ).

fof(f893,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1790,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_114
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f894]) ).

fof(f894,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f893]) ).

fof(f14505,plain,
    ( spl0_775
    | ~ spl0_93
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1069,f1013,f703,f14503]) ).

fof(f14503,plain,
    ( spl0_775
  <=> ! [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_775])]) ).

fof(f1069,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_93
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f704]) ).

fof(f14286,plain,
    ( spl0_774
    | ~ spl0_146
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1780,f1774,f1222,f14284]) ).

fof(f14284,plain,
    ( spl0_774
  <=> ! [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_774])]) ).

fof(f1222,plain,
    ( spl0_146
  <=> ! [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_146])]) ).

fof(f1780,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_146
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1223]) ).

fof(f1223,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1222]) ).

fof(f14282,plain,
    ( spl0_773
    | ~ spl0_158
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1433,f1370,f1295,f14280]) ).

fof(f14280,plain,
    ( spl0_773
  <=> ! [X0] :
        ( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f1433,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f1296]) ).

fof(f14278,plain,
    ( spl0_772
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1133,f1088,f629,f14276]) ).

fof(f14276,plain,
    ( spl0_772
  <=> ! [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_772])]) ).

fof(f1133,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_79
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f630]) ).

fof(f14274,plain,
    ( spl0_771
    | ~ spl0_79
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1115,f1084,f629,f14272]) ).

fof(f14272,plain,
    ( spl0_771
  <=> ! [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_771])]) ).

fof(f1115,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_79
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f630]) ).

fof(f14216,plain,
    ( spl0_770
    | ~ spl0_38
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1911,f1907,f373,f14214]) ).

fof(f14214,plain,
    ( spl0_770
  <=> ! [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_770])]) ).

fof(f1911,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_38
    | ~ spl0_206 ),
    inference(resolution,[],[f1908,f374]) ).

fof(f13915,plain,
    ( spl0_769
    | ~ spl0_106
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1859,f1813,f803,f13913]) ).

fof(f13913,plain,
    ( spl0_769
  <=> ! [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_769])]) ).

fof(f1859,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_106
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f804]) ).

fof(f13911,plain,
    ( spl0_768
    | ~ spl0_70
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1842,f1813,f569,f13909]) ).

fof(f13909,plain,
    ( spl0_768
  <=> ! [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_768])]) ).

fof(f1842,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_70
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f570]) ).

fof(f13907,plain,
    ( spl0_767
    | ~ spl0_106
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1833,f1804,f803,f13905]) ).

fof(f13905,plain,
    ( spl0_767
  <=> ! [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_767])]) ).

fof(f1833,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_106
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f804]) ).

fof(f13903,plain,
    ( spl0_766
    | ~ spl0_70
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1816,f1804,f569,f13901]) ).

fof(f13901,plain,
    ( spl0_766
  <=> ! [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_766])]) ).

fof(f1816,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_70
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f570]) ).

fof(f13836,plain,
    ( spl0_765
    | ~ spl0_184
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1787,f1774,f1550,f13834]) ).

fof(f13834,plain,
    ( spl0_765
  <=> ! [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_765])]) ).

fof(f1550,plain,
    ( spl0_184
  <=> ! [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_184])]) ).

fof(f1787,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_184
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1551]) ).

fof(f1551,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_184 ),
    inference(avatar_component_clause,[],[f1550]) ).

fof(f13832,plain,
    ( spl0_764
    | ~ spl0_158
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1491,f1453,f1295,f13830]) ).

fof(f13830,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f1491,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_158
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f1296]) ).

fof(f13828,plain,
    ( spl0_763
    | ~ spl0_93
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f852,f803,f703,f13826]) ).

fof(f13826,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(f852,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_93
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f704]) ).

fof(f13734,plain,
    ( spl0_762
    | ~ spl0_116
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1857,f1813,f920,f13732]) ).

fof(f13732,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(f920,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1857,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_116
    | ~ spl0_204 ),
    inference(resolution,[],[f1814,f921]) ).

fof(f921,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f920]) ).

fof(f13730,plain,
    ( spl0_761
    | ~ spl0_116
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1831,f1804,f920,f13728]) ).

fof(f13728,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(f1831,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_116
    | ~ spl0_202 ),
    inference(resolution,[],[f1805,f921]) ).

fof(f13726,plain,
    ( spl0_760
    | ~ spl0_341
    | ~ spl0_616 ),
    inference(avatar_split_clause,[],[f13449,f9350,f3478,f13723]) ).

fof(f13723,plain,
    ( spl0_760
  <=> null_class = intersection(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f9350,plain,
    ( spl0_616
  <=> ! [X0] : null_class = intersection(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f13449,plain,
    ( null_class = intersection(universal_class,null_class)
    | ~ spl0_341
    | ~ spl0_616 ),
    inference(superposition,[],[f9351,f3480]) ).

fof(f9351,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_616 ),
    inference(avatar_component_clause,[],[f9350]) ).

fof(f13721,plain,
    ( spl0_759
    | ~ spl0_44
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1649,f1640,f425,f13719]) ).

fof(f13719,plain,
    ( spl0_759
  <=> ! [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_759])]) ).

fof(f1649,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_44
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f426]) ).

fof(f13717,plain,
    ( spl0_758
    | ~ spl0_163
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1618,f1610,f1362,f13715]) ).

fof(f13715,plain,
    ( spl0_758
  <=> ! [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_758])]) ).

fof(f1362,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

fof(f1610,plain,
    ( spl0_191
  <=> ! [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_191])]) ).

fof(f1618,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_163
    | ~ spl0_191 ),
    inference(resolution,[],[f1611,f1363]) ).

fof(f1363,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_163 ),
    inference(avatar_component_clause,[],[f1362]) ).

fof(f1611,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_191 ),
    inference(avatar_component_clause,[],[f1610]) ).

fof(f13713,plain,
    ( spl0_757
    | ~ spl0_93
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f980,f920,f703,f13711]) ).

fof(f13711,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(f980,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_93
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f704]) ).

fof(f13581,plain,
    ( spl0_756
    | ~ spl0_106
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2027,f1999,f803,f13579]) ).

fof(f13579,plain,
    ( spl0_756
  <=> ! [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_756])]) ).

fof(f2027,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_106
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f804]) ).

fof(f13577,plain,
    ( spl0_755
    | ~ spl0_106
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2004,f1995,f803,f13575]) ).

fof(f13575,plain,
    ( spl0_755
  <=> ! [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_755])]) ).

fof(f2004,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_106
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f804]) ).

fof(f13448,plain,
    ( spl0_754
    | ~ spl0_111
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1928,f1924,f824,f13446]) ).

fof(f13446,plain,
    ( spl0_754
  <=> ! [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_754])]) ).

fof(f1928,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_111
    | ~ spl0_208 ),
    inference(resolution,[],[f1925,f825]) ).

fof(f13444,plain,
    ( spl0_753
    | ~ spl0_40
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1864,f1813,f381,f13442]) ).

fof(f13442,plain,
    ( spl0_753
  <=> ! [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_753])]) ).

fof(f1864,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_40
    | ~ spl0_204 ),
    inference(superposition,[],[f1814,f382]) ).

fof(f13440,plain,
    ( spl0_752
    | ~ spl0_162
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1393,f1366,f1352,f13438]) ).

fof(f13438,plain,
    ( spl0_752
  <=> ! [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_752])]) ).

fof(f1366,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

fof(f1393,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_162
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f1353]) ).

fof(f1367,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_164 ),
    inference(avatar_component_clause,[],[f1366]) ).

fof(f13409,plain,
    ( spl0_751
    | ~ spl0_38
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1889,f1869,f373,f13407]) ).

fof(f13407,plain,
    ( spl0_751
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f1889,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) )
    | ~ spl0_38
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f374]) ).

fof(f13405,plain,
    ( spl0_750
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1798,f1794,f381,f13403]) ).

fof(f13403,plain,
    ( spl0_750
  <=> ! [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_750])]) ).

fof(f1798,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_40
    | ~ spl0_201 ),
    inference(superposition,[],[f1795,f382]) ).

fof(f13343,plain,
    ( spl0_749
    | spl0_631
    | ~ spl0_79
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1262,f1248,f629,f9582,f13341]) ).

fof(f13341,plain,
    ( spl0_749
  <=> ! [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_749])]) ).

fof(f1262,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_79
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f630]) ).

fof(f12959,plain,
    ( spl0_748
    | ~ spl0_31
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1893,f1869,f336,f12957]) ).

fof(f12957,plain,
    ( spl0_748
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f336,plain,
    ( spl0_31
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1893,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) )
    | ~ spl0_31
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f337]) ).

fof(f337,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f336]) ).

fof(f12955,plain,
    ( spl0_747
    | ~ spl0_32
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1892,f1869,f340,f12953]) ).

fof(f12953,plain,
    ( spl0_747
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f1892,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) )
    | ~ spl0_32
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f341]) ).

fof(f12888,plain,
    ( spl0_746
    | ~ spl0_89
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1882,f1869,f683,f12886]) ).

fof(f12886,plain,
    ( spl0_746
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,compose(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),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),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f1882,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,compose(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),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),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f684]) ).

fof(f12884,plain,
    ( spl0_745
    | ~ spl0_85
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1751,f1746,f665,f12882]) ).

fof(f12882,plain,
    ( spl0_745
  <=> ! [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_745])]) ).

fof(f1751,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_85
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f666]) ).

fof(f12880,plain,
    ( spl0_744
    | ~ spl0_163
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1744,f1712,f1362,f12878]) ).

fof(f12878,plain,
    ( spl0_744
  <=> ! [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_744])]) ).

fof(f1744,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_163
    | ~ spl0_198 ),
    inference(superposition,[],[f1363,f1713]) ).

fof(f12876,plain,
    ( spl0_743
    | ~ spl0_91
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1726,f1712,f692,f12874]) ).

fof(f12874,plain,
    ( spl0_743
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | second(regular(cross_product(X0,X1))) = 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),X2),universal_class)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f692,plain,
    ( spl0_91
  <=> ! [X4,X0,X1] :
        ( 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),X0),universal_class))))))) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1726,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | second(regular(cross_product(X0,X1))) = 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),X2),universal_class)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_91
    | ~ spl0_198 ),
    inference(superposition,[],[f693,f1713]) ).

fof(f693,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
        | 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),X0),universal_class))))))) = X4 )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f692]) ).

fof(f12872,plain,
    ( spl0_742
    | ~ spl0_84
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1182,f1160,f655,f12870]) ).

fof(f12870,plain,
    ( spl0_742
  <=> ! [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_742])]) ).

fof(f1182,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_84
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f656]) ).

fof(f12868,plain,
    ( spl0_741
    | ~ spl0_79
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1046,f1009,f629,f12866]) ).

fof(f12866,plain,
    ( spl0_741
  <=> ! [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_741])]) ).

fof(f1046,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_79
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f630]) ).

fof(f12864,plain,
    ( spl0_740
    | ~ spl0_79
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1030,f1005,f629,f12862]) ).

fof(f12862,plain,
    ( spl0_740
  <=> ! [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_740])]) ).

fof(f1030,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_79
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f630]) ).

fof(f12790,plain,
    ( spl0_739
    | ~ spl0_341
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f11988,f9140,f3478,f12787]) ).

fof(f12787,plain,
    ( spl0_739
  <=> null_class = intersection(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f11988,plain,
    ( null_class = intersection(null_class,universal_class)
    | ~ spl0_341
    | ~ spl0_603 ),
    inference(superposition,[],[f9141,f3480]) ).

fof(f12551,plain,
    ( spl0_738
    | ~ spl0_9
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2028,f1999,f241,f12549]) ).

fof(f12549,plain,
    ( spl0_738
  <=> ! [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_738])]) ).

fof(f241,plain,
    ( spl0_9
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f2028,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_9
    | ~ spl0_212 ),
    inference(resolution,[],[f2000,f242]) ).

fof(f242,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f241]) ).

fof(f12547,plain,
    ( spl0_737
    | ~ spl0_9
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2005,f1995,f241,f12545]) ).

fof(f12545,plain,
    ( spl0_737
  <=> ! [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_737])]) ).

fof(f2005,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_9
    | ~ spl0_211 ),
    inference(resolution,[],[f1996,f242]) ).

fof(f12543,plain,
    ( spl0_736
    | ~ spl0_20
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1895,f1869,f288,f12541]) ).

fof(f12541,plain,
    ( spl0_736
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,complement(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f1895,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,complement(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) )
    | ~ spl0_20
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f289]) ).

fof(f12539,plain,
    ( spl0_735
    | spl0_150
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1784,f1774,f1239,f12536]) ).

fof(f12536,plain,
    ( spl0_735
  <=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f1239,plain,
    ( spl0_150
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1784,plain,
    ( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)))))
    | spl0_150
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1241]) ).

fof(f1241,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | spl0_150 ),
    inference(avatar_component_clause,[],[f1239]) ).

fof(f12534,plain,
    ( spl0_734
    | spl0_148
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1783,f1774,f1230,f12531]) ).

fof(f12531,plain,
    ( spl0_734
  <=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f1230,plain,
    ( spl0_148
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1783,plain,
    ( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)))))
    | spl0_148
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1232]) ).

fof(f1232,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | spl0_148 ),
    inference(avatar_component_clause,[],[f1230]) ).

fof(f12529,plain,
    ( spl0_733
    | ~ spl0_137
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1781,f1774,f1096,f12527]) ).

fof(f12527,plain,
    ( spl0_733
  <=> ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f1096,plain,
    ( spl0_137
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1781,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_137
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1097]) ).

fof(f1097,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1096]) ).

fof(f12198,plain,
    ( spl0_732
    | ~ spl0_235
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f12159,f12156,f2311,f12196]) ).

fof(f12196,plain,
    ( spl0_732
  <=> ! [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))))))),singleton_relation)
        | 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f12156,plain,
    ( spl0_723
  <=> ! [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_723])]) ).

fof(f12159,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))))))),singleton_relation)
        | 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) )
    | ~ spl0_235
    | ~ spl0_723 ),
    inference(forward_demodulation,[],[f12157,f2313]) ).

fof(f12157,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_723 ),
    inference(avatar_component_clause,[],[f12156]) ).

fof(f12194,plain,
    ( spl0_731
    | ~ spl0_235
    | ~ spl0_722 ),
    inference(avatar_split_clause,[],[f12154,f12151,f2311,f12192]) ).

fof(f12192,plain,
    ( spl0_731
  <=> ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | 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))))))),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(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f12151,plain,
    ( spl0_722
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(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))))))),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(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f12154,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | 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))))))),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(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_722 ),
    inference(forward_demodulation,[],[f12152,f2313]) ).

fof(f12152,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(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))))))),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(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_722 ),
    inference(avatar_component_clause,[],[f12151]) ).

fof(f12190,plain,
    ( spl0_730
    | ~ spl0_9
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1917,f1914,f241,f12188]) ).

fof(f12188,plain,
    ( spl0_730
  <=> ! [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_730])]) ).

fof(f1914,plain,
    ( spl0_207
  <=> ! [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_207])]) ).

fof(f1917,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_9
    | ~ spl0_207 ),
    inference(resolution,[],[f1915,f242]) ).

fof(f1915,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_207 ),
    inference(avatar_component_clause,[],[f1914]) ).

fof(f12186,plain,
    ( ~ spl0_729
    | ~ spl0_235
    | spl0_728 ),
    inference(avatar_split_clause,[],[f12181,f12177,f2311,f12183]) ).

fof(f12183,plain,
    ( spl0_729
  <=> subclass(composition_function,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f12177,plain,
    ( spl0_728
  <=> subclass(composition_function,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f12181,plain,
    ( ~ subclass(composition_function,singleton_relation)
    | ~ spl0_235
    | spl0_728 ),
    inference(forward_demodulation,[],[f12179,f2313]) ).

fof(f12179,plain,
    ( ~ subclass(composition_function,identity_relation)
    | spl0_728 ),
    inference(avatar_component_clause,[],[f12177]) ).

fof(f12180,plain,
    ( spl0_727
    | ~ spl0_728
    | ~ spl0_103
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1903,f1869,f762,f12177,f12174]) ).

fof(f12174,plain,
    ( spl0_727
  <=> ! [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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f762,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1903,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,identity_relation)
        | ~ 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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f763]) ).

fof(f763,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f762]) ).

fof(f12172,plain,
    ( ~ spl0_726
    | spl0_3
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f11993,f9140,f215,f12169]) ).

fof(f215,plain,
    ( spl0_3
  <=> universal_class = complement(intersection(complement(complement(x)),complement(x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f11993,plain,
    ( universal_class != complement(null_class)
    | spl0_3
    | ~ spl0_603 ),
    inference(superposition,[],[f217,f9141]) ).

fof(f217,plain,
    ( universal_class != complement(intersection(complement(complement(x)),complement(x)))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f12167,plain,
    ( spl0_725
    | ~ spl0_160
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1742,f1712,f1317,f12165]) ).

fof(f12165,plain,
    ( spl0_725
  <=> ! [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_725])]) ).

fof(f1317,plain,
    ( spl0_160
  <=> ! [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_160])]) ).

fof(f1742,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_160
    | ~ spl0_198 ),
    inference(superposition,[],[f1318,f1713]) ).

fof(f1318,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1317]) ).

fof(f12163,plain,
    ( spl0_724
    | ~ spl0_142
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1637,f1621,f1160,f12161]) ).

fof(f12161,plain,
    ( spl0_724
  <=> ! [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_724])]) ).

fof(f1637,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_142
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1161]) ).

fof(f12158,plain,
    ( spl0_723
    | ~ spl0_144
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1634,f1621,f1168,f12156]) ).

fof(f1634,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_144
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1169]) ).

fof(f12153,plain,
    ( spl0_722
    | ~ spl0_143
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1631,f1621,f1164,f12151]) ).

fof(f1631,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(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))))))),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(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1165]) ).

fof(f12111,plain,
    ( spl0_721
    | ~ spl0_39
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1789,f1774,f377,f12109]) ).

fof(f12109,plain,
    ( spl0_721
  <=> ! [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_721])]) ).

fof(f1789,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_39
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f378]) ).

fof(f12107,plain,
    ( spl0_720
    | ~ spl0_89
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1755,f1746,f683,f12105]) ).

fof(f12105,plain,
    ( spl0_720
  <=> ! [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_720])]) ).

fof(f1755,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_89
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f684]) ).

fof(f12103,plain,
    ( spl0_719
    | ~ spl0_94
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f882,f824,f719,f12101]) ).

fof(f12101,plain,
    ( spl0_719
  <=> ! [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_719])]) ).

fof(f719,plain,
    ( spl0_94
  <=> ! [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_94])]) ).

fof(f882,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_94
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f720]) ).

fof(f720,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_94 ),
    inference(avatar_component_clause,[],[f719]) ).

fof(f11903,plain,
    ( spl0_718
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1839,f1804,f453,f11901]) ).

fof(f11901,plain,
    ( spl0_718
  <=> ! [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_718])]) ).

fof(f1839,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_50
    | ~ spl0_202 ),
    inference(superposition,[],[f1805,f454]) ).

fof(f11899,plain,
    ( spl0_717
    | ~ spl0_132
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1741,f1712,f1021,f11897]) ).

fof(f11897,plain,
    ( spl0_717
  <=> ! [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_717])]) ).

fof(f1021,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1741,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_132
    | ~ spl0_198 ),
    inference(superposition,[],[f1022,f1713]) ).

fof(f1022,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1021]) ).

fof(f11895,plain,
    ( spl0_716
    | ~ spl0_48
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1625,f1621,f445,f11893]) ).

fof(f11893,plain,
    ( spl0_716
  <=> ! [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_716])]) ).

fof(f1625,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_48
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f446]) ).

fof(f11866,plain,
    ( spl0_715
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1800,f1794,f453,f11864]) ).

fof(f11864,plain,
    ( spl0_715
  <=> ! [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_715])]) ).

fof(f1800,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_50
    | ~ spl0_201 ),
    inference(superposition,[],[f1795,f454]) ).

fof(f11790,plain,
    ( spl0_714
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1797,f1794,f453,f11788]) ).

fof(f11788,plain,
    ( spl0_714
  <=> ! [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_714])]) ).

fof(f1797,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_50
    | ~ spl0_201 ),
    inference(superposition,[],[f1795,f454]) ).

fof(f11786,plain,
    ( spl0_713
    | ~ spl0_89
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1725,f1712,f683,f11784]) ).

fof(f11784,plain,
    ( spl0_713
  <=> ! [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_713])]) ).

fof(f1725,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_89
    | ~ spl0_198 ),
    inference(superposition,[],[f684,f1713]) ).

fof(f11758,plain,
    ( spl0_712
    | ~ spl0_77
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1934,f1924,f614,f11756]) ).

fof(f11756,plain,
    ( spl0_712
  <=> ! [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_712])]) ).

fof(f1934,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_77
    | ~ spl0_208 ),
    inference(duplicate_literal_removal,[],[f1927]) ).

fof(f1927,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_77
    | ~ spl0_208 ),
    inference(resolution,[],[f1925,f615]) ).

fof(f11754,plain,
    ( spl0_711
    | ~ spl0_136
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1777,f1774,f1092,f11752]) ).

fof(f11752,plain,
    ( spl0_711
  <=> ! [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_711])]) ).

fof(f1092,plain,
    ( spl0_136
  <=> ! [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_136])]) ).

fof(f1777,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_136
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f1093]) ).

fof(f1093,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1092]) ).

fof(f11740,plain,
    ( spl0_710
    | ~ spl0_30
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1736,f1712,f332,f11738]) ).

fof(f11738,plain,
    ( spl0_710
  <=> ! [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_710])]) ).

fof(f1736,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_30
    | ~ spl0_198 ),
    inference(superposition,[],[f333,f1713]) ).

fof(f11736,plain,
    ( ~ spl0_708
    | spl0_709
    | ~ spl0_165
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1569,f1557,f1370,f11734,f11730]) ).

fof(f11730,plain,
    ( spl0_708
  <=> subclass(domain_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_708])]) ).

fof(f11734,plain,
    ( spl0_709
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f1569,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,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_165
    | ~ spl0_185 ),
    inference(resolution,[],[f1558,f1371]) ).

fof(f11653,plain,
    ( spl0_707
    | ~ spl0_38
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1758,f1746,f373,f11651]) ).

fof(f11651,plain,
    ( spl0_707
  <=> ! [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_707])]) ).

fof(f1758,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_38
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f374]) ).

fof(f11647,plain,
    ( ~ spl0_706
    | ~ spl0_235
    | spl0_704 ),
    inference(avatar_split_clause,[],[f11642,f11634,f2311,f11644]) ).

fof(f11644,plain,
    ( spl0_706
  <=> 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))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f11634,plain,
    ( spl0_704
  <=> 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_704])]) ).

fof(f11642,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(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_704 ),
    inference(forward_demodulation,[],[f11636,f2313]) ).

fof(f11636,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(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_704 ),
    inference(avatar_component_clause,[],[f11634]) ).

fof(f11641,plain,
    ( ~ spl0_704
    | ~ spl0_705
    | spl0_430
    | ~ spl0_125
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1652,f1640,f960,f5491,f11638,f11634]) ).

fof(f11638,plain,
    ( spl0_705
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f5491,plain,
    ( spl0_430
  <=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f1652,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_125
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f961]) ).

fof(f11630,plain,
    ( ~ spl0_703
    | ~ spl0_235
    | spl0_700 ),
    inference(avatar_split_clause,[],[f11610,f11601,f2311,f11627]) ).

fof(f11627,plain,
    ( spl0_703
  <=> 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(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f11601,plain,
    ( spl0_700
  <=> 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(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f11610,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(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_700 ),
    inference(forward_demodulation,[],[f11603,f2313]) ).

fof(f11603,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(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | spl0_700 ),
    inference(avatar_component_clause,[],[f11601]) ).

fof(f11625,plain,
    ( ~ spl0_702
    | ~ spl0_235
    | spl0_701 ),
    inference(avatar_split_clause,[],[f11609,f11605,f2311,f11622]) ).

fof(f11622,plain,
    ( spl0_702
  <=> member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f11605,plain,
    ( spl0_701
  <=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f11609,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class)
    | ~ spl0_235
    | spl0_701 ),
    inference(forward_demodulation,[],[f11607,f2313]) ).

fof(f11607,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | spl0_701 ),
    inference(avatar_component_clause,[],[f11605]) ).

fof(f11608,plain,
    ( ~ spl0_700
    | ~ spl0_701
    | spl0_425
    | ~ spl0_124
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1650,f1640,f956,f5464,f11605,f11601]) ).

fof(f5464,plain,
    ( spl0_425
  <=> null_class = complement(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f1650,plain,
    ( null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ member(complement(complement(compose(element_relation,complement(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(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_124
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f957]) ).

fof(f11574,plain,
    ( spl0_699
    | ~ spl0_31
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1762,f1746,f336,f11572]) ).

fof(f11572,plain,
    ( spl0_699
  <=> ! [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_699])]) ).

fof(f1762,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_31
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f337]) ).

fof(f11570,plain,
    ( spl0_698
    | ~ spl0_32
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1761,f1746,f340,f11568]) ).

fof(f11568,plain,
    ( spl0_698
  <=> ! [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_698])]) ).

fof(f1761,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_32
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f341]) ).

fof(f11477,plain,
    ( spl0_697
    | ~ spl0_20
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1764,f1746,f288,f11475]) ).

fof(f11475,plain,
    ( spl0_697
  <=> ! [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_697])]) ).

fof(f1764,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_199 ),
    inference(resolution,[],[f1747,f289]) ).

fof(f11473,plain,
    ( spl0_696
    | ~ spl0_48
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1737,f1712,f445,f11471]) ).

fof(f11471,plain,
    ( spl0_696
  <=> ! [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_696])]) ).

fof(f1737,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_48
    | ~ spl0_198 ),
    inference(superposition,[],[f446,f1713]) ).

fof(f11454,plain,
    ( spl0_695
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1772,f1746,f732,f11452]) ).

fof(f11452,plain,
    ( spl0_695
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),singleton_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)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f732,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1772,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),singleton_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)))),element_relation) )
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f733]) ).

fof(f733,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f732]) ).

fof(f11449,plain,
    ( spl0_694
    | ~ spl0_103
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1770,f1746,f762,f11447]) ).

fof(f11447,plain,
    ( spl0_694
  <=> ! [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_694])]) ).

fof(f1770,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_103
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f763]) ).

fof(f11445,plain,
    ( spl0_693
    | ~ spl0_126
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1739,f1712,f964,f11443]) ).

fof(f11443,plain,
    ( spl0_693
  <=> ! [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_693])]) ).

fof(f964,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1739,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_126
    | ~ spl0_198 ),
    inference(superposition,[],[f965,f1713]) ).

fof(f965,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | null_class = X1
        | null_class = X0 )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f964]) ).

fof(f11042,plain,
    ( spl0_692
    | ~ spl0_38
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1710,f1705,f373,f11040]) ).

fof(f11040,plain,
    ( spl0_692
  <=> ! [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_692])]) ).

fof(f1710,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_38
    | ~ spl0_197 ),
    inference(resolution,[],[f1706,f374]) ).

fof(f11038,plain,
    ( spl0_691
    | ~ spl0_31
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1688,f1661,f336,f11036]) ).

fof(f11036,plain,
    ( spl0_691
  <=> ! [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_691])]) ).

fof(f1688,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_31
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f337]) ).

fof(f11034,plain,
    ( spl0_690
    | ~ spl0_32
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1687,f1661,f340,f11032]) ).

fof(f11032,plain,
    ( spl0_690
  <=> ! [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_690])]) ).

fof(f1687,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_32
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f341]) ).

fof(f11030,plain,
    ( spl0_689
    | ~ spl0_31
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1668,f1657,f336,f11028]) ).

fof(f11028,plain,
    ( spl0_689
  <=> ! [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_689])]) ).

fof(f1668,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_31
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f337]) ).

fof(f11026,plain,
    ( spl0_688
    | ~ spl0_32
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1667,f1657,f340,f11024]) ).

fof(f11024,plain,
    ( spl0_688
  <=> ! [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_688])]) ).

fof(f1667,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_32
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f341]) ).

fof(f11022,plain,
    ( spl0_687
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1409,f1366,f569,f453,f11020]) ).

fof(f11020,plain,
    ( spl0_687
  <=> ! [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_687])]) ).

fof(f1409,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_50
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(forward_demodulation,[],[f1396,f454]) ).

fof(f1396,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_70
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f570]) ).

fof(f10796,plain,
    ( spl0_686
    | spl0_122
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1782,f1774,f947,f10793]) ).

fof(f10793,plain,
    ( spl0_686
  <=> not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f947,plain,
    ( spl0_122
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1782,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
    | spl0_122
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f949]) ).

fof(f949,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | spl0_122 ),
    inference(avatar_component_clause,[],[f947]) ).

fof(f10791,plain,
    ( spl0_685
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f10437,f8668,f2311,f2305,f10788]) ).

fof(f10788,plain,
    ( spl0_685
  <=> member(regular(singleton_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f2305,plain,
    ( spl0_234
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f8668,plain,
    ( spl0_569
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f10437,plain,
    ( member(regular(singleton_relation),universal_class)
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_569 ),
    inference(forward_demodulation,[],[f10378,f2313]) ).

fof(f10378,plain,
    ( member(regular(identity_relation),universal_class)
    | ~ spl0_234
    | ~ spl0_569 ),
    inference(resolution,[],[f8669,f2307]) ).

fof(f2307,plain,
    ( member(regular(identity_relation),subset_relation)
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2305]) ).

fof(f8669,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_569 ),
    inference(avatar_component_clause,[],[f8668]) ).

fof(f10786,plain,
    ( spl0_684
    | spl0_120
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1779,f1774,f937,f10783]) ).

fof(f10783,plain,
    ( spl0_684
  <=> 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_684])]) ).

fof(f937,plain,
    ( spl0_120
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1779,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_120
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f939]) ).

fof(f939,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_120 ),
    inference(avatar_component_clause,[],[f937]) ).

fof(f10781,plain,
    ( spl0_683
    | spl0_118
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1778,f1774,f928,f10778]) ).

fof(f10778,plain,
    ( spl0_683
  <=> 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_683])]) ).

fof(f928,plain,
    ( spl0_118
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1778,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_118
    | ~ spl0_200 ),
    inference(resolution,[],[f1775,f930]) ).

fof(f930,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_118 ),
    inference(avatar_component_clause,[],[f928]) ).

fof(f10604,plain,
    ( spl0_682
    | ~ spl0_152
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1313,f1295,f1248,f10602]) ).

fof(f10602,plain,
    ( spl0_682
  <=> ! [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_682])]) ).

fof(f1313,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_152
    | ~ spl0_158 ),
    inference(resolution,[],[f1296,f1249]) ).

fof(f10600,plain,
    ( spl0_681
    | ~ spl0_96
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f843,f803,f728,f10598]) ).

fof(f10598,plain,
    ( spl0_681
  <=> ! [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_681])]) ).

fof(f843,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_96
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f729]) ).

fof(f10596,plain,
    ( spl0_680
    | ~ spl0_95
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f842,f803,f724,f10594]) ).

fof(f10594,plain,
    ( spl0_680
  <=> ! [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_680])]) ).

fof(f842,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_95
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f725]) ).

fof(f10563,plain,
    ( spl0_678
    | ~ spl0_679
    | ~ spl0_78
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1881,f1869,f625,f10560,f10557]) ).

fof(f10557,plain,
    ( spl0_678
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f10560,plain,
    ( spl0_679
  <=> subclass(composition_function,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f625,plain,
    ( spl0_78
  <=> ! [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_78])]) ).

fof(f1881,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_78
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f626]) ).

fof(f626,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_78 ),
    inference(avatar_component_clause,[],[f625]) ).

fof(f10555,plain,
    ( spl0_677
    | ~ spl0_78
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1754,f1746,f625,f10553]) ).

fof(f10553,plain,
    ( spl0_677
  <=> ! [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_677])]) ).

fof(f1754,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_78
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f626]) ).

fof(f10551,plain,
    ( spl0_676
    | ~ spl0_142
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1511,f1457,f1160,f10549]) ).

fof(f10549,plain,
    ( spl0_676
  <=> ! [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_676])]) ).

fof(f1511,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_142
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f1161]) ).

fof(f10547,plain,
    ( spl0_675
    | ~ spl0_435
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1505,f1457,f1164,f5515,f10545]) ).

fof(f10545,plain,
    ( spl0_675
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f5515,plain,
    ( spl0_435
  <=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1505,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_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))))),element_relation)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f1165]) ).

fof(f10447,plain,
    ( spl0_674
    | ~ spl0_131
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1740,f1712,f1017,f10445]) ).

fof(f10445,plain,
    ( spl0_674
  <=> ! [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_674])]) ).

fof(f1017,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f1740,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_131
    | ~ spl0_198 ),
    inference(superposition,[],[f1018,f1713]) ).

fof(f1018,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1017]) ).

fof(f10443,plain,
    ( spl0_673
    | ~ spl0_78
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1721,f1712,f625,f10441]) ).

fof(f10441,plain,
    ( spl0_673
  <=> ! [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_673])]) ).

fof(f1721,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_78
    | ~ spl0_198 ),
    inference(superposition,[],[f626,f1713]) ).

fof(f10374,plain,
    ( spl0_672
    | ~ spl0_20
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1690,f1661,f288,f10372]) ).

fof(f10372,plain,
    ( spl0_672
  <=> ! [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_672])]) ).

fof(f1690,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_196 ),
    inference(resolution,[],[f1662,f289]) ).

fof(f10370,plain,
    ( spl0_671
    | ~ spl0_20
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1670,f1657,f288,f10368]) ).

fof(f10368,plain,
    ( spl0_671
  <=> ! [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_671])]) ).

fof(f1670,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_195 ),
    inference(resolution,[],[f1658,f289]) ).

fof(f10363,plain,
    ( ~ spl0_669
    | ~ spl0_670
    | spl0_344
    | ~ spl0_111
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1646,f1640,f824,f3491,f10360,f10356]) ).

fof(f10356,plain,
    ( spl0_669
  <=> 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_669])]) ).

fof(f10360,plain,
    ( spl0_670
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f3491,plain,
    ( spl0_344
  <=> null_class = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f1646,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_111
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f825]) ).

fof(f9981,plain,
    ( spl0_668
    | ~ spl0_176
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1733,f1712,f1478,f9979]) ).

fof(f9979,plain,
    ( spl0_668
  <=> ! [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_668])]) ).

fof(f1733,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_176
    | ~ spl0_198 ),
    inference(superposition,[],[f1479,f1713]) ).

fof(f9977,plain,
    ( spl0_667
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1692,f1661,f889,f9975]) ).

fof(f9975,plain,
    ( spl0_667
  <=> ! [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_667])]) ).

fof(f889,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1692,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_113
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f890]) ).

fof(f890,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f889]) ).

fof(f9973,plain,
    ( spl0_666
    | ~ spl0_38
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1684,f1661,f373,f9971]) ).

fof(f9971,plain,
    ( spl0_666
  <=> ! [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_666])]) ).

fof(f1684,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_38
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f374]) ).

fof(f9969,plain,
    ( spl0_665
    | ~ spl0_113
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1672,f1657,f889,f9967]) ).

fof(f9967,plain,
    ( spl0_665
  <=> ! [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_665])]) ).

fof(f1672,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_113
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f890]) ).

fof(f9965,plain,
    ( spl0_664
    | ~ spl0_38
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1664,f1657,f373,f9963]) ).

fof(f9963,plain,
    ( spl0_664
  <=> ! [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_664])]) ).

fof(f1664,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_38
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f374]) ).

fof(f9961,plain,
    ( spl0_663
    | ~ spl0_123
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1653,f1640,f952,f9959]) ).

fof(f9959,plain,
    ( spl0_663
  <=> ! [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_663])]) ).

fof(f1653,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_123
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f953]) ).

fof(f9957,plain,
    ( spl0_662
    | ~ spl0_48
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1500,f1457,f445,f9955]) ).

fof(f9955,plain,
    ( spl0_662
  <=> ! [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_662])]) ).

fof(f1500,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_48
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f446]) ).

fof(f9953,plain,
    ( spl0_661
    | ~ spl0_142
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1493,f1453,f1160,f9951]) ).

fof(f9951,plain,
    ( spl0_661
  <=> ! [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_661])]) ).

fof(f1493,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_142
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f1161]) ).

fof(f9949,plain,
    ( ~ spl0_435
    | spl0_660
    | ~ spl0_143
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1487,f1453,f1164,f9947,f5515]) ).

fof(f9947,plain,
    ( spl0_660
  <=> ! [X0,X1] :
        ( ~ function(X0)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation)
        | ~ member(X1,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f1487,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f1165]) ).

fof(f9945,plain,
    ( spl0_659
    | ~ spl0_142
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1435,f1370,f1160,f9943]) ).

fof(f9943,plain,
    ( spl0_659
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,regular(X0))
        | ~ member(X1,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f1435,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,regular(X0))
        | ~ member(X1,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f1161]) ).

fof(f9940,plain,
    ( spl0_657
    | ~ spl0_658
    | ~ spl0_144
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1432,f1370,f1168,f9937,f9934]) ).

fof(f9934,plain,
    ( spl0_657
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f9937,plain,
    ( spl0_658
  <=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f1432,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f1169]) ).

fof(f9932,plain,
    ( ~ spl0_656
    | ~ spl0_235
    | spl0_655 ),
    inference(avatar_split_clause,[],[f9927,f9923,f2311,f9929]) ).

fof(f9929,plain,
    ( spl0_656
  <=> subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f9923,plain,
    ( spl0_655
  <=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f9927,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_655 ),
    inference(forward_demodulation,[],[f9925,f2313]) ).

fof(f9925,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
    | spl0_655 ),
    inference(avatar_component_clause,[],[f9923]) ).

fof(f9926,plain,
    ( spl0_654
    | ~ spl0_655
    | ~ spl0_143
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1429,f1370,f1164,f9923,f9920]) ).

fof(f9920,plain,
    ( spl0_654
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f1429,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f1165]) ).

fof(f9918,plain,
    ( spl0_652
    | ~ spl0_653
    | ~ spl0_9
    | ~ spl0_341
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6768,f6442,f3478,f241,f9915,f9912]) ).

fof(f9915,plain,
    ( spl0_653
  <=> subclass(domain_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f6442,plain,
    ( spl0_489
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f6768,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_9
    | ~ spl0_341
    | ~ spl0_489 ),
    inference(forward_demodulation,[],[f6745,f3480]) ).

fof(f6745,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(universal_class)) )
    | ~ spl0_9
    | ~ spl0_489 ),
    inference(resolution,[],[f6443,f242]) ).

fof(f6443,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | ~ member(X1,universal_class)
        | ~ subclass(domain_relation,complement(X0)) )
    | ~ spl0_489 ),
    inference(avatar_component_clause,[],[f6442]) ).

fof(f9910,plain,
    ( spl0_651
    | ~ spl0_79
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1064,f1013,f629,f9908]) ).

fof(f9908,plain,
    ( spl0_651
  <=> ! [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_651])]) ).

fof(f1064,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_79
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f630]) ).

fof(f9904,plain,
    ( spl0_650
    | ~ spl0_87
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1724,f1712,f674,f9902]) ).

fof(f9902,plain,
    ( spl0_650
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f674,plain,
    ( spl0_87
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f1724,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_87
    | ~ spl0_198 ),
    inference(superposition,[],[f675,f1713]) ).

fof(f675,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
        | compose(X0,X1) = X4 )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f674]) ).

fof(f9782,plain,
    ( spl0_649
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1883,f1869,f585,f9780]) ).

fof(f9780,plain,
    ( spl0_649
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f585,plain,
    ( spl0_72
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f1883,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) )
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f586]) ).

fof(f586,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
        | compose(X0,X1) = X4 )
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f585]) ).

fof(f9778,plain,
    ( spl0_648
    | ~ spl0_29
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1735,f1712,f328,f9776]) ).

fof(f9776,plain,
    ( spl0_648
  <=> ! [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_648])]) ).

fof(f1735,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_29
    | ~ spl0_198 ),
    inference(superposition,[],[f329,f1713]) ).

fof(f9774,plain,
    ( spl0_647
    | ~ spl0_48
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1482,f1453,f445,f9772]) ).

fof(f9772,plain,
    ( spl0_647
  <=> ! [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_647])]) ).

fof(f1482,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_48
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f446]) ).

fof(f9770,plain,
    ( spl0_646
    | ~ spl0_48
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1424,f1370,f445,f9768]) ).

fof(f9768,plain,
    ( spl0_646
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f1424,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 )
    | ~ spl0_48
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f446]) ).

fof(f9766,plain,
    ( spl0_645
    | ~ spl0_49
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1392,f1366,f449,f9764]) ).

fof(f9764,plain,
    ( spl0_645
  <=> ! [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_645])]) ).

fof(f1392,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_49
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f450]) ).

fof(f9762,plain,
    ( spl0_644
    | ~ spl0_115
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1359,f1352,f916,f9760]) ).

fof(f9760,plain,
    ( spl0_644
  <=> ! [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_644])]) ).

fof(f916,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1359,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_115
    | ~ spl0_162 ),
    inference(resolution,[],[f1353,f917]) ).

fof(f917,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f916]) ).

fof(f9721,plain,
    ( spl0_643
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(avatar_split_clause,[],[f9688,f9683,f2311,f9719]) ).

fof(f9719,plain,
    ( spl0_643
  <=> ! [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(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f9683,plain,
    ( spl0_637
  <=> ! [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_637])]) ).

fof(f9688,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(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f9687,f2313]) ).

fof(f9687,plain,
    ( ! [X0] :
        ( ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,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) )
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f9686,f2313]) ).

fof(f9686,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_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_235
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f9684,f2313]) ).

fof(f9684,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_637 ),
    inference(avatar_component_clause,[],[f9683]) ).

fof(f9717,plain,
    ( ~ spl0_641
    | spl0_642
    | ~ spl0_106
    | ~ spl0_360 ),
    inference(avatar_split_clause,[],[f3840,f3754,f803,f9715,f9711]) ).

fof(f9711,plain,
    ( spl0_641
  <=> subclass(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f9715,plain,
    ( spl0_642
  <=> ! [X0] : member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f3754,plain,
    ( spl0_360
  <=> ! [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_360])]) ).

fof(f3840,plain,
    ( ! [X0] :
        ( member(X0,universal_class)
        | ~ subclass(universal_class,subset_relation) )
    | ~ spl0_106
    | ~ spl0_360 ),
    inference(resolution,[],[f3755,f804]) ).

fof(f3755,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_360 ),
    inference(avatar_component_clause,[],[f3754]) ).

fof(f9700,plain,
    ( spl0_640
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(avatar_split_clause,[],[f9677,f9672,f2311,f9698]) ).

fof(f9698,plain,
    ( spl0_640
  <=> ! [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,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f9672,plain,
    ( spl0_635
  <=> ! [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_635])]) ).

fof(f9677,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,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(forward_demodulation,[],[f9676,f2313]) ).

fof(f9676,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_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,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(forward_demodulation,[],[f9675,f2313]) ).

fof(f9675,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_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_235
    | ~ spl0_635 ),
    inference(forward_demodulation,[],[f9673,f2313]) ).

fof(f9673,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_635 ),
    inference(avatar_component_clause,[],[f9672]) ).

fof(f9696,plain,
    ( spl0_639
    | ~ spl0_67
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1877,f1869,f557,f9694]) ).

fof(f9694,plain,
    ( spl0_639
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f557,plain,
    ( spl0_67
  <=> ! [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_67])]) ).

fof(f1877,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) )
    | ~ spl0_67
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f558]) ).

fof(f558,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_67 ),
    inference(avatar_component_clause,[],[f557]) ).

fof(f9692,plain,
    ( spl0_638
    | ~ spl0_97
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1697,f1661,f732,f9690]) ).

fof(f9690,plain,
    ( spl0_638
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(singleton_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(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f1697,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(singleton_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(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_97
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f733]) ).

fof(f9685,plain,
    ( spl0_637
    | ~ spl0_103
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1695,f1661,f762,f9683]) ).

fof(f1695,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_103
    | ~ spl0_196 ),
    inference(resolution,[],[f1662,f763]) ).

fof(f9681,plain,
    ( spl0_636
    | ~ spl0_97
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1677,f1657,f732,f9679]) ).

fof(f9679,plain,
    ( spl0_636
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,singleton_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,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f1677,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,singleton_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,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_97
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f733]) ).

fof(f9674,plain,
    ( spl0_635
    | ~ spl0_103
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1675,f1657,f762,f9672]) ).

fof(f1675,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_103
    | ~ spl0_195 ),
    inference(resolution,[],[f1658,f763]) ).

fof(f9667,plain,
    ( spl0_633
    | ~ spl0_634
    | ~ spl0_112
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1360,f1352,f885,f9664,f9660]) ).

fof(f9664,plain,
    ( spl0_634
  <=> 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_634])]) ).

fof(f885,plain,
    ( spl0_112
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1360,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_112
    | ~ spl0_162 ),
    inference(resolution,[],[f1353,f886]) ).

fof(f886,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f885]) ).

fof(f9658,plain,
    ( spl0_632
    | ~ spl0_4
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f3739,f3596,f220,f9656]) ).

fof(f9656,plain,
    ( spl0_632
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f220,plain,
    ( spl0_4
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f3596,plain,
    ( spl0_357
  <=> ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f3739,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_357 ),
    inference(resolution,[],[f3597,f221]) ).

fof(f221,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f220]) ).

fof(f3597,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f3596]) ).

fof(f9584,plain,
    ( spl0_630
    | spl0_631
    | ~ spl0_79
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f848,f803,f629,f9582,f9579]) ).

fof(f9579,plain,
    ( spl0_630
  <=> ! [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_630])]) ).

fof(f848,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_79
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f630]) ).

fof(f9528,plain,
    ( spl0_628
    | ~ spl0_629
    | ~ spl0_64
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1884,f1869,f540,f9525,f9522]) ).

fof(f9522,plain,
    ( spl0_628
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f9525,plain,
    ( spl0_629
  <=> subclass(composition_function,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f540,plain,
    ( spl0_64
  <=> ! [X0,X1] :
        ( domain_of(X0) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f1884,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_64
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f541]) ).

fof(f541,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f540]) ).

fof(f9520,plain,
    ( spl0_627
    | ~ spl0_89
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1416,f1370,f683,f9518]) ).

fof(f9518,plain,
    ( spl0_627
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,compose(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),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),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f1416,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,compose(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),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),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f684]) ).

fof(f9516,plain,
    ( spl0_626
    | ~ spl0_28
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1358,f1352,f324,f9514]) ).

fof(f9514,plain,
    ( spl0_626
  <=> ! [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_626])]) ).

fof(f324,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1358,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_28
    | ~ spl0_162 ),
    inference(resolution,[],[f1353,f325]) ).

fof(f325,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f324]) ).

fof(f9458,plain,
    ( spl0_625
    | ~ spl0_235
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3674,f3530,f2823,f2311,f9455]) ).

fof(f9455,plain,
    ( spl0_625
  <=> null_class = intersection(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f2823,plain,
    ( spl0_293
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f3530,plain,
    ( spl0_352
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f3674,plain,
    ( null_class = intersection(singleton_relation,complement(subset_relation))
    | ~ spl0_235
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(forward_demodulation,[],[f3665,f2313]) ).

fof(f3665,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3660]) ).

fof(f3660,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(resolution,[],[f3531,f2824]) ).

fof(f2824,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f2823]) ).

fof(f3531,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,complement(X1))),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_352 ),
    inference(avatar_component_clause,[],[f3530]) ).

fof(f9397,plain,
    ( spl0_624
    | ~ spl0_235
    | ~ spl0_619 ),
    inference(avatar_split_clause,[],[f9369,f9366,f2311,f9395]) ).

fof(f9395,plain,
    ( spl0_624
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
        | ~ 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))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f9366,plain,
    ( spl0_619
  <=> ! [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_619])]) ).

fof(f9369,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
        | ~ 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))))) )
    | ~ spl0_235
    | ~ spl0_619 ),
    inference(forward_demodulation,[],[f9367,f2313]) ).

fof(f9367,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_619 ),
    inference(avatar_component_clause,[],[f9366]) ).

fof(f9393,plain,
    ( spl0_623
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(avatar_split_clause,[],[f9364,f9359,f2311,f9391]) ).

fof(f9391,plain,
    ( spl0_623
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f9359,plain,
    ( spl0_618
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f9364,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) )
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9363,f2313]) ).

fof(f9363,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9362,f2313]) ).

fof(f9362,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9360,f2313]) ).

fof(f9360,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_618 ),
    inference(avatar_component_clause,[],[f9359]) ).

fof(f9381,plain,
    ( spl0_621
    | ~ spl0_622
    | ~ spl0_61
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1879,f1869,f525,f9378,f9375]) ).

fof(f9375,plain,
    ( spl0_621
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f9378,plain,
    ( spl0_622
  <=> subclass(composition_function,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f525,plain,
    ( spl0_61
  <=> ! [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_61])]) ).

fof(f1879,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_61
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f526]) ).

fof(f526,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f525]) ).

fof(f9373,plain,
    ( spl0_620
    | ~ spl0_38
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1624,f1621,f373,f9371]) ).

fof(f9371,plain,
    ( spl0_620
  <=> ! [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_620])]) ).

fof(f1624,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_38
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f374]) ).

fof(f9368,plain,
    ( spl0_619
    | ~ spl0_125
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1397,f1366,f960,f9366]) ).

fof(f1397,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_125
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f961]) ).

fof(f9361,plain,
    ( spl0_618
    | ~ spl0_124
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1395,f1366,f956,f9359]) ).

fof(f1395,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f957]) ).

fof(f9356,plain,
    ( spl0_617
    | ~ spl0_135
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1215,f1168,f1088,f9354]) ).

fof(f9354,plain,
    ( spl0_617
  <=> ! [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_617])]) ).

fof(f1215,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_135
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f1089]) ).

fof(f9352,plain,
    ( spl0_616
    | ~ spl0_128
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3669,f3530,f1005,f9350]) ).

fof(f3669,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_128
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3648]) ).

fof(f3648,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(X0))
        | null_class = intersection(X0,complement(X0)) )
    | ~ spl0_128
    | ~ spl0_352 ),
    inference(resolution,[],[f3531,f1006]) ).

fof(f9347,plain,
    ( spl0_615
    | ~ spl0_134
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1208,f1168,f1084,f9345]) ).

fof(f9345,plain,
    ( spl0_615
  <=> ! [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_615])]) ).

fof(f1208,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_134
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f1085]) ).

fof(f9340,plain,
    ( spl0_614
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1201,f1164,f1088,f9338]) ).

fof(f9338,plain,
    ( spl0_614
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
        | subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1201,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
        | subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) )
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f1089]) ).

fof(f9333,plain,
    ( spl0_613
    | ~ spl0_134
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1194,f1164,f1084,f9331]) ).

fof(f9331,plain,
    ( spl0_613
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
        | subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1194,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
        | subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) )
    | ~ spl0_134
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f1085]) ).

fof(f9329,plain,
    ( spl0_612
    | ~ spl0_88
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f883,f824,f678,f9327]) ).

fof(f9327,plain,
    ( spl0_612
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f678,plain,
    ( spl0_88
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f883,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) )
    | ~ spl0_88
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f679]) ).

fof(f679,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f678]) ).

fof(f9236,plain,
    ( spl0_611
    | ~ spl0_294
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3667,f3530,f2827,f9233]) ).

fof(f9233,plain,
    ( spl0_611
  <=> null_class = intersection(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f2827,plain,
    ( spl0_294
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f3667,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_294
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3651]) ).

fof(f3651,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_294
    | ~ spl0_352 ),
    inference(resolution,[],[f3531,f2828]) ).

fof(f2828,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_294 ),
    inference(avatar_component_clause,[],[f2827]) ).

fof(f9209,plain,
    ( spl0_610
    | ~ spl0_86
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1723,f1712,f670,f9207]) ).

fof(f9207,plain,
    ( spl0_610
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f670,plain,
    ( spl0_86
  <=> ! [X4,X0,X1] :
        ( member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1723,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_86
    | ~ spl0_198 ),
    inference(superposition,[],[f671,f1713]) ).

fof(f671,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
        | member(X1,domain_of(X0)) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f670]) ).

fof(f9205,plain,
    ( spl0_609
    | ~ spl0_85
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1722,f1712,f665,f9203]) ).

fof(f9203,plain,
    ( spl0_609
  <=> ! [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_609])]) ).

fof(f1722,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_85
    | ~ spl0_198 ),
    inference(superposition,[],[f666,f1713]) ).

fof(f9201,plain,
    ( spl0_608
    | ~ spl0_31
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1628,f1621,f336,f9199]) ).

fof(f9199,plain,
    ( spl0_608
  <=> ! [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_608])]) ).

fof(f1628,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_31
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f337]) ).

fof(f9197,plain,
    ( spl0_607
    | ~ spl0_32
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1627,f1621,f340,f9195]) ).

fof(f9195,plain,
    ( spl0_607
  <=> ! [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_607])]) ).

fof(f1627,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_32
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f341]) ).

fof(f9193,plain,
    ( spl0_606
    | ~ spl0_130
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1575,f1557,f1013,f9191]) ).

fof(f9191,plain,
    ( spl0_606
  <=> ! [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_606])]) ).

fof(f1575,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_130
    | ~ spl0_185 ),
    inference(resolution,[],[f1558,f1014]) ).

fof(f9189,plain,
    ( spl0_605
    | ~ spl0_44
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1394,f1366,f425,f9187]) ).

fof(f9187,plain,
    ( spl0_605
  <=> ! [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_605])]) ).

fof(f1394,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_44
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f426]) ).

fof(f9185,plain,
    ( spl0_604
    | ~ spl0_79
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f975,f920,f629,f9183]) ).

fof(f9183,plain,
    ( spl0_604
  <=> ! [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_604])]) ).

fof(f975,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_79
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f630]) ).

fof(f9142,plain,
    ( spl0_603
    | ~ spl0_129
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3641,f3526,f1009,f9140]) ).

fof(f3526,plain,
    ( spl0_351
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f3641,plain,
    ( ! [X0] : null_class = intersection(complement(X0),X0)
    | ~ spl0_129
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3618]) ).

fof(f3618,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(X0),X0)
        | null_class = intersection(complement(X0),X0) )
    | ~ spl0_129
    | ~ spl0_351 ),
    inference(resolution,[],[f3527,f1010]) ).

fof(f3527,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(complement(X0),X1)),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_351 ),
    inference(avatar_component_clause,[],[f3526]) ).

fof(f9132,plain,
    ( ~ spl0_602
    | ~ spl0_235
    | spl0_601 ),
    inference(avatar_split_clause,[],[f9127,f9123,f2311,f9129]) ).

fof(f9129,plain,
    ( spl0_602
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f9123,plain,
    ( spl0_601
  <=> 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))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f9127,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_235
    | spl0_601 ),
    inference(forward_demodulation,[],[f9124,f2313]) ).

fof(f9124,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))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | spl0_601 ),
    inference(avatar_component_clause,[],[f9123]) ).

fof(f9126,plain,
    ( ~ spl0_548
    | spl0_233
    | spl0_601
    | ~ spl0_43
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1703,f1661,f394,f9123,f2301,f8196]) ).

fof(f8196,plain,
    ( spl0_548
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f2301,plain,
    ( spl0_233
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f394,plain,
    ( spl0_43
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f1703,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))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ member(identity_relation,universal_class)
    | ~ spl0_43
    | ~ spl0_196 ),
    inference(superposition,[],[f1662,f396]) ).

fof(f396,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f9121,plain,
    ( spl0_600
    | ~ spl0_20
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1630,f1621,f288,f9119]) ).

fof(f9119,plain,
    ( spl0_600
  <=> ! [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_600])]) ).

fof(f1630,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_193 ),
    inference(resolution,[],[f1622,f289]) ).

fof(f9116,plain,
    ( spl0_599
    | ~ spl0_129
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1214,f1168,f1009,f9114]) ).

fof(f9114,plain,
    ( spl0_599
  <=> ! [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_599])]) ).

fof(f1214,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_129
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f1010]) ).

fof(f9111,plain,
    ( spl0_598
    | ~ spl0_128
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1212,f1168,f1005,f9109]) ).

fof(f9109,plain,
    ( spl0_598
  <=> ! [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_598])]) ).

fof(f1212,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_128
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f1006]) ).

fof(f9104,plain,
    ( spl0_597
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1200,f1164,f1009,f9102]) ).

fof(f9102,plain,
    ( spl0_597
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
        | member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
        | null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f1200,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
        | member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
        | null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f1010]) ).

fof(f9097,plain,
    ( spl0_596
    | ~ spl0_128
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1198,f1164,f1005,f9095]) ).

fof(f9095,plain,
    ( spl0_596
  <=> ! [X0] :
        ( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
        | member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
        | null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f1198,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
        | member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
        | null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_128
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f1006]) ).

fof(f9093,plain,
    ( spl0_595
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f971,f916,f569,f453,f9091]) ).

fof(f9091,plain,
    ( spl0_595
  <=> ! [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_595])]) ).

fof(f971,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_50
    | ~ spl0_70
    | ~ spl0_115 ),
    inference(forward_demodulation,[],[f970,f454]) ).

fof(f970,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_70
    | ~ spl0_115 ),
    inference(resolution,[],[f917,f570]) ).

fof(f9079,plain,
    ( spl0_594
    | ~ spl0_300
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3639,f3526,f2931,f9076]) ).

fof(f9076,plain,
    ( spl0_594
  <=> null_class = intersection(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f2931,plain,
    ( spl0_300
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f3639,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_300
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3621]) ).

fof(f3621,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_300
    | ~ spl0_351 ),
    inference(resolution,[],[f3527,f2932]) ).

fof(f2932,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f2931]) ).

fof(f9065,plain,
    ( spl0_593
    | ~ spl0_235
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f8996,f8993,f2311,f9063]) ).

fof(f9063,plain,
    ( spl0_593
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | 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_593])]) ).

fof(f8993,plain,
    ( spl0_590
  <=> ! [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_590])]) ).

fof(f8996,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | 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_235
    | ~ spl0_590 ),
    inference(forward_demodulation,[],[f8994,f2313]) ).

fof(f8994,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_590 ),
    inference(avatar_component_clause,[],[f8993]) ).

fof(f9004,plain,
    ( spl0_592
    | ~ spl0_72
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1756,f1746,f585,f9002]) ).

fof(f9002,plain,
    ( spl0_592
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose_class(X3))
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f1756,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose_class(X3))
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) )
    | ~ spl0_72
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f586]) ).

fof(f9000,plain,
    ( spl0_591
    | ~ spl0_97
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1638,f1621,f732,f8998]) ).

fof(f8998,plain,
    ( spl0_591
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,singleton_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))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f1638,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,singleton_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))))))),element_relation) )
    | ~ spl0_97
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f733]) ).

fof(f8995,plain,
    ( spl0_590
    | ~ spl0_103
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1636,f1621,f762,f8993]) ).

fof(f1636,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_103
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f763]) ).

fof(f8991,plain,
    ( spl0_589
    | ~ spl0_116
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1572,f1557,f920,f8989]) ).

fof(f8989,plain,
    ( spl0_589
  <=> ! [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_589])]) ).

fof(f1572,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_116
    | ~ spl0_185 ),
    inference(resolution,[],[f1558,f921]) ).

fof(f8987,plain,
    ( spl0_588
    | ~ spl0_89
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f833,f803,f683,f8985]) ).

fof(f8985,plain,
    ( spl0_588
  <=> ! [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_588])]) ).

fof(f833,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_89
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f684]) ).

fof(f8983,plain,
    ( spl0_587
    | ~ spl0_312
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3637,f3526,f3119,f8980]) ).

fof(f8980,plain,
    ( spl0_587
  <=> null_class = intersection(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f3119,plain,
    ( spl0_312
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f3637,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_312
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3630]) ).

fof(f3630,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_312
    | ~ spl0_351 ),
    inference(resolution,[],[f3527,f3120]) ).

fof(f3120,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f3119]) ).

fof(f8856,plain,
    ( spl0_586
    | ~ spl0_77
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1720,f1712,f614,f8854]) ).

fof(f8854,plain,
    ( spl0_586
  <=> ! [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_586])]) ).

fof(f1720,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_77
    | ~ spl0_198 ),
    inference(superposition,[],[f615,f1713]) ).

fof(f8849,plain,
    ( ~ spl0_584
    | spl0_274
    | spl0_585
    | ~ spl0_76
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1701,f1661,f609,f8846,f2536,f8842]) ).

fof(f8842,plain,
    ( spl0_584
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f2536,plain,
    ( spl0_274
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f8846,plain,
    ( spl0_585
  <=> 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)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f609,plain,
    ( spl0_76
  <=> 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_76])]) ).

fof(f1701,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_76
    | ~ spl0_196 ),
    inference(superposition,[],[f1662,f611]) ).

fof(f611,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_76 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f8840,plain,
    ( spl0_583
    | ~ spl0_152
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1644,f1640,f1248,f8838]) ).

fof(f8838,plain,
    ( spl0_583
  <=> ! [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_583])]) ).

fof(f1644,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_152
    | ~ spl0_194 ),
    inference(resolution,[],[f1641,f1249]) ).

fof(f8836,plain,
    ( spl0_582
    | ~ spl0_28
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3130,f3093,f324,f8834]) ).

fof(f8834,plain,
    ( spl0_582
  <=> ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f3093,plain,
    ( spl0_310
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f3130,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_310 ),
    inference(duplicate_literal_removal,[],[f3122]) ).

fof(f3122,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,subset_relation) )
    | ~ spl0_28
    | ~ spl0_310 ),
    inference(resolution,[],[f3094,f325]) ).

fof(f3094,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f3093]) ).

fof(f8832,plain,
    ( spl0_581
    | ~ spl0_38
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1583,f1579,f373,f8830]) ).

fof(f8830,plain,
    ( spl0_581
  <=> ! [X2,X0,X1] :
        ( ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class)
        | ~ subclass(compose_class(X0),X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1583,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class)
        | ~ subclass(compose_class(X0),X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) )
    | ~ spl0_38
    | ~ spl0_186 ),
    inference(resolution,[],[f1580,f374]) ).

fof(f8828,plain,
    ( ~ spl0_579
    | spl0_580
    | ~ spl0_106
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1574,f1557,f803,f8826,f8822]) ).

fof(f8822,plain,
    ( spl0_579
  <=> 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_579])]) ).

fof(f8826,plain,
    ( spl0_580
  <=> ! [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_580])]) ).

fof(f1574,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_106
    | ~ spl0_185 ),
    inference(resolution,[],[f1558,f804]) ).

fof(f8820,plain,
    ( spl0_578
    | ~ spl0_76
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1402,f1366,f609,f8818]) ).

fof(f8818,plain,
    ( spl0_578
  <=> ! [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_578])]) ).

fof(f1402,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_76
    | ~ spl0_164 ),
    inference(superposition,[],[f1367,f611]) ).

fof(f8816,plain,
    ( spl0_577
    | ~ spl0_130
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1315,f1295,f1013,f8814]) ).

fof(f8814,plain,
    ( spl0_577
  <=> ! [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_577])]) ).

fof(f1315,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_130
    | ~ spl0_158 ),
    inference(resolution,[],[f1296,f1014]) ).

fof(f8729,plain,
    ( spl0_576
    | ~ spl0_28
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f3104,f2941,f324,f8727]) ).

fof(f8727,plain,
    ( spl0_576
  <=> ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f2941,plain,
    ( spl0_302
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f3104,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_302 ),
    inference(duplicate_literal_removal,[],[f3096]) ).

fof(f3096,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,element_relation) )
    | ~ spl0_28
    | ~ spl0_302 ),
    inference(resolution,[],[f2942,f325]) ).

fof(f2942,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),element_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302 ),
    inference(avatar_component_clause,[],[f2941]) ).

fof(f8725,plain,
    ( spl0_575
    | ~ spl0_64
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1757,f1746,f540,f8723]) ).

fof(f8723,plain,
    ( spl0_575
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f1757,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) )
    | ~ spl0_64
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f541]) ).

fof(f8721,plain,
    ( spl0_574
    | ~ spl0_114
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1386,f1362,f893,f8719]) ).

fof(f8719,plain,
    ( spl0_574
  <=> ! [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_574])]) ).

fof(f1386,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_114
    | ~ spl0_163 ),
    inference(resolution,[],[f1363,f894]) ).

fof(f8717,plain,
    ( spl0_573
    | ~ spl0_142
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1271,f1248,f1160,f8715]) ).

fof(f8715,plain,
    ( spl0_573
  <=> ! [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_573])]) ).

fof(f1271,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_142
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f1161]) ).

fof(f8713,plain,
    ( spl0_572
    | ~ spl0_435
    | ~ spl0_143
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1266,f1248,f1164,f5515,f8711]) ).

fof(f8711,plain,
    ( spl0_572
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f1266,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f1165]) ).

fof(f8709,plain,
    ( spl0_571
    | ~ spl0_76
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1257,f1244,f609,f8707]) ).

fof(f8707,plain,
    ( spl0_571
  <=> ! [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_571])]) ).

fof(f1244,plain,
    ( spl0_151
  <=> ! [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_151])]) ).

fof(f1257,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_76
    | ~ spl0_151 ),
    inference(superposition,[],[f1245,f611]) ).

fof(f1245,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1244]) ).

fof(f8705,plain,
    ( spl0_570
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f900,f885,f569,f453,f8703]) ).

fof(f8703,plain,
    ( spl0_570
  <=> ! [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_570])]) ).

fof(f900,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_50
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(forward_demodulation,[],[f899,f454]) ).

fof(f899,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_70
    | ~ spl0_112 ),
    inference(resolution,[],[f886,f570]) ).

fof(f8670,plain,
    ( spl0_569
    | ~ spl0_4
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f2962,f2815,f220,f8668]) ).

fof(f2815,plain,
    ( spl0_291
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f2962,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_291 ),
    inference(resolution,[],[f2816,f221]) ).

fof(f2816,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f2815]) ).

fof(f8358,plain,
    ( spl0_568
    | ~ spl0_61
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1752,f1746,f525,f8356]) ).

fof(f8356,plain,
    ( spl0_568
  <=> ! [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_568])]) ).

fof(f1752,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_61
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f526]) ).

fof(f8354,plain,
    ( spl0_567
    | ~ spl0_72
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1719,f1712,f585,f8352]) ).

fof(f8352,plain,
    ( spl0_567
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f1719,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_72
    | ~ spl0_198 ),
    inference(superposition,[],[f586,f1713]) ).

fof(f8350,plain,
    ( spl0_566
    | ~ spl0_103
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2871,f2311,f762,f8348]) ).

fof(f8348,plain,
    ( spl0_566
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f2871,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103
    | ~ spl0_235 ),
    inference(superposition,[],[f763,f2313]) ).

fof(f8346,plain,
    ( spl0_565
    | ~ spl0_134
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1607,f1585,f1084,f8344]) ).

fof(f8344,plain,
    ( spl0_565
  <=> ! [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_565])]) ).

fof(f1585,plain,
    ( spl0_187
  <=> ! [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_187])]) ).

fof(f1607,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_134
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1602]) ).

fof(f1602,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_134
    | ~ spl0_187 ),
    inference(resolution,[],[f1586,f1085]) ).

fof(f1586,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_187 ),
    inference(avatar_component_clause,[],[f1585]) ).

fof(f8342,plain,
    ( spl0_564
    | ~ spl0_135
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1606,f1585,f1088,f8340]) ).

fof(f8340,plain,
    ( spl0_564
  <=> ! [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_564])]) ).

fof(f1606,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_135
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1603]) ).

fof(f1603,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_135
    | ~ spl0_187 ),
    inference(resolution,[],[f1586,f1089]) ).

fof(f8338,plain,
    ( spl0_563
    | ~ spl0_63
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1438,f1374,f533,f8336]) ).

fof(f8336,plain,
    ( spl0_563
  <=> ! [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_563])]) ).

fof(f533,plain,
    ( spl0_63
  <=> ! [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_63])]) ).

fof(f1374,plain,
    ( spl0_166
  <=> ! [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_166])]) ).

fof(f1438,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_63
    | ~ spl0_166 ),
    inference(resolution,[],[f1375,f534]) ).

fof(f534,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f533]) ).

fof(f1375,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_166 ),
    inference(avatar_component_clause,[],[f1374]) ).

fof(f8324,plain,
    ( spl0_562
    | ~ spl0_14
    | ~ spl0_85
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1412,f1370,f665,f263,f8322]) ).

fof(f8322,plain,
    ( spl0_562
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ member(X0,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f263,plain,
    ( spl0_14
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f1412,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | ~ member(X0,domain_of(X0)) )
    | ~ spl0_85
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f666]) ).

fof(f8320,plain,
    ( spl0_561
    | ~ spl0_123
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1398,f1366,f952,f8318]) ).

fof(f8318,plain,
    ( spl0_561
  <=> ! [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_561])]) ).

fof(f1398,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_123
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f953]) ).

fof(f8316,plain,
    ( spl0_560
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1391,f1366,f824,f8314]) ).

fof(f8314,plain,
    ( spl0_560
  <=> ! [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_560])]) ).

fof(f1391,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_111
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f825]) ).

fof(f8311,plain,
    ( spl0_559
    | ~ spl0_27
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1207,f1168,f320,f8309]) ).

fof(f8309,plain,
    ( spl0_559
  <=> ! [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_559])]) ).

fof(f1207,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_27
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f321]) ).

fof(f8304,plain,
    ( spl0_558
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1193,f1164,f320,f8302]) ).

fof(f8302,plain,
    ( spl0_558
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
        | member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
        | subclass(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f1193,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
        | member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
        | subclass(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f321]) ).

fof(f8300,plain,
    ( spl0_557
    | ~ spl0_135
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1187,f1160,f1088,f8298]) ).

fof(f8298,plain,
    ( spl0_557
  <=> ! [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_557])]) ).

fof(f1187,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_135
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f1089]) ).

fof(f8237,plain,
    ( spl0_556
    | ~ spl0_134
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1180,f1160,f1084,f8235]) ).

fof(f8235,plain,
    ( spl0_556
  <=> ! [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_556])]) ).

fof(f1180,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_134
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f1085]) ).

fof(f8233,plain,
    ( spl0_555
    | ~ spl0_48
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1132,f1088,f445,f8231]) ).

fof(f8231,plain,
    ( spl0_555
  <=> ! [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_555])]) ).

fof(f1132,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_48
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f446]) ).

fof(f8229,plain,
    ( spl0_554
    | ~ spl0_48
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1114,f1084,f445,f8227]) ).

fof(f8227,plain,
    ( spl0_554
  <=> ! [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_554])]) ).

fof(f1114,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_48
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f446]) ).

fof(f8225,plain,
    ( spl0_553
    | ~ spl0_85
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f879,f824,f665,f8223]) ).

fof(f8223,plain,
    ( spl0_553
  <=> ! [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_553])]) ).

fof(f879,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_85
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f666]) ).

fof(f8221,plain,
    ( ~ spl0_1
    | ~ spl0_551
    | spl0_552
    | ~ spl0_63
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f873,f820,f533,f8218,f8214,f205]) ).

fof(f205,plain,
    ( spl0_1
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f8214,plain,
    ( spl0_551
  <=> 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_551])]) ).

fof(f8218,plain,
    ( spl0_552
  <=> 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_552])]) ).

fof(f820,plain,
    ( spl0_110
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f873,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_63
    | ~ spl0_110 ),
    inference(resolution,[],[f821,f534]) ).

fof(f821,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f820]) ).

fof(f8210,plain,
    ( ~ spl0_550
    | ~ spl0_235
    | spl0_549 ),
    inference(avatar_split_clause,[],[f8204,f8200,f2311,f8207]) ).

fof(f8207,plain,
    ( spl0_550
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f8200,plain,
    ( spl0_549
  <=> 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_549])]) ).

fof(f8204,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_235
    | spl0_549 ),
    inference(forward_demodulation,[],[f8201,f2313]) ).

fof(f8201,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_549 ),
    inference(avatar_component_clause,[],[f8200]) ).

fof(f8203,plain,
    ( spl0_233
    | ~ spl0_548
    | spl0_549
    | ~ spl0_84
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f777,f762,f655,f8200,f8196,f2301]) ).

fof(f777,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_84
    | ~ spl0_103 ),
    inference(resolution,[],[f763,f656]) ).

fof(f8194,plain,
    ( spl0_547
    | ~ spl0_55
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f7331,f5171,f478,f8191]) ).

fof(f8191,plain,
    ( spl0_547
  <=> universal_class = intersection(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f5171,plain,
    ( spl0_423
  <=> ! [X0] : subclass(X0,intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f7331,plain,
    ( universal_class = intersection(universal_class,universal_class)
    | ~ spl0_55
    | ~ spl0_423 ),
    inference(resolution,[],[f5172,f479]) ).

fof(f5172,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_423 ),
    inference(avatar_component_clause,[],[f5171]) ).

fof(f8187,plain,
    ( spl0_231
    | ~ spl0_545
    | spl0_546
    | ~ spl0_84
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f773,f732,f655,f8184,f8180,f2283]) ).

fof(f2283,plain,
    ( spl0_231
  <=> null_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f8180,plain,
    ( spl0_545
  <=> member(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f8184,plain,
    ( spl0_546
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f773,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
    | ~ member(singleton_relation,universal_class)
    | null_class = singleton_relation
    | ~ spl0_84
    | ~ spl0_97 ),
    inference(resolution,[],[f733,f656]) ).

fof(f8161,plain,
    ( spl0_544
    | ~ spl0_67
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1750,f1746,f557,f8159]) ).

fof(f8159,plain,
    ( spl0_544
  <=> ! [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_544])]) ).

fof(f1750,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_67
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f558]) ).

fof(f8157,plain,
    ( spl0_543
    | ~ spl0_68
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1749,f1746,f561,f8155]) ).

fof(f8155,plain,
    ( spl0_543
  <=> ! [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_543])]) ).

fof(f561,plain,
    ( spl0_68
  <=> ! [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_68])]) ).

fof(f1749,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_68
    | ~ spl0_199 ),
    inference(resolution,[],[f1747,f562]) ).

fof(f562,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_68 ),
    inference(avatar_component_clause,[],[f561]) ).

fof(f8152,plain,
    ( spl0_542
    | ~ spl0_228
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f7330,f5171,f2266,f8149]) ).

fof(f8149,plain,
    ( spl0_542
  <=> member(null_class,intersection(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f7330,plain,
    ( member(null_class,intersection(universal_class,universal_class))
    | ~ spl0_228
    | ~ spl0_423 ),
    inference(resolution,[],[f5172,f2267]) ).

fof(f8147,plain,
    ( spl0_541
    | ~ spl0_39
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1384,f1362,f377,f8145]) ).

fof(f8145,plain,
    ( spl0_541
  <=> ! [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_541])]) ).

fof(f1384,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_39
    | ~ spl0_163 ),
    inference(resolution,[],[f1363,f378]) ).

fof(f8143,plain,
    ( spl0_540
    | ~ spl0_106
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1314,f1295,f803,f8141]) ).

fof(f8141,plain,
    ( spl0_540
  <=> ! [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_540])]) ).

fof(f1314,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_106
    | ~ spl0_158 ),
    inference(resolution,[],[f1296,f804]) ).

fof(f8139,plain,
    ( spl0_539
    | ~ spl0_48
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1261,f1248,f445,f8137]) ).

fof(f8137,plain,
    ( spl0_539
  <=> ! [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_539])]) ).

fof(f1261,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_48
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f446]) ).

fof(f7473,plain,
    ( spl0_538
    | ~ spl0_64
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1716,f1712,f540,f7471]) ).

fof(f7471,plain,
    ( spl0_538
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_relation)
        | second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1716,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_relation)
        | second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_64
    | ~ spl0_198 ),
    inference(superposition,[],[f541,f1713]) ).

fof(f7469,plain,
    ( spl0_537
    | ~ spl0_22
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1555,f1550,f296,f7467]) ).

fof(f7467,plain,
    ( spl0_537
  <=> ! [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_537])]) ).

fof(f1555,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_184 ),
    inference(resolution,[],[f1551,f297]) ).

fof(f7465,plain,
    ( spl0_536
    | ~ spl0_38
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1514,f1478,f373,f7463]) ).

fof(f7463,plain,
    ( spl0_536
  <=> ! [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_536])]) ).

fof(f1514,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_38
    | ~ spl0_176 ),
    inference(resolution,[],[f1479,f374]) ).

fof(f7461,plain,
    ( spl0_535
    | ~ spl0_38
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1499,f1457,f373,f7459]) ).

fof(f7459,plain,
    ( spl0_535
  <=> ! [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_535])]) ).

fof(f1499,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_38
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f374]) ).

fof(f7457,plain,
    ( spl0_534
    | ~ spl0_38
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1481,f1453,f373,f7455]) ).

fof(f7455,plain,
    ( spl0_534
  <=> ! [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_534])]) ).

fof(f1481,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_38
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f374]) ).

fof(f7447,plain,
    ( spl0_533
    | ~ spl0_57
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1437,f1374,f504,f7445]) ).

fof(f7445,plain,
    ( spl0_533
  <=> ! [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_533])]) ).

fof(f504,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f1437,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_57
    | ~ spl0_166 ),
    inference(resolution,[],[f1375,f505]) ).

fof(f505,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f504]) ).

fof(f7443,plain,
    ( spl0_532
    | ~ spl0_110
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1385,f1362,f820,f7441]) ).

fof(f7441,plain,
    ( spl0_532
  <=> ! [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_532])]) ).

fof(f1385,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_110
    | ~ spl0_163 ),
    inference(resolution,[],[f1363,f821]) ).

fof(f7439,plain,
    ( spl0_531
    | ~ spl0_116
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1312,f1295,f920,f7437]) ).

fof(f7437,plain,
    ( spl0_531
  <=> ! [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_531])]) ).

fof(f1312,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_116
    | ~ spl0_158 ),
    inference(resolution,[],[f1296,f921]) ).

fof(f7434,plain,
    ( ~ spl0_530
    | ~ spl0_235
    | spl0_528 ),
    inference(avatar_split_clause,[],[f7426,f7418,f2311,f7431]) ).

fof(f7431,plain,
    ( spl0_530
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f7418,plain,
    ( spl0_528
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f7426,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
    | ~ spl0_235
    | spl0_528 ),
    inference(forward_demodulation,[],[f7419,f2313]) ).

fof(f7419,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | spl0_528 ),
    inference(avatar_component_clause,[],[f7418]) ).

fof(f7425,plain,
    ( spl0_527
    | spl0_528
    | ~ spl0_529
    | ~ spl0_23
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1211,f1168,f300,f7422,f7418,f7414]) ).

fof(f7422,plain,
    ( spl0_529
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f1211,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_144 ),
    inference(resolution,[],[f1169,f301]) ).

fof(f7401,plain,
    ( ~ spl0_526
    | ~ spl0_235
    | spl0_522 ),
    inference(avatar_split_clause,[],[f7385,f7376,f2311,f7398]) ).

fof(f7398,plain,
    ( spl0_526
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f7376,plain,
    ( spl0_522
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f7385,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
    | ~ spl0_235
    | spl0_522 ),
    inference(forward_demodulation,[],[f7377,f2313]) ).

fof(f7377,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | spl0_522 ),
    inference(avatar_component_clause,[],[f7376]) ).

fof(f7396,plain,
    ( ~ spl0_525
    | ~ spl0_235
    | spl0_523 ),
    inference(avatar_split_clause,[],[f7384,f7380,f2311,f7393]) ).

fof(f7393,plain,
    ( spl0_525
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f7380,plain,
    ( spl0_523
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f7384,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
    | ~ spl0_235
    | spl0_523 ),
    inference(forward_demodulation,[],[f7382,f2313]) ).

fof(f7382,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | spl0_523 ),
    inference(avatar_component_clause,[],[f7380]) ).

fof(f7391,plain,
    ( ~ spl0_524
    | ~ spl0_235
    | spl0_521 ),
    inference(avatar_split_clause,[],[f7386,f7372,f2311,f7388]) ).

fof(f7388,plain,
    ( spl0_524
  <=> null_class = complement(compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f7386,plain,
    ( null_class != complement(compose(element_relation,complement(singleton_relation)))
    | ~ spl0_235
    | spl0_521 ),
    inference(forward_demodulation,[],[f7373,f2313]) ).

fof(f7373,plain,
    ( null_class != complement(compose(element_relation,complement(identity_relation)))
    | spl0_521 ),
    inference(avatar_component_clause,[],[f7372]) ).

fof(f7383,plain,
    ( spl0_521
    | spl0_522
    | ~ spl0_523
    | ~ spl0_23
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1197,f1164,f300,f7380,f7376,f7372]) ).

fof(f1197,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_23
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f301]) ).

fof(f7370,plain,
    ( spl0_520
    | ~ spl0_129
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1186,f1160,f1009,f7368]) ).

fof(f7368,plain,
    ( spl0_520
  <=> ! [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_520])]) ).

fof(f1186,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_129
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f1010]) ).

fof(f7366,plain,
    ( spl0_519
    | ~ spl0_128
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1184,f1160,f1005,f7364]) ).

fof(f7364,plain,
    ( spl0_519
  <=> ! [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_519])]) ).

fof(f1184,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_128
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f1006]) ).

fof(f7362,plain,
    ( spl0_518
    | ~ spl0_48
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1045,f1009,f445,f7360]) ).

fof(f7360,plain,
    ( spl0_518
  <=> ! [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_518])]) ).

fof(f1045,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_48
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f446]) ).

fof(f7358,plain,
    ( spl0_517
    | ~ spl0_48
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1029,f1005,f445,f7356]) ).

fof(f7356,plain,
    ( spl0_517
  <=> ! [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_517])]) ).

fof(f1029,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_48
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f446]) ).

fof(f7050,plain,
    ( spl0_516
    | ~ spl0_61
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1715,f1712,f525,f7048]) ).

fof(f7048,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f1715,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_61
    | ~ spl0_198 ),
    inference(superposition,[],[f526,f1713]) ).

fof(f7038,plain,
    ( spl0_515
    | ~ spl0_130
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1605,f1585,f1013,f7036]) ).

fof(f7036,plain,
    ( spl0_515
  <=> ! [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_515])]) ).

fof(f1605,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_130
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1604]) ).

fof(f1604,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_130
    | ~ spl0_187 ),
    inference(resolution,[],[f1586,f1014]) ).

fof(f7034,plain,
    ( ~ spl0_514
    | ~ spl0_182
    | spl0_192
    | ~ spl0_12
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1564,f1557,f255,f1614,f1539,f7031]) ).

fof(f7031,plain,
    ( spl0_514
  <=> inductive(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_514])]) ).

fof(f1539,plain,
    ( spl0_182
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1614,plain,
    ( spl0_192
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f1564,plain,
    ( member(null_class,subset_relation)
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_12
    | ~ spl0_185 ),
    inference(resolution,[],[f1558,f256]) ).

fof(f7029,plain,
    ( spl0_513
    | ~ spl0_31
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1503,f1457,f336,f7027]) ).

fof(f7027,plain,
    ( spl0_513
  <=> ! [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_513])]) ).

fof(f1503,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_31
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f337]) ).

fof(f7025,plain,
    ( spl0_512
    | ~ spl0_32
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1502,f1457,f340,f7023]) ).

fof(f7023,plain,
    ( spl0_512
  <=> ! [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_512])]) ).

fof(f1502,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_32
    | ~ spl0_171 ),
    inference(resolution,[],[f1458,f341]) ).

fof(f7021,plain,
    ( spl0_511
    | ~ spl0_31
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1485,f1453,f336,f7019]) ).

fof(f7019,plain,
    ( spl0_511
  <=> ! [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_511])]) ).

fof(f1485,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_31
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f337]) ).

fof(f7017,plain,
    ( spl0_510
    | ~ spl0_32
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1484,f1453,f340,f7015]) ).

fof(f7015,plain,
    ( spl0_510
  <=> ! [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_510])]) ).

fof(f1484,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_32
    | ~ spl0_170 ),
    inference(resolution,[],[f1454,f341]) ).

fof(f7013,plain,
    ( spl0_509
    | ~ spl0_38
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1423,f1370,f373,f7011]) ).

fof(f7011,plain,
    ( spl0_509
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f1423,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) )
    | ~ spl0_38
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f374]) ).

fof(f7009,plain,
    ( spl0_508
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1347,f1317,f1160,f7007]) ).

fof(f7007,plain,
    ( spl0_508
  <=> ! [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_508])]) ).

fof(f1347,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_142
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1326]) ).

fof(f1326,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_142
    | ~ spl0_160 ),
    inference(superposition,[],[f1161,f1318]) ).

fof(f7005,plain,
    ( spl0_507
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1342,f1317,f1160,f7003]) ).

fof(f7003,plain,
    ( spl0_507
  <=> ! [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_507])]) ).

fof(f1342,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_142
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1331]) ).

fof(f1331,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_142
    | ~ spl0_160 ),
    inference(superposition,[],[f1161,f1318]) ).

fof(f6993,plain,
    ( spl0_506
    | ~ spl0_49
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f968,f916,f449,f6991]) ).

fof(f6991,plain,
    ( spl0_506
  <=> ! [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_506])]) ).

fof(f968,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_49
    | ~ spl0_115 ),
    inference(resolution,[],[f917,f450]) ).

fof(f6845,plain,
    ( spl0_505
    | ~ spl0_235
    | ~ spl0_497 ),
    inference(avatar_split_clause,[],[f6807,f6804,f2311,f6843]) ).

fof(f6843,plain,
    ( spl0_505
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f6804,plain,
    ( spl0_497
  <=> ! [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_497])]) ).

fof(f6807,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_235
    | ~ spl0_497 ),
    inference(forward_demodulation,[],[f6805,f2313]) ).

fof(f6805,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_497 ),
    inference(avatar_component_clause,[],[f6804]) ).

fof(f6835,plain,
    ( spl0_504
    | ~ spl0_68
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1876,f1869,f561,f6833]) ).

fof(f6833,plain,
    ( spl0_504
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f1876,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f562]) ).

fof(f6831,plain,
    ( spl0_503
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1504,f1457,f288,f6829]) ).

fof(f6829,plain,
    ( spl0_503
  <=> ! [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_503])]) ).

fof(f1504,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_171 ),
    inference(resolution,[],[f1458,f289]) ).

fof(f6827,plain,
    ( spl0_502
    | ~ spl0_20
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1486,f1453,f288,f6825]) ).

fof(f6825,plain,
    ( spl0_502
  <=> ! [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_502])]) ).

fof(f1486,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_170 ),
    inference(resolution,[],[f1454,f289]) ).

fof(f6823,plain,
    ( spl0_501
    | ~ spl0_31
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1427,f1370,f336,f6821]) ).

fof(f6821,plain,
    ( spl0_501
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f1427,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) )
    | ~ spl0_31
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f337]) ).

fof(f6819,plain,
    ( spl0_500
    | ~ spl0_32
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1426,f1370,f340,f6817]) ).

fof(f6817,plain,
    ( spl0_500
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f1426,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) )
    | ~ spl0_32
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f341]) ).

fof(f6815,plain,
    ( spl0_499
    | ~ spl0_109
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1383,f1362,f816,f6813]) ).

fof(f6813,plain,
    ( spl0_499
  <=> ! [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_499])]) ).

fof(f816,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1383,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_109
    | ~ spl0_163 ),
    inference(resolution,[],[f1363,f817]) ).

fof(f817,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f816]) ).

fof(f6811,plain,
    ( spl0_498
    | ~ spl0_38
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1357,f1352,f373,f6809]) ).

fof(f6809,plain,
    ( spl0_498
  <=> ! [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_498])]) ).

fof(f1357,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_38
    | ~ spl0_162 ),
    inference(resolution,[],[f1353,f374]) ).

fof(f6806,plain,
    ( spl0_497
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1218,f1168,f569,f453,f6804]) ).

fof(f1218,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_50
    | ~ spl0_70
    | ~ spl0_144 ),
    inference(forward_demodulation,[],[f1205,f454]) ).

fof(f1205,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_70
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f570]) ).

fof(f6600,plain,
    ( spl0_496
    | ~ spl0_235
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f6419,f6416,f2311,f6598]) ).

fof(f6598,plain,
    ( spl0_496
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | ~ member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f6416,plain,
    ( spl0_483
  <=> ! [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_483])]) ).

fof(f6419,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | ~ member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_235
    | ~ spl0_483 ),
    inference(forward_demodulation,[],[f6417,f2313]) ).

fof(f6417,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_483 ),
    inference(avatar_component_clause,[],[f6416]) ).

fof(f6596,plain,
    ( spl0_495
    | ~ spl0_235
    | ~ spl0_482 ),
    inference(avatar_split_clause,[],[f6414,f6411,f2311,f6594]) ).

fof(f6594,plain,
    ( spl0_495
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f6411,plain,
    ( spl0_482
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f6414,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1) )
    | ~ spl0_235
    | ~ spl0_482 ),
    inference(forward_demodulation,[],[f6412,f2313]) ).

fof(f6412,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) )
    | ~ spl0_482 ),
    inference(avatar_component_clause,[],[f6411]) ).

fof(f6464,plain,
    ( spl0_493
    | ~ spl0_494
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1873,f1869,f670,f6461,f6458]) ).

fof(f6458,plain,
    ( spl0_493
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f6461,plain,
    ( spl0_494
  <=> subclass(composition_function,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f1873,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X1,domain_of(X0)) )
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(resolution,[],[f1870,f671]) ).

fof(f6456,plain,
    ( spl0_492
    | ~ spl0_68
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1718,f1712,f561,f6454]) ).

fof(f6454,plain,
    ( spl0_492
  <=> ! [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_492])]) ).

fof(f1718,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_68
    | ~ spl0_198 ),
    inference(superposition,[],[f562,f1713]) ).

fof(f6452,plain,
    ( spl0_491
    | ~ spl0_67
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1717,f1712,f557,f6450]) ).

fof(f6450,plain,
    ( spl0_491
  <=> ! [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_491])]) ).

fof(f1717,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_67
    | ~ spl0_198 ),
    inference(superposition,[],[f558,f1713]) ).

fof(f6448,plain,
    ( spl0_490
    | ~ spl0_22
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1441,f1374,f296,f6446]) ).

fof(f6446,plain,
    ( spl0_490
  <=> ! [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_490])]) ).

fof(f1441,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_166 ),
    inference(resolution,[],[f1375,f297]) ).

fof(f6444,plain,
    ( spl0_489
    | ~ spl0_20
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1428,f1370,f288,f6442]) ).

fof(f1428,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) )
    | ~ spl0_20
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f289]) ).

fof(f6440,plain,
    ( spl0_488
    | ~ spl0_131
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1382,f1362,f1017,f6438]) ).

fof(f6438,plain,
    ( spl0_488
  <=> ! [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_488])]) ).

fof(f1382,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_131
    | ~ spl0_163 ),
    inference(resolution,[],[f1363,f1018]) ).

fof(f6436,plain,
    ( spl0_487
    | ~ spl0_132
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1381,f1362,f1021,f6434]) ).

fof(f6434,plain,
    ( spl0_487
  <=> ! [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_487])]) ).

fof(f1381,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_132
    | ~ spl0_163 ),
    inference(resolution,[],[f1363,f1022]) ).

fof(f6432,plain,
    ( ~ spl0_485
    | spl0_486
    | ~ spl0_114
    | ~ spl0_398 ),
    inference(avatar_split_clause,[],[f6329,f4365,f893,f6429,f6425]) ).

fof(f6425,plain,
    ( spl0_485
  <=> single_valued_class(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f6429,plain,
    ( spl0_486
  <=> function(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f4365,plain,
    ( spl0_398
  <=> subclass(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f6329,plain,
    ( function(singleton_relation)
    | ~ single_valued_class(singleton_relation)
    | ~ spl0_114
    | ~ spl0_398 ),
    inference(resolution,[],[f4367,f894]) ).

fof(f4367,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_398 ),
    inference(avatar_component_clause,[],[f4365]) ).

fof(f6423,plain,
    ( spl0_484
    | ~ spl0_38
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1348,f1321,f373,f6421]) ).

fof(f6421,plain,
    ( spl0_484
  <=> ! [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_484])]) ).

fof(f1321,plain,
    ( spl0_161
  <=> ! [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_161])]) ).

fof(f1348,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_38
    | ~ spl0_161 ),
    inference(resolution,[],[f1322,f374]) ).

fof(f1322,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_161 ),
    inference(avatar_component_clause,[],[f1321]) ).

fof(f6418,plain,
    ( spl0_483
    | ~ spl0_130
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1217,f1168,f1013,f6416]) ).

fof(f1217,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_130
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f1014]) ).

fof(f6413,plain,
    ( spl0_482
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1203,f1164,f1013,f6411]) ).

fof(f1203,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f1014]) ).

fof(f6409,plain,
    ( spl0_481
    | ~ spl0_130
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1189,f1160,f1013,f6407]) ).

fof(f6407,plain,
    ( spl0_481
  <=> ! [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_481])]) ).

fof(f1189,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_130
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f1014]) ).

fof(f6405,plain,
    ( spl0_480
    | ~ spl0_76
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1144,f1088,f609,f6403]) ).

fof(f6403,plain,
    ( spl0_480
  <=> ! [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_480])]) ).

fof(f1144,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_76
    | ~ spl0_135 ),
    inference(superposition,[],[f1089,f611]) ).

fof(f6401,plain,
    ( spl0_479
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f897,f885,f449,f6399]) ).

fof(f6399,plain,
    ( spl0_479
  <=> ! [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_479])]) ).

fof(f897,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(resolution,[],[f886,f450]) ).

fof(f6237,plain,
    ( spl0_478
    | ~ spl0_27
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1608,f1585,f320,f6235]) ).

fof(f6235,plain,
    ( spl0_478
  <=> ! [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_478])]) ).

fof(f1608,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_27
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1601]) ).

fof(f1601,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_27
    | ~ spl0_187 ),
    inference(resolution,[],[f1586,f321]) ).

fof(f6233,plain,
    ( spl0_477
    | ~ spl0_49
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1577,f1557,f449,f6231]) ).

fof(f6231,plain,
    ( spl0_477
  <=> ! [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_477])]) ).

fof(f1577,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_49
    | ~ spl0_185 ),
    inference(duplicate_literal_removal,[],[f1561]) ).

fof(f1561,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_49
    | ~ spl0_185 ),
    inference(resolution,[],[f1558,f450]) ).

fof(f6229,plain,
    ( ~ spl0_476
    | ~ spl0_235
    | spl0_475 ),
    inference(avatar_split_clause,[],[f6224,f6220,f2311,f6226]) ).

fof(f6226,plain,
    ( spl0_476
  <=> subclass(domain_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f6220,plain,
    ( spl0_475
  <=> subclass(domain_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f6224,plain,
    ( ~ subclass(domain_relation,singleton_relation)
    | ~ spl0_235
    | spl0_475 ),
    inference(forward_demodulation,[],[f6222,f2313]) ).

fof(f6222,plain,
    ( ~ subclass(domain_relation,identity_relation)
    | spl0_475 ),
    inference(avatar_component_clause,[],[f6220]) ).

fof(f6223,plain,
    ( spl0_474
    | ~ spl0_475
    | ~ spl0_103
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1434,f1370,f762,f6220,f6217]) ).

fof(f6217,plain,
    ( spl0_474
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f1434,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,identity_relation)
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f763]) ).

fof(f6215,plain,
    ( spl0_473
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1345,f1317,f920,f6213]) ).

fof(f6213,plain,
    ( spl0_473
  <=> ! [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_473])]) ).

fof(f1345,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_116
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1328]) ).

fof(f1328,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_116
    | ~ spl0_160 ),
    inference(superposition,[],[f921,f1318]) ).

fof(f6211,plain,
    ( spl0_472
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1340,f1317,f920,f6209]) ).

fof(f6209,plain,
    ( spl0_472
  <=> ! [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_472])]) ).

fof(f1340,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_116
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1333]) ).

fof(f1333,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_116
    | ~ spl0_160 ),
    inference(superposition,[],[f921,f1318]) ).

fof(f6207,plain,
    ( spl0_471
    | ~ spl0_27
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1179,f1160,f320,f6205]) ).

fof(f6205,plain,
    ( spl0_471
  <=> ! [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_471])]) ).

fof(f1179,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_27
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f321]) ).

fof(f6195,plain,
    ( spl0_274
    | spl0_470
    | ~ spl0_76
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1057,f1009,f609,f6192,f2536]) ).

fof(f6192,plain,
    ( spl0_470
  <=> 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_470])]) ).

fof(f1057,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_76
    | ~ spl0_129 ),
    inference(superposition,[],[f1010,f611]) ).

fof(f6190,plain,
    ( spl0_469
    | ~ spl0_44
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f969,f916,f425,f6188]) ).

fof(f6188,plain,
    ( spl0_469
  <=> ! [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_469])]) ).

fof(f969,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_44
    | ~ spl0_115 ),
    inference(resolution,[],[f917,f426]) ).

fof(f6186,plain,
    ( spl0_468
    | ~ spl0_79
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f876,f824,f629,f6184]) ).

fof(f6184,plain,
    ( spl0_468
  <=> ! [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_468])]) ).

fof(f876,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_79
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f630]) ).

fof(f6181,plain,
    ( spl0_466
    | ~ spl0_467
    | ~ spl0_85
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f829,f803,f665,f6178,f6175]) ).

fof(f6175,plain,
    ( spl0_466
  <=> ! [X0,X1] :
        ( 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_466])]) ).

fof(f6178,plain,
    ( spl0_467
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f829,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,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_85
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f666]) ).

fof(f6023,plain,
    ( spl0_465
    | ~ spl0_235
    | ~ spl0_457 ),
    inference(avatar_split_clause,[],[f5905,f5902,f2311,f6021]) ).

fof(f6021,plain,
    ( spl0_465
  <=> ! [X0] :
        ( member(regular(X0),singleton_relation)
        | ~ member(regular(X0),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f5902,plain,
    ( spl0_457
  <=> ! [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_457])]) ).

fof(f5905,plain,
    ( ! [X0] :
        ( member(regular(X0),singleton_relation)
        | ~ member(regular(X0),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_235
    | ~ spl0_457 ),
    inference(forward_demodulation,[],[f5903,f2313]) ).

fof(f5903,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_457 ),
    inference(avatar_component_clause,[],[f5902]) ).

fof(f6019,plain,
    ( spl0_464
    | ~ spl0_235
    | ~ spl0_456 ),
    inference(avatar_split_clause,[],[f5900,f5897,f2311,f6017]) ).

fof(f6017,plain,
    ( spl0_464
  <=> ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f5897,plain,
    ( spl0_456
  <=> ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f5900,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | null_class = X0 )
    | ~ spl0_235
    | ~ spl0_456 ),
    inference(forward_demodulation,[],[f5898,f2313]) ).

fof(f5898,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 )
    | ~ spl0_456 ),
    inference(avatar_component_clause,[],[f5897]) ).

fof(f5930,plain,
    ( spl0_463
    | ~ spl0_235
    | ~ spl0_453 ),
    inference(avatar_split_clause,[],[f5887,f5884,f2311,f5928]) ).

fof(f5928,plain,
    ( spl0_463
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f5884,plain,
    ( spl0_453
  <=> ! [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_453])]) ).

fof(f5887,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_235
    | ~ spl0_453 ),
    inference(forward_demodulation,[],[f5885,f2313]) ).

fof(f5885,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_453 ),
    inference(avatar_component_clause,[],[f5884]) ).

fof(f5926,plain,
    ( spl0_462
    | ~ spl0_235
    | ~ spl0_452 ),
    inference(avatar_split_clause,[],[f5882,f5878,f2311,f5924]) ).

fof(f5924,plain,
    ( spl0_462
  <=> ! [X0] :
        ( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
        | ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f5878,plain,
    ( spl0_452
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f5882,plain,
    ( ! [X0] :
        ( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
        | ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f5881,f2313]) ).

fof(f5881,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_235
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f5879,f2313]) ).

fof(f5879,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_452 ),
    inference(avatar_component_clause,[],[f5878]) ).

fof(f5922,plain,
    ( spl0_461
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1344,f1317,f381,f5920]) ).

fof(f5920,plain,
    ( spl0_461
  <=> ! [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_461])]) ).

fof(f1344,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1329]) ).

fof(f1329,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_40
    | ~ spl0_160 ),
    inference(superposition,[],[f382,f1318]) ).

fof(f5918,plain,
    ( ~ spl0_459
    | spl0_460
    | ~ spl0_114
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f5811,f4207,f893,f5915,f5911]) ).

fof(f5911,plain,
    ( spl0_459
  <=> single_valued_class(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f5915,plain,
    ( spl0_460
  <=> function(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f4207,plain,
    ( spl0_383
  <=> subclass(subset_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f5811,plain,
    ( function(subset_relation)
    | ~ single_valued_class(subset_relation)
    | ~ spl0_114
    | ~ spl0_383 ),
    inference(resolution,[],[f4209,f894]) ).

fof(f4209,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f4207]) ).

fof(f5909,plain,
    ( spl0_458
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1339,f1317,f381,f5907]) ).

fof(f5907,plain,
    ( spl0_458
  <=> ! [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_458])]) ).

fof(f1339,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1334]) ).

fof(f1334,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_40
    | ~ spl0_160 ),
    inference(superposition,[],[f382,f1318]) ).

fof(f5904,plain,
    ( spl0_457
    | ~ spl0_116
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1213,f1168,f920,f5902]) ).

fof(f1213,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_116
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f921]) ).

fof(f5899,plain,
    ( spl0_456
    | ~ spl0_116
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1199,f1164,f920,f5897]) ).

fof(f1199,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f921]) ).

fof(f5895,plain,
    ( spl0_455
    | ~ spl0_116
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1185,f1160,f920,f5893]) ).

fof(f5893,plain,
    ( spl0_455
  <=> ! [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_455])]) ).

fof(f1185,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f921]) ).

fof(f5891,plain,
    ( spl0_454
    | ~ spl0_48
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1063,f1013,f445,f5889]) ).

fof(f5889,plain,
    ( spl0_454
  <=> ! [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_454])]) ).

fof(f1063,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_48
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f446]) ).

fof(f5886,plain,
    ( spl0_453
    | ~ spl0_115
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1000,f960,f916,f5884]) ).

fof(f1000,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_115
    | ~ spl0_125 ),
    inference(resolution,[],[f961,f917]) ).

fof(f5880,plain,
    ( spl0_452
    | ~ spl0_115
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f996,f956,f916,f5878]) ).

fof(f996,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_115
    | ~ spl0_124 ),
    inference(resolution,[],[f957,f917]) ).

fof(f5819,plain,
    ( spl0_451
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f5567,f5562,f2311,f5817]) ).

fof(f5817,plain,
    ( spl0_451
  <=> ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f5562,plain,
    ( spl0_446
  <=> ! [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_446])]) ).

fof(f5567,plain,
    ( ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) )
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5566,f2313]) ).

fof(f5566,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | subclass(X0,identity_relation) )
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5565,f2313]) ).

fof(f5565,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5563,f2313]) ).

fof(f5563,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_446 ),
    inference(avatar_component_clause,[],[f5562]) ).

fof(f5810,plain,
    ( spl0_450
    | ~ spl0_235
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f5560,f5557,f2311,f5808]) ).

fof(f5808,plain,
    ( spl0_450
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f5557,plain,
    ( spl0_445
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f5560,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_445 ),
    inference(forward_demodulation,[],[f5558,f2313]) ).

fof(f5558,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_445 ),
    inference(avatar_component_clause,[],[f5557]) ).

fof(f5579,plain,
    ( spl0_448
    | ~ spl0_449
    | ~ spl0_78
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1415,f1370,f625,f5576,f5573]) ).

fof(f5573,plain,
    ( spl0_448
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f5576,plain,
    ( spl0_449
  <=> subclass(domain_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1415,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,successor_relation)
        | ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
    | ~ spl0_78
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f626]) ).

fof(f5571,plain,
    ( spl0_447
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3453,f3333,f324,f5569]) ).

fof(f5569,plain,
    ( spl0_447
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f3333,plain,
    ( spl0_335
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f3453,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation)
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3440]) ).

fof(f3440,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),subset_relation)
        | subclass(intersection(X0,singleton_relation),subset_relation) )
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(resolution,[],[f3334,f325]) ).

fof(f3334,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f3333]) ).

fof(f5564,plain,
    ( spl0_446
    | ~ spl0_43
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1404,f1366,f394,f5562]) ).

fof(f1404,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_43
    | ~ spl0_164 ),
    inference(superposition,[],[f1367,f396]) ).

fof(f5559,plain,
    ( spl0_445
    | ~ spl0_41
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1403,f1366,f385,f5557]) ).

fof(f385,plain,
    ( spl0_41
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1403,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_41
    | ~ spl0_164 ),
    inference(superposition,[],[f1367,f387]) ).

fof(f387,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f385]) ).

fof(f5555,plain,
    ( spl0_444
    | ~ spl0_40
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1399,f1366,f381,f5553]) ).

fof(f5553,plain,
    ( spl0_444
  <=> ! [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_444])]) ).

fof(f1399,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_40
    | ~ spl0_164 ),
    inference(superposition,[],[f1367,f382]) ).

fof(f5551,plain,
    ( spl0_443
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1346,f1317,f952,f5549]) ).

fof(f5549,plain,
    ( spl0_443
  <=> ! [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_443])]) ).

fof(f1346,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1327]) ).

fof(f1327,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_123
    | ~ spl0_160 ),
    inference(superposition,[],[f953,f1318]) ).

fof(f5547,plain,
    ( spl0_442
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1341,f1317,f952,f5545]) ).

fof(f5545,plain,
    ( spl0_442
  <=> ! [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_442])]) ).

fof(f1341,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1332]) ).

fof(f1332,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_123
    | ~ spl0_160 ),
    inference(superposition,[],[f953,f1318]) ).

fof(f5543,plain,
    ( spl0_441
    | ~ spl0_38
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1260,f1248,f373,f5541]) ).

fof(f5541,plain,
    ( spl0_441
  <=> ! [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_441])]) ).

fof(f1260,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_38
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f374]) ).

fof(f5539,plain,
    ( ~ spl0_439
    | spl0_440
    | ~ spl0_106
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1216,f1168,f803,f5537,f5533]) ).

fof(f5533,plain,
    ( spl0_439
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f5537,plain,
    ( spl0_440
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f1216,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_106
    | ~ spl0_144 ),
    inference(resolution,[],[f1169,f804]) ).

fof(f5531,plain,
    ( ~ spl0_438
    | ~ spl0_235
    | spl0_435 ),
    inference(avatar_split_clause,[],[f5522,f5515,f2311,f5528]) ).

fof(f5528,plain,
    ( spl0_438
  <=> subclass(universal_class,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f5522,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_435 ),
    inference(forward_demodulation,[],[f5517,f2313]) ).

fof(f5517,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
    | spl0_435 ),
    inference(avatar_component_clause,[],[f5515]) ).

fof(f5526,plain,
    ( spl0_437
    | ~ spl0_28
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3414,f3311,f324,f5524]) ).

fof(f5524,plain,
    ( spl0_437
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f3311,plain,
    ( spl0_332
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f3414,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation)
    | ~ spl0_28
    | ~ spl0_332 ),
    inference(duplicate_literal_removal,[],[f3401]) ).

fof(f3401,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),subset_relation)
        | subclass(intersection(singleton_relation,X0),subset_relation) )
    | ~ spl0_28
    | ~ spl0_332 ),
    inference(resolution,[],[f3312,f325]) ).

fof(f3312,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f3311]) ).

fof(f5521,plain,
    ( ~ spl0_435
    | spl0_436
    | ~ spl0_106
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1202,f1164,f803,f5519,f5515]) ).

fof(f5519,plain,
    ( spl0_436
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1202,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation)
        | ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_106
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f804]) ).

fof(f5513,plain,
    ( spl0_434
    | ~ spl0_106
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1188,f1160,f803,f5511]) ).

fof(f5511,plain,
    ( spl0_434
  <=> ! [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_434])]) ).

fof(f1188,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_106
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f804]) ).

fof(f5509,plain,
    ( spl0_433
    | ~ spl0_23
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1183,f1160,f300,f5507]) ).

fof(f5507,plain,
    ( spl0_433
  <=> ! [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_433])]) ).

fof(f1183,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) )
    | ~ spl0_23
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f301]) ).

fof(f5504,plain,
    ( ~ spl0_432
    | ~ spl0_235
    | spl0_431 ),
    inference(avatar_split_clause,[],[f5499,f5495,f2311,f5501]) ).

fof(f5501,plain,
    ( spl0_432
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f5495,plain,
    ( spl0_431
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f5499,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
    | ~ spl0_235
    | spl0_431 ),
    inference(forward_demodulation,[],[f5497,f2313]) ).

fof(f5497,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | spl0_431 ),
    inference(avatar_component_clause,[],[f5495]) ).

fof(f5498,plain,
    ( spl0_430
    | ~ spl0_431
    | ~ spl0_112
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1002,f960,f885,f5495,f5491]) ).

fof(f1002,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_112
    | ~ spl0_125 ),
    inference(resolution,[],[f961,f886]) ).

fof(f5488,plain,
    ( ~ spl0_429
    | ~ spl0_235
    | spl0_426 ),
    inference(avatar_split_clause,[],[f5472,f5468,f2311,f5485]) ).

fof(f5485,plain,
    ( spl0_429
  <=> member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f5468,plain,
    ( spl0_426
  <=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f5472,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
    | ~ spl0_235
    | spl0_426 ),
    inference(forward_demodulation,[],[f5470,f2313]) ).

fof(f5470,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | spl0_426 ),
    inference(avatar_component_clause,[],[f5468]) ).

fof(f5483,plain,
    ( spl0_428
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3387,f3211,f2365,f2311,f5480]) ).

fof(f5480,plain,
    ( spl0_428
  <=> subclass(singleton_relation,intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f2365,plain,
    ( spl0_244
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f3211,plain,
    ( spl0_327
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f3387,plain,
    ( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(forward_demodulation,[],[f3372,f2313]) ).

fof(f3372,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3363]) ).

fof(f3363,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(resolution,[],[f3212,f2366]) ).

fof(f2366,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2365]) ).

fof(f3212,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f3211]) ).

fof(f5478,plain,
    ( ~ spl0_427
    | ~ spl0_235
    | spl0_425 ),
    inference(avatar_split_clause,[],[f5473,f5464,f2311,f5475]) ).

fof(f5475,plain,
    ( spl0_427
  <=> null_class = complement(complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f5473,plain,
    ( null_class != complement(complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_425 ),
    inference(forward_demodulation,[],[f5465,f2313]) ).

fof(f5465,plain,
    ( null_class != complement(complement(compose(element_relation,complement(identity_relation))))
    | spl0_425 ),
    inference(avatar_component_clause,[],[f5464]) ).

fof(f5471,plain,
    ( spl0_425
    | ~ spl0_426
    | ~ spl0_112
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f997,f956,f885,f5468,f5464]) ).

fof(f997,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_112
    | ~ spl0_124 ),
    inference(resolution,[],[f957,f886]) ).

fof(f5462,plain,
    ( spl0_424
    | ~ spl0_44
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f898,f885,f425,f5460]) ).

fof(f5460,plain,
    ( spl0_424
  <=> ! [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_424])]) ).

fof(f898,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_44
    | ~ spl0_112 ),
    inference(resolution,[],[f886,f426]) ).

fof(f5173,plain,
    ( spl0_423
    | ~ spl0_27
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3381,f3211,f320,f5171]) ).

fof(f3381,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_27
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3346]) ).

fof(f3346,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(X0,X0))
        | subclass(X0,intersection(X0,X0)) )
    | ~ spl0_27
    | ~ spl0_327 ),
    inference(resolution,[],[f3212,f321]) ).

fof(f5146,plain,
    ( spl0_422
    | ~ spl0_235
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f4811,f4808,f2311,f5144]) ).

fof(f5144,plain,
    ( spl0_422
  <=> ! [X0,X1] :
        ( ~ subclass(singleton_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_422])]) ).

fof(f4808,plain,
    ( spl0_411
  <=> ! [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_411])]) ).

fof(f4811,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_235
    | ~ spl0_411 ),
    inference(forward_demodulation,[],[f4809,f2313]) ).

fof(f4809,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_411 ),
    inference(avatar_component_clause,[],[f4808]) ).

fof(f5142,plain,
    ( spl0_421
    | ~ spl0_235
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f4802,f4799,f2311,f5140]) ).

fof(f5140,plain,
    ( spl0_421
  <=> ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f4799,plain,
    ( spl0_409
  <=> ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f4802,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_235
    | ~ spl0_409 ),
    inference(forward_demodulation,[],[f4800,f2313]) ).

fof(f4800,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f4799]) ).

fof(f4857,plain,
    ( spl0_420
    | ~ spl0_243
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3376,f3211,f2361,f4854]) ).

fof(f4854,plain,
    ( spl0_420
  <=> subclass(singleton_relation,intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f2361,plain,
    ( spl0_243
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f3376,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_243
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3352]) ).

fof(f3352,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_243
    | ~ spl0_327 ),
    inference(resolution,[],[f3212,f2362]) ).

fof(f2362,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f2361]) ).

fof(f4852,plain,
    ( spl0_419
    | ~ spl0_235
    | ~ spl0_403 ),
    inference(avatar_split_clause,[],[f4777,f4774,f2311,f4850]) ).

fof(f4850,plain,
    ( spl0_419
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f4774,plain,
    ( spl0_403
  <=> ! [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_403])]) ).

fof(f4777,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_235
    | ~ spl0_403 ),
    inference(forward_demodulation,[],[f4775,f2313]) ).

fof(f4775,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_403 ),
    inference(avatar_component_clause,[],[f4774]) ).

fof(f4848,plain,
    ( spl0_418
    | ~ spl0_235
    | ~ spl0_402 ),
    inference(avatar_split_clause,[],[f4772,f4768,f2311,f4846]) ).

fof(f4846,plain,
    ( spl0_418
  <=> ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f4768,plain,
    ( spl0_402
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f4772,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_402 ),
    inference(forward_demodulation,[],[f4771,f2313]) ).

fof(f4771,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_235
    | ~ spl0_402 ),
    inference(forward_demodulation,[],[f4769,f2313]) ).

fof(f4769,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_402 ),
    inference(avatar_component_clause,[],[f4768]) ).

fof(f4835,plain,
    ( spl0_417
    | ~ spl0_134
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1407,f1366,f1084,f4833]) ).

fof(f4833,plain,
    ( spl0_417
  <=> ! [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_417])]) ).

fof(f1407,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_134
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1388]) ).

fof(f1388,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_134
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f1085]) ).

fof(f4831,plain,
    ( spl0_416
    | ~ spl0_135
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1406,f1366,f1088,f4829]) ).

fof(f4829,plain,
    ( spl0_416
  <=> ! [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_416])]) ).

fof(f1406,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_135
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1389]) ).

fof(f1389,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_135
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f1089]) ).

fof(f4827,plain,
    ( spl0_415
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1343,f1317,f300,f4825]) ).

fof(f4825,plain,
    ( spl0_415
  <=> ! [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_415])]) ).

fof(f1343,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1330]) ).

fof(f1330,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_160 ),
    inference(superposition,[],[f301,f1318]) ).

fof(f4823,plain,
    ( spl0_414
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1338,f1317,f300,f4821]) ).

fof(f4821,plain,
    ( spl0_414
  <=> ! [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_414])]) ).

fof(f1338,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1335]) ).

fof(f1335,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_160 ),
    inference(superposition,[],[f301,f1318]) ).

fof(f4819,plain,
    ( spl0_413
    | ~ spl0_31
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1264,f1248,f336,f4817]) ).

fof(f4817,plain,
    ( spl0_413
  <=> ! [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_413])]) ).

fof(f1264,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_31
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f337]) ).

fof(f4815,plain,
    ( spl0_412
    | ~ spl0_32
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1263,f1248,f340,f4813]) ).

fof(f4813,plain,
    ( spl0_412
  <=> ! [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_412])]) ).

fof(f1263,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_32
    | ~ spl0_152 ),
    inference(resolution,[],[f1249,f341]) ).

fof(f4810,plain,
    ( spl0_411
    | ~ spl0_43
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1259,f1244,f394,f4808]) ).

fof(f1259,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_43
    | ~ spl0_151 ),
    inference(superposition,[],[f1245,f396]) ).

fof(f4806,plain,
    ( spl0_410
    | ~ spl0_28
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f3345,f3194,f324,f4804]) ).

fof(f4804,plain,
    ( spl0_410
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f3194,plain,
    ( spl0_324
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f3345,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),element_relation)
    | ~ spl0_28
    | ~ spl0_324 ),
    inference(duplicate_literal_removal,[],[f3336]) ).

fof(f3336,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),element_relation)
        | subclass(intersection(X0,singleton_relation),element_relation) )
    | ~ spl0_28
    | ~ spl0_324 ),
    inference(resolution,[],[f3195,f325]) ).

fof(f3195,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f3194]) ).

fof(f4801,plain,
    ( spl0_409
    | ~ spl0_41
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1258,f1244,f385,f4799]) ).

fof(f1258,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_41
    | ~ spl0_151 ),
    inference(superposition,[],[f1245,f387]) ).

fof(f4797,plain,
    ( spl0_408
    | ~ spl0_40
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1254,f1244,f381,f4795]) ).

fof(f4795,plain,
    ( spl0_408
  <=> ! [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_408])]) ).

fof(f1254,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_151 ),
    inference(superposition,[],[f1245,f382]) ).

fof(f4793,plain,
    ( spl0_407
    | ~ spl0_31
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1135,f1088,f336,f4791]) ).

fof(f4791,plain,
    ( spl0_407
  <=> ! [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_407])]) ).

fof(f1135,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_31
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f337]) ).

fof(f4789,plain,
    ( spl0_406
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1134,f1088,f340,f4787]) ).

fof(f4787,plain,
    ( spl0_406
  <=> ! [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_406])]) ).

fof(f1134,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f341]) ).

fof(f4785,plain,
    ( spl0_405
    | ~ spl0_31
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1117,f1084,f336,f4783]) ).

fof(f4783,plain,
    ( spl0_405
  <=> ! [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_405])]) ).

fof(f1117,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_31
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f337]) ).

fof(f4781,plain,
    ( spl0_404
    | ~ spl0_32
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1116,f1084,f340,f4779]) ).

fof(f4779,plain,
    ( spl0_404
  <=> ! [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_404])]) ).

fof(f1116,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_32
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f341]) ).

fof(f4776,plain,
    ( spl0_403
    | ~ spl0_28
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f999,f960,f324,f4774]) ).

fof(f999,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_28
    | ~ spl0_125 ),
    inference(resolution,[],[f961,f325]) ).

fof(f4770,plain,
    ( spl0_402
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f995,f956,f324,f4768]) ).

fof(f995,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(resolution,[],[f957,f325]) ).

fof(f4766,plain,
    ( spl0_401
    | ~ spl0_48
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f974,f920,f445,f4764]) ).

fof(f4764,plain,
    ( spl0_401
  <=> ! [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_401])]) ).

fof(f974,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_48
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f446]) ).

fof(f4739,plain,
    ( spl0_400
    | ~ spl0_28
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f3323,f3173,f324,f4737]) ).

fof(f4737,plain,
    ( spl0_400
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f3173,plain,
    ( spl0_320
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f3323,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),element_relation)
    | ~ spl0_28
    | ~ spl0_320 ),
    inference(duplicate_literal_removal,[],[f3314]) ).

fof(f3314,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),element_relation)
        | subclass(intersection(singleton_relation,X0),element_relation) )
    | ~ spl0_28
    | ~ spl0_320 ),
    inference(resolution,[],[f3174,f325]) ).

fof(f3174,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_320 ),
    inference(avatar_component_clause,[],[f3173]) ).

fof(f4644,plain,
    ( spl0_399
    | ~ spl0_235
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4247,f4244,f2311,f4642]) ).

fof(f4642,plain,
    ( spl0_399
  <=> ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f4244,plain,
    ( spl0_392
  <=> ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f4247,plain,
    ( ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_235
    | ~ spl0_392 ),
    inference(forward_demodulation,[],[f4245,f2313]) ).

fof(f4245,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_392 ),
    inference(avatar_component_clause,[],[f4244]) ).

fof(f4368,plain,
    ( spl0_398
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3238,f3138,f2365,f2311,f4365]) ).

fof(f3138,plain,
    ( spl0_313
  <=> ! [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_313])]) ).

fof(f3238,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(forward_demodulation,[],[f3237,f2313]) ).

fof(f3237,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3226]) ).

fof(f3226,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(resolution,[],[f3139,f2366]) ).

fof(f3139,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f3138]) ).

fof(f4273,plain,
    ( spl0_397
    | ~ spl0_130
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1405,f1366,f1013,f4271]) ).

fof(f4271,plain,
    ( spl0_397
  <=> ! [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_397])]) ).

fof(f1405,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_130
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1390]) ).

fof(f1390,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_130
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f1014]) ).

fof(f4269,plain,
    ( ~ spl0_395
    | spl0_396
    | ~ spl0_12
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1311,f1295,f255,f4266,f4262]) ).

fof(f4262,plain,
    ( spl0_395
  <=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f4266,plain,
    ( spl0_396
  <=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1311,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_12
    | ~ spl0_158 ),
    inference(resolution,[],[f1296,f256]) ).

fof(f4260,plain,
    ( spl0_394
    | ~ spl0_20
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1265,f1248,f288,f4258]) ).

fof(f4258,plain,
    ( spl0_394
  <=> ! [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_394])]) ).

fof(f1265,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_152 ),
    inference(resolution,[],[f1249,f289]) ).

fof(f4252,plain,
    ( spl0_182
    | ~ spl0_6
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f2512,f2480,f229,f1539]) ).

fof(f229,plain,
    ( spl0_6
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f2480,plain,
    ( spl0_265
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f2512,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_265 ),
    inference(resolution,[],[f2481,f230]) ).

fof(f230,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f2481,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f2480]) ).

fof(f4251,plain,
    ( spl0_393
    | ~ spl0_22
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1253,f1244,f296,f4249]) ).

fof(f4249,plain,
    ( spl0_393
  <=> ! [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_393])]) ).

fof(f1253,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_151 ),
    inference(resolution,[],[f1245,f297]) ).

fof(f4246,plain,
    ( spl0_392
    | ~ spl0_44
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1192,f1164,f425,f4244]) ).

fof(f1192,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_44
    | ~ spl0_143 ),
    inference(resolution,[],[f1165,f426]) ).

fof(f4242,plain,
    ( spl0_391
    | ~ spl0_113
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1137,f1088,f889,f4240]) ).

fof(f4240,plain,
    ( spl0_391
  <=> ! [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_391])]) ).

fof(f1137,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 )
    | ~ spl0_113
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f890]) ).

fof(f4238,plain,
    ( spl0_390
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1131,f1088,f373,f4236]) ).

fof(f4236,plain,
    ( spl0_390
  <=> ! [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_390])]) ).

fof(f1131,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f374]) ).

fof(f4234,plain,
    ( spl0_389
    | ~ spl0_113
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1119,f1084,f889,f4232]) ).

fof(f4232,plain,
    ( spl0_389
  <=> ! [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_389])]) ).

fof(f1119,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 )
    | ~ spl0_113
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f890]) ).

fof(f4230,plain,
    ( spl0_388
    | ~ spl0_38
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1113,f1084,f373,f4228]) ).

fof(f4228,plain,
    ( spl0_388
  <=> ! [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_388])]) ).

fof(f1113,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_38
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f374]) ).

fof(f4226,plain,
    ( spl0_387
    | ~ spl0_31
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1048,f1009,f336,f4224]) ).

fof(f4224,plain,
    ( spl0_387
  <=> ! [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_387])]) ).

fof(f1048,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_31
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f337]) ).

fof(f4222,plain,
    ( spl0_386
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1047,f1009,f340,f4220]) ).

fof(f4220,plain,
    ( spl0_386
  <=> ! [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_386])]) ).

fof(f1047,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f341]) ).

fof(f4218,plain,
    ( spl0_385
    | ~ spl0_31
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1032,f1005,f336,f4216]) ).

fof(f4216,plain,
    ( spl0_385
  <=> ! [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_385])]) ).

fof(f1032,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_31
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f337]) ).

fof(f4214,plain,
    ( spl0_384
    | ~ spl0_32
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1031,f1005,f340,f4212]) ).

fof(f4212,plain,
    ( spl0_384
  <=> ! [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_384])]) ).

fof(f1031,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_32
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f341]) ).

fof(f4210,plain,
    ( spl0_383
    | ~ spl0_76
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2239,f2224,f609,f4207]) ).

fof(f2239,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_76
    | ~ spl0_223 ),
    inference(superposition,[],[f2225,f611]) ).

fof(f4205,plain,
    ( spl0_382
    | ~ spl0_115
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f991,f952,f916,f4203]) ).

fof(f4203,plain,
    ( spl0_382
  <=> ! [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_382])]) ).

fof(f991,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) )
    | ~ spl0_115
    | ~ spl0_123 ),
    inference(resolution,[],[f953,f917]) ).

fof(f4201,plain,
    ( spl0_381
    | ~ spl0_48
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f847,f803,f445,f4199]) ).

fof(f4199,plain,
    ( spl0_381
  <=> ! [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_381])]) ).

fof(f847,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_48
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f446]) ).

fof(f3837,plain,
    ( spl0_380
    | ~ spl0_106
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1738,f1712,f803,f3835]) ).

fof(f3835,plain,
    ( spl0_380
  <=> ! [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_380])]) ).

fof(f1738,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_106
    | ~ spl0_198 ),
    inference(superposition,[],[f804,f1713]) ).

fof(f3833,plain,
    ( spl0_379
    | ~ spl0_32
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1355,f1352,f340,f3831]) ).

fof(f3831,plain,
    ( spl0_379
  <=> ! [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_379])]) ).

fof(f1355,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_32
    | ~ spl0_162 ),
    inference(resolution,[],[f1353,f341]) ).

fof(f3829,plain,
    ( spl0_378
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1337,f1317,f3827]) ).

fof(f3827,plain,
    ( spl0_378
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f1337,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_160 ),
    inference(equality_factoring,[],[f1318]) ).

fof(f3825,plain,
    ( spl0_377
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1336,f1317,f3823]) ).

fof(f3823,plain,
    ( spl0_377
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f1336,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_160 ),
    inference(equality_factoring,[],[f1318]) ).

fof(f3821,plain,
    ( spl0_376
    | ~ spl0_134
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1308,f1291,f1084,f3819]) ).

fof(f3819,plain,
    ( spl0_376
  <=> ! [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_376])]) ).

fof(f1291,plain,
    ( spl0_157
  <=> ! [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_157])]) ).

fof(f1308,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_134
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1303]) ).

fof(f1303,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_134
    | ~ spl0_157 ),
    inference(resolution,[],[f1292,f1085]) ).

fof(f1292,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_157 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f3817,plain,
    ( spl0_375
    | ~ spl0_135
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1307,f1291,f1088,f3815]) ).

fof(f3815,plain,
    ( spl0_375
  <=> ! [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_375])]) ).

fof(f1307,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1304]) ).

fof(f1304,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_135
    | ~ spl0_157 ),
    inference(resolution,[],[f1292,f1089]) ).

fof(f3813,plain,
    ( spl0_374
    | ~ spl0_22
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1177,f1156,f296,f3811]) ).

fof(f3811,plain,
    ( spl0_374
  <=> ! [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_374])]) ).

fof(f1156,plain,
    ( spl0_141
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1177,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_22
    | ~ spl0_141 ),
    inference(resolution,[],[f1157,f297]) ).

fof(f1157,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1156]) ).

fof(f3809,plain,
    ( spl0_373
    | ~ spl0_20
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1136,f1088,f288,f3807]) ).

fof(f3807,plain,
    ( spl0_373
  <=> ! [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_373])]) ).

fof(f1136,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_20
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f289]) ).

fof(f3805,plain,
    ( spl0_372
    | ~ spl0_20
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1118,f1084,f288,f3803]) ).

fof(f3803,plain,
    ( spl0_372
  <=> ! [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_372])]) ).

fof(f1118,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_20
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f289]) ).

fof(f3801,plain,
    ( ~ spl0_370
    | spl0_371
    | ~ spl0_114
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f3159,f2728,f893,f3798,f3794]) ).

fof(f3794,plain,
    ( spl0_370
  <=> single_valued_class(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f3798,plain,
    ( spl0_371
  <=> function(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f3159,plain,
    ( function(null_class)
    | ~ single_valued_class(null_class)
    | ~ spl0_114
    | ~ spl0_284 ),
    inference(resolution,[],[f2729,f894]) ).

fof(f3792,plain,
    ( spl0_369
    | ~ spl0_113
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1068,f1013,f889,f3790]) ).

fof(f3790,plain,
    ( spl0_369
  <=> ! [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_369])]) ).

fof(f1068,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 )
    | ~ spl0_113
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f890]) ).

fof(f3788,plain,
    ( spl0_368
    | ~ spl0_38
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1062,f1013,f373,f3786]) ).

fof(f3786,plain,
    ( spl0_368
  <=> ! [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_368])]) ).

fof(f1062,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_38
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f374]) ).

fof(f3784,plain,
    ( spl0_367
    | ~ spl0_113
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1050,f1009,f889,f3782]) ).

fof(f3782,plain,
    ( spl0_367
  <=> ! [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_367])]) ).

fof(f1050,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 )
    | ~ spl0_113
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f890]) ).

fof(f3780,plain,
    ( spl0_366
    | ~ spl0_38
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1044,f1009,f373,f3778]) ).

fof(f3778,plain,
    ( spl0_366
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f1044,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_38
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f374]) ).

fof(f3776,plain,
    ( spl0_365
    | ~ spl0_113
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1034,f1005,f889,f3774]) ).

fof(f3774,plain,
    ( spl0_365
  <=> ! [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_365])]) ).

fof(f1034,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 )
    | ~ spl0_113
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f890]) ).

fof(f3772,plain,
    ( spl0_364
    | ~ spl0_38
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1028,f1005,f373,f3770]) ).

fof(f3770,plain,
    ( spl0_364
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f1028,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_38
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f374]) ).

fof(f3768,plain,
    ( spl0_363
    | ~ spl0_112
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f992,f952,f885,f3766]) ).

fof(f3766,plain,
    ( spl0_363
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f992,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) )
    | ~ spl0_112
    | ~ spl0_123 ),
    inference(resolution,[],[f953,f886]) ).

fof(f3764,plain,
    ( spl0_362
    | ~ spl0_111
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f967,f916,f824,f3762]) ).

fof(f3762,plain,
    ( spl0_362
  <=> ! [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_362])]) ).

fof(f967,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_111
    | ~ spl0_115 ),
    inference(resolution,[],[f917,f825]) ).

fof(f3760,plain,
    ( spl0_361
    | ~ spl0_67
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f881,f824,f557,f3758]) ).

fof(f3758,plain,
    ( spl0_361
  <=> ! [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_361])]) ).

fof(f881,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_67
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f558]) ).

fof(f3756,plain,
    ( spl0_360
    | ~ spl0_68
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f880,f824,f561,f3754]) ).

fof(f880,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f562]) ).

fof(f3748,plain,
    ( spl0_359
    | ~ spl0_57
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f859,f816,f504,f3746]) ).

fof(f3746,plain,
    ( spl0_359
  <=> ! [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_359])]) ).

fof(f859,plain,
    ( ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_57
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f505]) ).

fof(f3617,plain,
    ( spl0_358
    | ~ spl0_235
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f3519,f3516,f2311,f3615]) ).

fof(f3615,plain,
    ( spl0_358
  <=> ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f3516,plain,
    ( spl0_349
  <=> ! [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_349])]) ).

fof(f3519,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_235
    | ~ spl0_349 ),
    inference(forward_demodulation,[],[f3517,f2313]) ).

fof(f3517,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f3516]) ).

fof(f3598,plain,
    ( spl0_357
    | ~ spl0_235
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3514,f3511,f2311,f3596]) ).

fof(f3511,plain,
    ( spl0_348
  <=> ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f3514,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_235
    | ~ spl0_348 ),
    inference(forward_demodulation,[],[f3512,f2313]) ).

fof(f3512,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_348 ),
    inference(avatar_component_clause,[],[f3511]) ).

fof(f3548,plain,
    ( spl0_356
    | ~ spl0_72
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1417,f1370,f585,f3546]) ).

fof(f3546,plain,
    ( spl0_356
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f1417,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) )
    | ~ spl0_72
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f586]) ).

fof(f3544,plain,
    ( spl0_355
    | ~ spl0_130
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1306,f1291,f1013,f3542]) ).

fof(f3542,plain,
    ( spl0_355
  <=> ! [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_355])]) ).

fof(f1306,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_130
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1305]) ).

fof(f1305,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_130
    | ~ spl0_157 ),
    inference(resolution,[],[f1292,f1014]) ).

fof(f3540,plain,
    ( spl0_354
    | ~ spl0_31
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1066,f1013,f336,f3538]) ).

fof(f3538,plain,
    ( spl0_354
  <=> ! [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_354])]) ).

fof(f1066,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_31
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f337]) ).

fof(f3536,plain,
    ( spl0_353
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1065,f1013,f340,f3534]) ).

fof(f3534,plain,
    ( spl0_353
  <=> ! [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_353])]) ).

fof(f1065,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f341]) ).

fof(f3532,plain,
    ( spl0_352
    | ~ spl0_20
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1049,f1009,f288,f3530]) ).

fof(f1049,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_20
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f289]) ).

fof(f3528,plain,
    ( spl0_351
    | ~ spl0_20
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1033,f1005,f288,f3526]) ).

fof(f1033,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_20
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f289]) ).

fof(f3524,plain,
    ( spl0_350
    | ~ spl0_234
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2877,f2311,f2305,f3521]) ).

fof(f3521,plain,
    ( spl0_350
  <=> member(regular(singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f2877,plain,
    ( member(regular(singleton_relation),subset_relation)
    | ~ spl0_234
    | ~ spl0_235 ),
    inference(superposition,[],[f2307,f2313]) ).

fof(f3518,plain,
    ( spl0_349
    | ~ spl0_38
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f998,f960,f373,f3516]) ).

fof(f998,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_125 ),
    inference(resolution,[],[f961,f374]) ).

fof(f3513,plain,
    ( spl0_348
    | ~ spl0_38
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f994,f956,f373,f3511]) ).

fof(f994,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_124 ),
    inference(resolution,[],[f957,f374]) ).

fof(f3509,plain,
    ( spl0_347
    | ~ spl0_28
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f990,f952,f324,f3507]) ).

fof(f3507,plain,
    ( spl0_347
  <=> ! [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_347])]) ).

fof(f990,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_28
    | ~ spl0_123 ),
    inference(resolution,[],[f953,f325]) ).

fof(f3505,plain,
    ( spl0_346
    | ~ spl0_38
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f989,f952,f373,f3503]) ).

fof(f3503,plain,
    ( spl0_346
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f989,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_123 ),
    inference(resolution,[],[f953,f374]) ).

fof(f3501,plain,
    ( spl0_345
    | ~ spl0_38
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f973,f920,f373,f3499]) ).

fof(f3499,plain,
    ( spl0_345
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f973,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_38
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f374]) ).

fof(f3494,plain,
    ( ~ spl0_343
    | spl0_344
    | ~ spl0_111
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f896,f885,f824,f3491,f3487]) ).

fof(f3487,plain,
    ( spl0_343
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f896,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | ~ spl0_111
    | ~ spl0_112 ),
    inference(resolution,[],[f886,f825]) ).

fof(f3485,plain,
    ( spl0_342
    | spl0_339
    | ~ spl0_51
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f867,f816,f457,f3466,f3483]) ).

fof(f3483,plain,
    ( spl0_342
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f3466,plain,
    ( spl0_339
  <=> member(null_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f457,plain,
    ( spl0_51
  <=> ! [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_51])]) ).

fof(f867,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f458]) ).

fof(f458,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f457]) ).

fof(f3481,plain,
    ( spl0_341
    | ~ spl0_4
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f2485,f2453,f220,f3478]) ).

fof(f2453,plain,
    ( spl0_262
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f2485,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_4
    | ~ spl0_262 ),
    inference(resolution,[],[f2454,f221]) ).

fof(f2454,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f2453]) ).

fof(f3475,plain,
    ( ~ spl0_340
    | ~ spl0_235
    | spl0_339 ),
    inference(avatar_split_clause,[],[f3470,f3466,f2311,f3472]) ).

fof(f3472,plain,
    ( spl0_340
  <=> member(null_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f3470,plain,
    ( ~ member(null_class,singleton_relation)
    | ~ spl0_235
    | spl0_339 ),
    inference(forward_demodulation,[],[f3467,f2313]) ).

fof(f3467,plain,
    ( ~ member(null_class,identity_relation)
    | spl0_339 ),
    inference(avatar_component_clause,[],[f3466]) ).

fof(f3469,plain,
    ( spl0_338
    | spl0_339
    | ~ spl0_52
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f866,f816,f461,f3466,f3463]) ).

fof(f3463,plain,
    ( spl0_338
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f461,plain,
    ( spl0_52
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f866,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f462]) ).

fof(f462,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f461]) ).

fof(f3461,plain,
    ( spl0_336
    | ~ spl0_337
    | ~ spl0_78
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f832,f803,f625,f3458,f3455]) ).

fof(f3455,plain,
    ( spl0_336
  <=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f3458,plain,
    ( spl0_337
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f832,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_78
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f626]) ).

fof(f3335,plain,
    ( spl0_335
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3192,f3188,f2311,f3333]) ).

fof(f3188,plain,
    ( spl0_323
  <=> ! [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_323])]) ).

fof(f3192,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3191,f2313]) ).

fof(f3191,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3189,f2313]) ).

fof(f3189,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f3188]) ).

fof(f3331,plain,
    ( spl0_334
    | ~ spl0_235
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3186,f3182,f2311,f3329]) ).

fof(f3329,plain,
    ( spl0_334
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f3182,plain,
    ( spl0_322
  <=> ! [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_322])]) ).

fof(f3186,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_235
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f3185,f2313]) ).

fof(f3185,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_235
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f3183,f2313]) ).

fof(f3183,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f3182]) ).

fof(f3327,plain,
    ( spl0_333
    | ~ spl0_235
    | ~ spl0_321 ),
    inference(avatar_split_clause,[],[f3180,f3177,f2311,f3325]) ).

fof(f3325,plain,
    ( spl0_333
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f3177,plain,
    ( spl0_321
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f3180,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_321 ),
    inference(forward_demodulation,[],[f3178,f2313]) ).

fof(f3178,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f3177]) ).

fof(f3313,plain,
    ( spl0_332
    | ~ spl0_235
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3171,f3167,f2311,f3311]) ).

fof(f3167,plain,
    ( spl0_319
  <=> ! [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_319])]) ).

fof(f3171,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_235
    | ~ spl0_319 ),
    inference(forward_demodulation,[],[f3170,f2313]) ).

fof(f3170,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_235
    | ~ spl0_319 ),
    inference(forward_demodulation,[],[f3168,f2313]) ).

fof(f3168,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f3167]) ).

fof(f3309,plain,
    ( spl0_331
    | ~ spl0_235
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2881,f2467,f2311,f3306]) ).

fof(f3306,plain,
    ( spl0_331
  <=> subclass(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f2881,plain,
    ( subclass(singleton_relation,subset_relation)
    | ~ spl0_235
    | ~ spl0_264 ),
    inference(superposition,[],[f2469,f2313]) ).

fof(f3225,plain,
    ( spl0_330
    | ~ spl0_6
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1443,f1378,f229,f3223]) ).

fof(f3223,plain,
    ( spl0_330
  <=> ! [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_330])]) ).

fof(f1378,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

fof(f1443,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_6
    | ~ spl0_167 ),
    inference(resolution,[],[f1379,f230]) ).

fof(f1379,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_167 ),
    inference(avatar_component_clause,[],[f1378]) ).

fof(f3221,plain,
    ( spl0_329
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1442,f1378,f504,f3219]) ).

fof(f3219,plain,
    ( spl0_329
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f1442,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(resolution,[],[f1379,f505]) ).

fof(f3217,plain,
    ( spl0_328
    | ~ spl0_67
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1411,f1370,f557,f3215]) ).

fof(f3215,plain,
    ( spl0_328
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f1411,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_67
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f558]) ).

fof(f3213,plain,
    ( spl0_327
    | ~ spl0_27
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1408,f1366,f320,f3211]) ).

fof(f1408,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1387]) ).

fof(f1387,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0))
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_164 ),
    inference(resolution,[],[f1367,f321]) ).

fof(f3204,plain,
    ( spl0_325
    | spl0_326
    | ~ spl0_12
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1181,f1160,f255,f3201,f3198]) ).

fof(f3198,plain,
    ( spl0_325
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f3201,plain,
    ( spl0_326
  <=> member(null_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f1181,plain,
    ( ! [X0] :
        ( member(null_class,null_class)
        | ~ member(null_class,X0)
        | null_class = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_12
    | ~ spl0_142 ),
    inference(resolution,[],[f1161,f256]) ).

fof(f3196,plain,
    ( spl0_324
    | ~ spl0_97
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1140,f1088,f732,f3194]) ).

fof(f1140,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f733]) ).

fof(f3190,plain,
    ( spl0_323
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1139,f1088,f762,f3188]) ).

fof(f1139,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f763]) ).

fof(f3184,plain,
    ( spl0_322
    | ~ spl0_43
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1128,f1084,f394,f3182]) ).

fof(f1128,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_43
    | ~ spl0_134 ),
    inference(superposition,[],[f1085,f396]) ).

fof(f3179,plain,
    ( spl0_321
    | ~ spl0_41
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1127,f1084,f385,f3177]) ).

fof(f1127,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_41
    | ~ spl0_134 ),
    inference(superposition,[],[f1085,f387]) ).

fof(f3175,plain,
    ( spl0_320
    | ~ spl0_97
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1122,f1084,f732,f3173]) ).

fof(f1122,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f733]) ).

fof(f3169,plain,
    ( spl0_319
    | ~ spl0_103
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1121,f1084,f762,f3167]) ).

fof(f1121,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f763]) ).

fof(f3165,plain,
    ( spl0_318
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1079,f1021,f296,f3163]) ).

fof(f3163,plain,
    ( spl0_318
  <=> ! [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_318])]) ).

fof(f1079,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(resolution,[],[f1022,f297]) ).

fof(f3156,plain,
    ( spl0_317
    | ~ spl0_22
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1076,f1017,f296,f3154]) ).

fof(f3154,plain,
    ( spl0_317
  <=> ! [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_317])]) ).

fof(f1076,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_131 ),
    inference(resolution,[],[f1018,f297]) ).

fof(f3152,plain,
    ( spl0_316
    | ~ spl0_20
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1067,f1013,f288,f3150]) ).

fof(f3150,plain,
    ( spl0_316
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f1067,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_20
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f289]) ).

fof(f3148,plain,
    ( spl0_315
    | ~ spl0_31
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f977,f920,f336,f3146]) ).

fof(f3146,plain,
    ( spl0_315
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f977,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_31
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f337]) ).

fof(f3144,plain,
    ( spl0_314
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f976,f920,f340,f3142]) ).

fof(f3142,plain,
    ( spl0_314
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f976,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f341]) ).

fof(f3140,plain,
    ( spl0_313
    | ~ spl0_28
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f878,f824,f324,f3138]) ).

fof(f878,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_28
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f325]) ).

fof(f3121,plain,
    ( spl0_312
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f3052,f2924,f2311,f3119]) ).

fof(f2924,plain,
    ( spl0_299
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f3052,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2927,f2313]) ).

fof(f2927,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2925,f2313]) ).

fof(f2925,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f2924]) ).

fof(f3109,plain,
    ( ~ spl0_311
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_262
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2587,f2500,f2453,f241,f220,f3106]) ).

fof(f3106,plain,
    ( spl0_311
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f2500,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f2587,plain,
    ( ~ subclass(universal_class,null_class)
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_262
    | ~ spl0_268 ),
    inference(forward_demodulation,[],[f2566,f2485]) ).

fof(f2566,plain,
    ( ~ subclass(universal_class,complement(universal_class))
    | ~ spl0_9
    | ~ spl0_268 ),
    inference(resolution,[],[f2501,f242]) ).

fof(f2501,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f2500]) ).

fof(f3095,plain,
    ( spl0_310
    | ~ spl0_235
    | ~ spl0_301 ),
    inference(avatar_split_clause,[],[f2939,f2936,f2311,f3093]) ).

fof(f2936,plain,
    ( spl0_301
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f2939,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_235
    | ~ spl0_301 ),
    inference(forward_demodulation,[],[f2937,f2313]) ).

fof(f2937,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_301 ),
    inference(avatar_component_clause,[],[f2936]) ).

fof(f3074,plain,
    ( spl0_309
    | ~ spl0_235
    | ~ spl0_296 ),
    inference(avatar_split_clause,[],[f3058,f2852,f2311,f3071]) ).

fof(f3071,plain,
    ( spl0_309
  <=> member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f2852,plain,
    ( spl0_296
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f3058,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_235
    | ~ spl0_296 ),
    inference(forward_demodulation,[],[f2854,f2313]) ).

fof(f2854,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_296 ),
    inference(avatar_component_clause,[],[f2852]) ).

fof(f3069,plain,
    ( spl0_308
    | ~ spl0_235
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f3053,f2831,f2311,f3066]) ).

fof(f3066,plain,
    ( spl0_308
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f2831,plain,
    ( spl0_295
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f3053,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | ~ spl0_295 ),
    inference(forward_demodulation,[],[f2833,f2313]) ).

fof(f2833,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f2831]) ).

fof(f3064,plain,
    ( ~ spl0_307
    | ~ spl0_111
    | spl0_298 ),
    inference(avatar_split_clause,[],[f2920,f2916,f824,f3061]) ).

fof(f3061,plain,
    ( spl0_307
  <=> member(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f2916,plain,
    ( spl0_298
  <=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f2920,plain,
    ( ~ member(singleton_relation,subset_relation)
    | ~ spl0_111
    | spl0_298 ),
    inference(resolution,[],[f2918,f825]) ).

fof(f2918,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | spl0_298 ),
    inference(avatar_component_clause,[],[f2916]) ).

fof(f3056,plain,
    ( spl0_231
    | ~ spl0_233
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2865,f2311,f2301,f2283]) ).

fof(f2865,plain,
    ( null_class = singleton_relation
    | ~ spl0_233
    | ~ spl0_235 ),
    inference(forward_demodulation,[],[f2303,f2313]) ).

fof(f2303,plain,
    ( null_class = identity_relation
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2301]) ).

fof(f3045,plain,
    ( spl0_306
    | ~ spl0_231
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f2929,f2924,f2311,f2283,f3043]) ).

fof(f3043,plain,
    ( spl0_306
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f2929,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) )
    | ~ spl0_231
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2928,f2313]) ).

fof(f2928,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_231
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2927,f2285]) ).

fof(f2285,plain,
    ( null_class = singleton_relation
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f2283]) ).

fof(f2956,plain,
    ( spl0_305
    | ~ spl0_9
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1734,f1712,f241,f2954]) ).

fof(f2954,plain,
    ( spl0_305
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f1734,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_9
    | ~ spl0_198 ),
    inference(superposition,[],[f242,f1713]) ).

fof(f2952,plain,
    ( spl0_304
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1410,f1370,f561,f2950]) ).

fof(f2950,plain,
    ( spl0_304
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f1410,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f562]) ).

fof(f2948,plain,
    ( ~ spl0_303
    | ~ spl0_2
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2921,f2504,f210,f2945]) ).

fof(f2945,plain,
    ( spl0_303
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f210,plain,
    ( spl0_2
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f2504,plain,
    ( spl0_269
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f2921,plain,
    ( ~ inductive(choice)
    | ~ spl0_2
    | ~ spl0_269 ),
    inference(resolution,[],[f2505,f212]) ).

fof(f212,plain,
    ( function(choice)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f2505,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f2504]) ).

fof(f2943,plain,
    ( spl0_302
    | ~ spl0_97
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1071,f1013,f732,f2941]) ).

fof(f1071,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f733]) ).

fof(f2938,plain,
    ( spl0_301
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1070,f1013,f762,f2936]) ).

fof(f1070,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f763]) ).

fof(f2933,plain,
    ( spl0_300
    | ~ spl0_97
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1053,f1009,f732,f2931]) ).

fof(f1053,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) )
    | ~ spl0_97
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f733]) ).

fof(f2926,plain,
    ( spl0_299
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1052,f1009,f762,f2924]) ).

fof(f1052,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(resolution,[],[f1010,f763]) ).

fof(f2919,plain,
    ( ~ spl0_298
    | ~ spl0_235
    | spl0_257 ),
    inference(avatar_split_clause,[],[f2912,f2424,f2311,f2916]) ).

fof(f2424,plain,
    ( spl0_257
  <=> member(identity_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f2912,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_235
    | spl0_257 ),
    inference(forward_demodulation,[],[f2425,f2313]) ).

fof(f2425,plain,
    ( ~ member(identity_relation,cross_product(universal_class,universal_class))
    | spl0_257 ),
    inference(avatar_component_clause,[],[f2424]) ).

fof(f2908,plain,
    ( spl0_297
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f2893,f2424,f2311,f373,f2906]) ).

fof(f2906,plain,
    ( spl0_297
  <=> ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f2893,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) )
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_257 ),
    inference(forward_demodulation,[],[f2887,f2313]) ).

fof(f2887,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(identity_relation,X0) )
    | ~ spl0_38
    | ~ spl0_257 ),
    inference(resolution,[],[f2426,f374]) ).

fof(f2426,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_257 ),
    inference(avatar_component_clause,[],[f2424]) ).

fof(f2855,plain,
    ( spl0_233
    | spl0_296
    | ~ spl0_43
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1043,f1005,f394,f2852,f2301]) ).

fof(f1043,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ spl0_43
    | ~ spl0_128 ),
    inference(superposition,[],[f1006,f396]) ).

fof(f2834,plain,
    ( spl0_231
    | spl0_295
    | ~ spl0_41
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1042,f1005,f385,f2831,f2283]) ).

fof(f1042,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | null_class = singleton_relation
    | ~ spl0_41
    | ~ spl0_128 ),
    inference(superposition,[],[f1006,f387]) ).

fof(f2829,plain,
    ( spl0_294
    | ~ spl0_97
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1037,f1005,f732,f2827]) ).

fof(f1037,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) )
    | ~ spl0_97
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f733]) ).

fof(f2825,plain,
    ( spl0_293
    | ~ spl0_103
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1036,f1005,f762,f2823]) ).

fof(f1036,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_128 ),
    inference(resolution,[],[f1006,f763]) ).

fof(f2821,plain,
    ( spl0_292
    | ~ spl0_20
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f978,f920,f288,f2819]) ).

fof(f2819,plain,
    ( spl0_292
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f978,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_20
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f289]) ).

fof(f2817,plain,
    ( spl0_291
    | ~ spl0_38
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f877,f824,f373,f2815]) ).

fof(f877,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_111 ),
    inference(resolution,[],[f825,f374]) ).

fof(f2813,plain,
    ( spl0_290
    | ~ spl0_38
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f846,f803,f373,f2811]) ).

fof(f2811,plain,
    ( spl0_290
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f846,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_38
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f374]) ).

fof(f2750,plain,
    ( spl0_288
    | ~ spl0_289
    | ~ spl0_61
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1413,f1370,f525,f2747,f2744]) ).

fof(f2744,plain,
    ( spl0_288
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f2747,plain,
    ( spl0_289
  <=> subclass(domain_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f1413,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,element_relation)
        | ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) )
    | ~ spl0_61
    | ~ spl0_165 ),
    inference(resolution,[],[f1371,f526]) ).

fof(f2742,plain,
    ( spl0_287
    | ~ spl0_27
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1309,f1291,f320,f2740]) ).

fof(f1309,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1302]) ).

fof(f1302,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_157 ),
    inference(resolution,[],[f1292,f321]) ).

fof(f2738,plain,
    ( spl0_286
    | ~ spl0_76
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1126,f1084,f609,f2736]) ).

fof(f2736,plain,
    ( spl0_286
  <=> ! [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_286])]) ).

fof(f1126,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_134 ),
    inference(superposition,[],[f1085,f611]) ).

fof(f2734,plain,
    ( spl0_285
    | ~ spl0_97
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f982,f920,f732,f2732]) ).

fof(f2732,plain,
    ( spl0_285
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f982,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) )
    | ~ spl0_97
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f733]) ).

fof(f2730,plain,
    ( spl0_284
    | ~ spl0_4
    | ~ spl0_262
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2489,f2457,f2453,f220,f2728]) ).

fof(f2457,plain,
    ( spl0_263
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f2489,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_4
    | ~ spl0_262
    | ~ spl0_263 ),
    inference(forward_demodulation,[],[f2487,f2485]) ).

fof(f2487,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_4
    | ~ spl0_263 ),
    inference(resolution,[],[f2458,f221]) ).

fof(f2458,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2457]) ).

fof(f2726,plain,
    ( spl0_283
    | ~ spl0_103
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f981,f920,f762,f2724]) ).

fof(f2724,plain,
    ( spl0_283
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f981,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) )
    | ~ spl0_103
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f763]) ).

fof(f2714,plain,
    ( spl0_281
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f2713,f2699,f2536,f2705]) ).

fof(f2705,plain,
    ( spl0_281
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f2699,plain,
    ( spl0_280
  <=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f2713,plain,
    ( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(forward_demodulation,[],[f2701,f2538]) ).

fof(f2538,plain,
    ( null_class = subset_relation
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2536]) ).

fof(f2701,plain,
    ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_280 ),
    inference(avatar_component_clause,[],[f2699]) ).

fof(f2712,plain,
    ( spl0_282
    | spl0_280
    | ~ spl0_34
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f862,f816,f348,f2699,f2710]) ).

fof(f2710,plain,
    ( spl0_282
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f348,plain,
    ( spl0_34
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f862,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_34
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f349]) ).

fof(f349,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f2708,plain,
    ( ~ spl0_281
    | ~ spl0_274
    | spl0_280 ),
    inference(avatar_split_clause,[],[f2703,f2699,f2536,f2705]) ).

fof(f2703,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_274
    | spl0_280 ),
    inference(forward_demodulation,[],[f2700,f2538]) ).

fof(f2700,plain,
    ( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_280 ),
    inference(avatar_component_clause,[],[f2699]) ).

fof(f2702,plain,
    ( spl0_279
    | spl0_280
    | ~ spl0_33
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f861,f816,f344,f2699,f2696]) ).

fof(f2696,plain,
    ( spl0_279
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f344,plain,
    ( spl0_33
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f861,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_33
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f345]) ).

fof(f345,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f344]) ).

fof(f2692,plain,
    ( spl0_278
    | ~ spl0_31
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f850,f803,f336,f2690]) ).

fof(f2690,plain,
    ( spl0_278
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f850,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_31
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f337]) ).

fof(f2688,plain,
    ( spl0_277
    | ~ spl0_32
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f849,f803,f340,f2686]) ).

fof(f2686,plain,
    ( spl0_277
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f849,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_32
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f341]) ).

fof(f2561,plain,
    ( spl0_276
    | ~ spl0_4
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1251,f1244,f220,f2559]) ).

fof(f2559,plain,
    ( spl0_276
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f1251,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_151 ),
    inference(resolution,[],[f1245,f221]) ).

fof(f2543,plain,
    ( spl0_274
    | spl0_275
    | ~ spl0_76
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1041,f1005,f609,f2540,f2536]) ).

fof(f2540,plain,
    ( spl0_275
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f1041,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_76
    | ~ spl0_128 ),
    inference(superposition,[],[f1006,f611]) ).

fof(f2532,plain,
    ( spl0_273
    | ~ spl0_20
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f993,f956,f288,f2530]) ).

fof(f2530,plain,
    ( spl0_273
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f993,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_20
    | ~ spl0_124 ),
    inference(resolution,[],[f957,f289]) ).

fof(f2528,plain,
    ( ~ spl0_272
    | spl0_271
    | ~ spl0_25
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f871,f816,f309,f2519,f2525]) ).

fof(f2525,plain,
    ( spl0_272
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f2519,plain,
    ( spl0_271
  <=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f309,plain,
    ( spl0_25
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f871,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_25
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f311]) ).

fof(f311,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f309]) ).

fof(f2522,plain,
    ( ~ spl0_270
    | spl0_271
    | ~ spl0_24
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f869,f816,f304,f2519,f2515]) ).

fof(f2515,plain,
    ( spl0_270
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f869,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_24
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f306]) ).

fof(f306,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f2506,plain,
    ( spl0_269
    | spl0_182
    | ~ spl0_22
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f857,f816,f296,f1539,f2504]) ).

fof(f857,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f297]) ).

fof(f2502,plain,
    ( spl0_268
    | ~ spl0_20
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f851,f803,f288,f2500]) ).

fof(f851,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_20
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f289]) ).

fof(f2498,plain,
    ( ~ spl0_267
    | ~ spl0_111
    | spl0_230 ),
    inference(avatar_split_clause,[],[f2281,f2277,f824,f2495]) ).

fof(f2495,plain,
    ( spl0_267
  <=> member(omega,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2277,plain,
    ( spl0_230
  <=> member(omega,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f2281,plain,
    ( ~ member(omega,subset_relation)
    | ~ spl0_111
    | spl0_230 ),
    inference(resolution,[],[f2278,f825]) ).

fof(f2278,plain,
    ( ~ member(omega,cross_product(universal_class,universal_class))
    | spl0_230 ),
    inference(avatar_component_clause,[],[f2277]) ).

fof(f2493,plain,
    ( spl0_266
    | ~ spl0_72
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f834,f803,f585,f2491]) ).

fof(f2491,plain,
    ( spl0_266
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f834,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_72
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f586]) ).

fof(f2482,plain,
    ( spl0_265
    | ~ spl0_38
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2430,f1539,f373,f2480]) ).

fof(f2430,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_182 ),
    inference(resolution,[],[f1540,f374]) ).

fof(f1540,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f1539]) ).

fof(f2470,plain,
    ( spl0_264
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2252,f2228,f394,f2467]) ).

fof(f2252,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(superposition,[],[f2229,f396]) ).

fof(f2459,plain,
    ( spl0_263
    | ~ spl0_115
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1072,f1013,f916,f2457]) ).

fof(f1072,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_115
    | ~ spl0_130 ),
    inference(duplicate_literal_removal,[],[f1061]) ).

fof(f1061,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_115
    | ~ spl0_130 ),
    inference(resolution,[],[f1014,f917]) ).

fof(f2455,plain,
    ( spl0_262
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f983,f920,f885,f2453]) ).

fof(f983,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(duplicate_literal_removal,[],[f972]) ).

fof(f972,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(resolution,[],[f921,f886]) ).

fof(f2451,plain,
    ( spl0_261
    | ~ spl0_21
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f912,f893,f292,f2449]) ).

fof(f2449,plain,
    ( spl0_261
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f292,plain,
    ( spl0_21
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f912,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_114 ),
    inference(resolution,[],[f894,f293]) ).

fof(f293,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f292]) ).

fof(f2447,plain,
    ( ~ spl0_259
    | spl0_260
    | ~ spl0_6
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f907,f893,f229,f2444,f2440]) ).

fof(f2440,plain,
    ( spl0_259
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f2444,plain,
    ( spl0_260
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f907,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_114 ),
    inference(resolution,[],[f894,f230]) ).

fof(f2436,plain,
    ( ~ spl0_258
    | ~ spl0_111
    | spl0_257 ),
    inference(avatar_split_clause,[],[f2431,f2424,f824,f2433]) ).

fof(f2433,plain,
    ( spl0_258
  <=> member(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f2431,plain,
    ( ~ member(identity_relation,subset_relation)
    | ~ spl0_111
    | spl0_257 ),
    inference(resolution,[],[f2425,f825]) ).

fof(f2427,plain,
    ( spl0_257
    | ~ spl0_182
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2422,f2301,f1539,f2424]) ).

fof(f2422,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_182
    | ~ spl0_233 ),
    inference(forward_demodulation,[],[f1540,f2303]) ).

fof(f2417,plain,
    ( spl0_256
    | spl0_182
    | ~ spl0_18
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f868,f816,f280,f1539,f2415]) ).

fof(f2415,plain,
    ( spl0_256
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f280,plain,
    ( spl0_18
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f868,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f281]) ).

fof(f281,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f280]) ).

fof(f2413,plain,
    ( spl0_254
    | ~ spl0_255
    | ~ spl0_97
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f854,f803,f732,f2410,f2407]) ).

fof(f2407,plain,
    ( spl0_254
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f2410,plain,
    ( spl0_255
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f854,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f733]) ).

fof(f2405,plain,
    ( spl0_252
    | ~ spl0_253
    | ~ spl0_103
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f853,f803,f762,f2402,f2399]) ).

fof(f2399,plain,
    ( spl0_252
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f2402,plain,
    ( spl0_253
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f853,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f763]) ).

fof(f2397,plain,
    ( spl0_251
    | ~ spl0_41
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2251,f2228,f385,f2394]) ).

fof(f2251,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_41
    | ~ spl0_224 ),
    inference(superposition,[],[f2229,f387]) ).

fof(f2392,plain,
    ( spl0_249
    | ~ spl0_250
    | ~ spl0_87
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f838,f803,f674,f2389,f2386]) ).

fof(f2386,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f2389,plain,
    ( spl0_250
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f838,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_87
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f675]) ).

fof(f2384,plain,
    ( spl0_248
    | ~ spl0_67
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f828,f803,f557,f2382]) ).

fof(f2382,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f828,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f558]) ).

fof(f2380,plain,
    ( spl0_247
    | ~ spl0_68
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f827,f803,f561,f2378]) ).

fof(f2378,plain,
    ( spl0_247
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f827,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f562]) ).

fof(f2375,plain,
    ( spl0_245
    | ~ spl0_246
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f783,f390,f381,f2372,f2369]) ).

fof(f2369,plain,
    ( spl0_245
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f2372,plain,
    ( spl0_246
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f390,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f783,plain,
    ( ! [X0] :
        ( ~ inductive(null_class)
        | member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(superposition,[],[f391,f382]) ).

fof(f391,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(null_class,X0) )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f390]) ).

fof(f2367,plain,
    ( spl0_244
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f775,f762,f320,f2365]) ).

fof(f775,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(resolution,[],[f763,f321]) ).

fof(f2363,plain,
    ( spl0_243
    | ~ spl0_27
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f771,f732,f320,f2361]) ).

fof(f771,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_27
    | ~ spl0_97 ),
    inference(resolution,[],[f733,f321]) ).

fof(f2359,plain,
    ( spl0_242
    | ~ spl0_37
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f538,f512,f360,f2357]) ).

fof(f2357,plain,
    ( spl0_242
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f360,plain,
    ( spl0_37
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f512,plain,
    ( spl0_59
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f538,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_37
    | ~ spl0_59 ),
    inference(resolution,[],[f513,f361]) ).

fof(f361,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f360]) ).

fof(f513,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f512]) ).

fof(f2355,plain,
    ( ~ spl0_241
    | spl0_182
    | ~ spl0_14
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f870,f816,f263,f1539,f2352]) ).

fof(f2352,plain,
    ( spl0_241
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f870,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_14
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f265]) ).

fof(f265,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f263]) ).

fof(f2350,plain,
    ( ~ spl0_240
    | spl0_182
    | ~ spl0_11
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f863,f816,f250,f1539,f2347]) ).

fof(f2347,plain,
    ( spl0_240
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f250,plain,
    ( spl0_11
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f863,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_11
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f252]) ).

fof(f252,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f2345,plain,
    ( spl0_238
    | ~ spl0_239
    | ~ spl0_86
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f837,f803,f670,f2342,f2339]) ).

fof(f2339,plain,
    ( spl0_238
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2342,plain,
    ( spl0_239
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f837,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_86
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f671]) ).

fof(f2337,plain,
    ( spl0_236
    | ~ spl0_237
    | ~ spl0_64
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f835,f803,f540,f2334,f2331]) ).

fof(f2331,plain,
    ( spl0_236
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f2334,plain,
    ( spl0_237
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f835,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_64
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f541]) ).

fof(f2314,plain,
    ( spl0_235
    | ~ spl0_231
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2309,f2301,f2283,f2311]) ).

fof(f2309,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_231
    | ~ spl0_233 ),
    inference(forward_demodulation,[],[f2303,f2285]) ).

fof(f2308,plain,
    ( spl0_233
    | spl0_234
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f778,f762,f300,f2305,f2301]) ).

fof(f778,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(resolution,[],[f763,f301]) ).

fof(f2290,plain,
    ( spl0_231
    | spl0_232
    | ~ spl0_23
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f774,f732,f300,f2287,f2283]) ).

fof(f2287,plain,
    ( spl0_232
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f774,plain,
    ( member(regular(singleton_relation),element_relation)
    | null_class = singleton_relation
    | ~ spl0_23
    | ~ spl0_97 ),
    inference(resolution,[],[f733,f301]) ).

fof(f2280,plain,
    ( ~ spl0_229
    | spl0_230
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f767,f440,f296,f2277,f2273]) ).

fof(f2273,plain,
    ( spl0_229
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f440,plain,
    ( spl0_47
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f767,plain,
    ( member(omega,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(resolution,[],[f441,f297]) ).

fof(f441,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f2268,plain,
    ( spl0_228
    | ~ spl0_38
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f2172,f637,f373,f2266]) ).

fof(f2172,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_80 ),
    inference(resolution,[],[f638,f374]) ).

fof(f638,plain,
    ( member(null_class,universal_class)
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f637]) ).

fof(f2264,plain,
    ( spl0_227
    | ~ spl0_18
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f913,f893,f280,f2262]) ).

fof(f2262,plain,
    ( spl0_227
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f913,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_114 ),
    inference(resolution,[],[f894,f281]) ).

fof(f2260,plain,
    ( spl0_225
    | ~ spl0_226
    | ~ spl0_61
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f830,f803,f525,f2257,f2254]) ).

fof(f2254,plain,
    ( spl0_225
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2257,plain,
    ( spl0_226
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f830,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_61
    | ~ spl0_106 ),
    inference(resolution,[],[f804,f526]) ).

fof(f2230,plain,
    ( spl0_224
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1147,f1088,f324,f2228]) ).

fof(f1147,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(duplicate_literal_removal,[],[f1130]) ).

fof(f1130,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(resolution,[],[f1089,f325]) ).

fof(f2226,plain,
    ( spl0_223
    | ~ spl0_28
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1129,f1084,f324,f2224]) ).

fof(f1129,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_28
    | ~ spl0_134 ),
    inference(duplicate_literal_removal,[],[f1112]) ).

fof(f1112,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_28
    | ~ spl0_134 ),
    inference(resolution,[],[f1085,f325]) ).

fof(f2142,plain,
    ( ~ spl0_1
    | ~ spl0_222 ),
    inference(avatar_contradiction_clause,[],[f2141]) ).

fof(f2141,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_222 ),
    inference(resolution,[],[f2139,f207]) ).

fof(f207,plain,
    ( inductive(omega)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f205]) ).

fof(f2139,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f2138]) ).

fof(f2138,plain,
    ( spl0_222
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f2140,plain,
    ( spl0_222
    | spl0_80
    | ~ spl0_4
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f855,f816,f220,f637,f2138]) ).

fof(f855,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_4
    | ~ spl0_109 ),
    inference(resolution,[],[f817,f221]) ).

fof(f2127,plain,
    ( spl0_221
    | ~ spl0_90
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f707,f703,f687,f2125]) ).

fof(f2125,plain,
    ( spl0_221
  <=> ! [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_221])]) ).

fof(f707,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_90
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f688]) ).

fof(f2123,plain,
    ( spl0_220
    | ~ spl0_50
    | ~ spl0_90
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f756,f751,f687,f453,f2121]) ).

fof(f2121,plain,
    ( spl0_220
  <=> ! [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_220])]) ).

fof(f751,plain,
    ( spl0_101
  <=> ! [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_101])]) ).

fof(f756,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_50
    | ~ spl0_90
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f754,f454]) ).

fof(f754,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_90
    | ~ spl0_101 ),
    inference(resolution,[],[f752,f688]) ).

fof(f752,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_101 ),
    inference(avatar_component_clause,[],[f751]) ).

fof(f2113,plain,
    ( spl0_219
    | ~ spl0_70
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f755,f751,f569,f2111]) ).

fof(f2111,plain,
    ( spl0_219
  <=> ! [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_219])]) ).

fof(f755,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_70
    | ~ spl0_101 ),
    inference(resolution,[],[f752,f570]) ).

fof(f2100,plain,
    ( spl0_218
    | ~ spl0_84
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f710,f703,f655,f2098]) ).

fof(f2098,plain,
    ( spl0_218
  <=> ! [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_218])]) ).

fof(f710,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_84
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f656]) ).

fof(f2096,plain,
    ( spl0_217
    | ~ spl0_79
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f660,f655,f629,f2094]) ).

fof(f2094,plain,
    ( spl0_217
  <=> ! [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_217])]) ).

fof(f660,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_79
    | ~ spl0_84 ),
    inference(resolution,[],[f656,f630]) ).

fof(f2083,plain,
    ( spl0_216
    | ~ spl0_27
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f708,f703,f320,f2081]) ).

fof(f708,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_27
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f321]) ).

fof(f2070,plain,
    ( spl0_215
    | ~ spl0_23
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f711,f703,f300,f2068]) ).

fof(f711,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_93 ),
    inference(resolution,[],[f704,f301]) ).

fof(f2059,plain,
    ( ~ spl0_214
    | spl0_192
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f776,f762,f255,f1614,f2056]) ).

fof(f2056,plain,
    ( spl0_214
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f776,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(resolution,[],[f763,f256]) ).

fof(f2054,plain,
    ( spl0_213
    | ~ spl0_77
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f749,f746,f614,f2052]) ).

fof(f749,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class)))))))))),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(cross_product(unordered_pair(X0,X0),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(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) )
    | ~ spl0_77
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f615]) ).

fof(f2001,plain,
    ( spl0_212
    | ~ spl0_77
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f744,f740,f614,f1999]) ).

fof(f744,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_77
    | ~ spl0_99 ),
    inference(resolution,[],[f741,f615]) ).

fof(f1997,plain,
    ( spl0_211
    | ~ spl0_77
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f743,f736,f614,f1995]) ).

fof(f743,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_77
    | ~ spl0_98 ),
    inference(resolution,[],[f737,f615]) ).

fof(f1948,plain,
    ( spl0_210
    | ~ spl0_77
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f632,f629,f614,f1946]) ).

fof(f1946,plain,
    ( spl0_210
  <=> ! [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_210])]) ).

fof(f632,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_77
    | ~ spl0_79 ),
    inference(resolution,[],[f630,f615]) ).

fof(f1938,plain,
    ( spl0_209
    | ~ spl0_40
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f716,f703,f381,f1936]) ).

fof(f716,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_40
    | ~ spl0_93 ),
    inference(superposition,[],[f704,f382]) ).

fof(f1926,plain,
    ( spl0_208
    | ~ spl0_70
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f706,f703,f569,f1924]) ).

fof(f706,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_70
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f570]) ).

fof(f1916,plain,
    ( spl0_207
    | ~ spl0_48
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f659,f655,f445,f1914]) ).

fof(f659,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_48
    | ~ spl0_84 ),
    inference(resolution,[],[f656,f446]) ).

fof(f1909,plain,
    ( spl0_206
    | ~ spl0_40
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f713,f703,f381,f1907]) ).

fof(f713,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_40
    | ~ spl0_93 ),
    inference(superposition,[],[f704,f382]) ).

fof(f1871,plain,
    ( spl0_205
    | ~ spl0_38
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f701,f697,f373,f1869]) ).

fof(f697,plain,
    ( spl0_92
  <=> ! [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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f701,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
    | ~ spl0_38
    | ~ spl0_92 ),
    inference(resolution,[],[f698,f374]) ).

fof(f698,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f697]) ).

fof(f1815,plain,
    ( spl0_204
    | ~ spl0_50
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f715,f703,f453,f1813]) ).

fof(f715,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_50
    | ~ spl0_93 ),
    inference(superposition,[],[f704,f454]) ).

fof(f1811,plain,
    ( ~ spl0_203
    | ~ spl0_12
    | spl0_192 ),
    inference(avatar_split_clause,[],[f1708,f1614,f255,f1808]) ).

fof(f1808,plain,
    ( spl0_203
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1708,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_12
    | spl0_192 ),
    inference(resolution,[],[f1616,f256]) ).

fof(f1616,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_192 ),
    inference(avatar_component_clause,[],[f1614]) ).

fof(f1806,plain,
    ( spl0_202
    | ~ spl0_50
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f712,f703,f453,f1804]) ).

fof(f712,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_50
    | ~ spl0_93 ),
    inference(superposition,[],[f704,f454]) ).

fof(f1796,plain,
    ( spl0_201
    | ~ spl0_12
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f709,f703,f255,f1794]) ).

fof(f709,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_12
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f256]) ).

fof(f1776,plain,
    ( spl0_200
    | ~ spl0_27
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f635,f629,f320,f1774]) ).

fof(f635,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_27
    | ~ spl0_79 ),
    inference(resolution,[],[f630,f321]) ).

fof(f1748,plain,
    ( spl0_199
    | ~ spl0_38
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f690,f687,f373,f1746]) ).

fof(f690,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_38
    | ~ spl0_90 ),
    inference(resolution,[],[f688,f374]) ).

fof(f1714,plain,
    ( spl0_198
    | ~ spl0_23
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f634,f629,f300,f1712]) ).

fof(f634,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_79 ),
    inference(resolution,[],[f630,f301]) ).

fof(f1707,plain,
    ( spl0_197
    | ~ spl0_77
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f722,f719,f614,f1705]) ).

fof(f722,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_77
    | ~ spl0_94 ),
    inference(resolution,[],[f720,f615]) ).

fof(f1663,plain,
    ( spl0_196
    | ~ spl0_31
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f662,f655,f336,f1661]) ).

fof(f662,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_31
    | ~ spl0_84 ),
    inference(resolution,[],[f656,f337]) ).

fof(f1659,plain,
    ( spl0_195
    | ~ spl0_32
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f661,f655,f340,f1657]) ).

fof(f661,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_32
    | ~ spl0_84 ),
    inference(resolution,[],[f656,f341]) ).

fof(f1642,plain,
    ( spl0_194
    | ~ spl0_20
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f663,f655,f288,f1640]) ).

fof(f663,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_84 ),
    inference(resolution,[],[f656,f289]) ).

fof(f1623,plain,
    ( spl0_193
    | ~ spl0_38
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f658,f655,f373,f1621]) ).

fof(f658,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_38
    | ~ spl0_84 ),
    inference(resolution,[],[f656,f374]) ).

fof(f1617,plain,
    ( ~ spl0_192
    | ~ spl0_111
    | spl0_182 ),
    inference(avatar_split_clause,[],[f1547,f1539,f824,f1614]) ).

fof(f1547,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_111
    | spl0_182 ),
    inference(resolution,[],[f1541,f825]) ).

fof(f1541,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_182 ),
    inference(avatar_component_clause,[],[f1539]) ).

fof(f1612,plain,
    ( spl0_191
    | ~ spl0_39
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f536,f533,f377,f1610]) ).

fof(f536,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_39
    | ~ spl0_63 ),
    inference(resolution,[],[f534,f378]) ).

fof(f1600,plain,
    ( ~ spl0_188
    | ~ spl0_189
    | spl0_190
    | ~ spl0_73
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f617,f609,f589,f1597,f1593,f1589]) ).

fof(f1589,plain,
    ( spl0_188
  <=> 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_188])]) ).

fof(f1593,plain,
    ( spl0_189
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1597,plain,
    ( spl0_190
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f589,plain,
    ( spl0_73
  <=> ! [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_73])]) ).

fof(f617,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_73
    | ~ spl0_76 ),
    inference(superposition,[],[f590,f611]) ).

fof(f590,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_73 ),
    inference(avatar_component_clause,[],[f589]) ).

fof(f1587,plain,
    ( spl0_187
    | ~ spl0_28
    | ~ spl0_50
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f583,f569,f453,f324,f1585]) ).

fof(f583,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_28
    | ~ spl0_50
    | ~ spl0_70 ),
    inference(forward_demodulation,[],[f582,f454]) ).

fof(f582,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_28
    | ~ spl0_70 ),
    inference(resolution,[],[f570,f325]) ).

fof(f1581,plain,
    ( spl0_186
    | ~ spl0_77
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f681,f678,f614,f1579]) ).

fof(f681,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_88 ),
    inference(resolution,[],[f679,f615]) ).

fof(f1559,plain,
    ( spl0_185
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f618,f609,f449,f1557]) ).

fof(f618,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_49
    | ~ spl0_76 ),
    inference(superposition,[],[f450,f611]) ).

fof(f1552,plain,
    ( spl0_184
    | ~ spl0_38
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f623,f614,f373,f1550]) ).

fof(f623,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_38
    | ~ spl0_77 ),
    inference(resolution,[],[f615,f374]) ).

fof(f1546,plain,
    ( ~ spl0_181
    | ~ spl0_182
    | spl0_183
    | ~ spl0_22
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f607,f597,f296,f1543,f1539,f1535]) ).

fof(f1535,plain,
    ( spl0_181
  <=> 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_181])]) ).

fof(f1543,plain,
    ( spl0_183
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f597,plain,
    ( spl0_75
  <=> ! [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_75])]) ).

fof(f607,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_75 ),
    inference(resolution,[],[f598,f297]) ).

fof(f598,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_75 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f1533,plain,
    ( spl0_180
    | ~ spl0_39
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f515,f504,f377,f1531]) ).

fof(f1531,plain,
    ( spl0_180
  <=> ! [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_180])]) ).

fof(f515,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_39
    | ~ spl0_57 ),
    inference(resolution,[],[f505,f378]) ).

fof(f1526,plain,
    ( spl0_178
    | spl0_179
    | ~ spl0_40
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f602,f589,f381,f1523,f1520]) ).

fof(f1520,plain,
    ( spl0_178
  <=> ! [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_178])]) ).

fof(f602,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_40
    | ~ spl0_73 ),
    inference(superposition,[],[f590,f382]) ).

fof(f1518,plain,
    ( spl0_177
    | ~ spl0_63
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f548,f544,f533,f1516]) ).

fof(f1516,plain,
    ( spl0_177
  <=> ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f544,plain,
    ( spl0_65
  <=> ! [X1,X8] :
        ( ~ function(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | maps(X8,domain_of(X8),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f548,plain,
    ( ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) )
    | ~ spl0_63
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f534]) ).

fof(f545,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f544]) ).

fof(f1480,plain,
    ( spl0_176
    | ~ spl0_77
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f668,f665,f614,f1478]) ).

fof(f668,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_77
    | ~ spl0_85 ),
    inference(resolution,[],[f666,f615]) ).

fof(f1476,plain,
    ( ~ spl0_174
    | spl0_175
    | ~ spl0_14
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f914,f893,f263,f1473,f1469]) ).

fof(f1469,plain,
    ( spl0_174
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f1473,plain,
    ( spl0_175
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f914,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_14
    | ~ spl0_114 ),
    inference(resolution,[],[f894,f265]) ).

fof(f1467,plain,
    ( spl0_172
    | spl0_173
    | ~ spl0_12
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f633,f629,f255,f1464,f1461]) ).

fof(f1461,plain,
    ( spl0_172
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1464,plain,
    ( spl0_173
  <=> 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_173])]) ).

fof(f633,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_12
    | ~ spl0_79 ),
    inference(resolution,[],[f630,f256]) ).

fof(f1459,plain,
    ( spl0_171
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f604,f593,f373,f1457]) ).

fof(f593,plain,
    ( spl0_74
  <=> ! [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_74])]) ).

fof(f604,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_38
    | ~ spl0_74 ),
    inference(resolution,[],[f594,f374]) ).

fof(f594,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_74 ),
    inference(avatar_component_clause,[],[f593]) ).

fof(f1455,plain,
    ( spl0_170
    | ~ spl0_38
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f600,f589,f373,f1453]) ).

fof(f600,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_38
    | ~ spl0_73 ),
    inference(resolution,[],[f590,f374]) ).

fof(f1451,plain,
    ( spl0_169
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f495,f461,f377,f1449]) ).

fof(f1449,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

fof(f495,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_39
    | ~ spl0_52 ),
    inference(resolution,[],[f462,f378]) ).

fof(f1447,plain,
    ( spl0_168
    | ~ spl0_39
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f494,f457,f377,f1445]) ).

fof(f1445,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

fof(f494,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_39
    | ~ spl0_51 ),
    inference(resolution,[],[f458,f378]) ).

fof(f1380,plain,
    ( spl0_167
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f649,f646,f1378]) ).

fof(f646,plain,
    ( spl0_82
  <=> ! [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_82])]) ).

fof(f649,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_82 ),
    inference(equality_resolution,[],[f647]) ).

fof(f647,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_82 ),
    inference(avatar_component_clause,[],[f646]) ).

fof(f1376,plain,
    ( spl0_166
    | ~ spl0_38
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f581,f569,f373,f1374]) ).

fof(f581,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_38
    | ~ spl0_70 ),
    inference(resolution,[],[f570,f374]) ).

fof(f1372,plain,
    ( spl0_165
    | ~ spl0_38
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f573,f553,f373,f1370]) ).

fof(f573,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
    | ~ spl0_38
    | ~ spl0_66 ),
    inference(resolution,[],[f554,f374]) ).

fof(f1368,plain,
    ( spl0_164
    | ~ spl0_28
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f484,f449,f324,f1366]) ).

fof(f484,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_28
    | ~ spl0_49 ),
    inference(resolution,[],[f450,f325]) ).

fof(f1364,plain,
    ( spl0_163
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f476,f445,f320,f1362]) ).

fof(f476,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_27
    | ~ spl0_48 ),
    inference(resolution,[],[f446,f321]) ).

fof(f1354,plain,
    ( spl0_162
    | ~ spl0_32
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f619,f609,f340,f1352]) ).

fof(f619,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_32
    | ~ spl0_76 ),
    inference(superposition,[],[f341,f611]) ).

fof(f1323,plain,
    ( spl0_161
    | ~ spl0_50
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f601,f589,f453,f1321]) ).

fof(f601,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_50
    | ~ spl0_73 ),
    inference(superposition,[],[f590,f454]) ).

fof(f1319,plain,
    ( spl0_160
    | ~ spl0_23
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f475,f445,f300,f1317]) ).

fof(f475,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_48 ),
    inference(resolution,[],[f446,f301]) ).

fof(f1301,plain,
    ( spl0_159
    | ~ spl0_22
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f551,f544,f296,f1299]) ).

fof(f1299,plain,
    ( spl0_159
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f551,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_22
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f297]) ).

fof(f1297,plain,
    ( spl0_158
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f523,f517,f381,f1295]) ).

fof(f517,plain,
    ( spl0_60
  <=> ! [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_60])]) ).

fof(f523,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_40
    | ~ spl0_60 ),
    inference(trivial_inequality_removal,[],[f521]) ).

fof(f521,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_40
    | ~ spl0_60 ),
    inference(superposition,[],[f518,f382]) ).

fof(f518,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f517]) ).

fof(f1293,plain,
    ( spl0_157
    | ~ spl0_28
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f438,f425,f324,f1291]) ).

fof(f438,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_28
    | ~ spl0_44 ),
    inference(resolution,[],[f426,f325]) ).

fof(f1289,plain,
    ( ~ spl0_155
    | spl0_156
    | ~ spl0_11
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f910,f893,f250,f1286,f1282]) ).

fof(f1282,plain,
    ( spl0_155
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1286,plain,
    ( spl0_156
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f910,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_11
    | ~ spl0_114 ),
    inference(resolution,[],[f894,f252]) ).

fof(f1280,plain,
    ( spl0_154
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f410,f377,f348,f1278]) ).

fof(f410,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_34
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f349]) ).

fof(f1276,plain,
    ( spl0_153
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f409,f377,f344,f1274]) ).

fof(f409,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_33
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f345]) ).

fof(f1250,plain,
    ( spl0_152
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f498,f469,f373,f1248]) ).

fof(f469,plain,
    ( spl0_54
  <=> ! [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_54])]) ).

fof(f498,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(resolution,[],[f470,f374]) ).

fof(f470,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f469]) ).

fof(f1246,plain,
    ( spl0_151
    | ~ spl0_38
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f483,f449,f373,f1244]) ).

fof(f483,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_38
    | ~ spl0_49 ),
    inference(resolution,[],[f450,f374]) ).

fof(f1242,plain,
    ( spl0_149
    | ~ spl0_150
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f417,f377,f309,f1239,f1235]) ).

fof(f1235,plain,
    ( spl0_149
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f417,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f311]) ).

fof(f1233,plain,
    ( spl0_147
    | ~ spl0_148
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f415,f377,f304,f1230,f1226]) ).

fof(f1226,plain,
    ( spl0_147
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f415,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f306]) ).

fof(f1224,plain,
    ( spl0_146
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f413,f377,f292,f1222]) ).

fof(f413,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_39 ),
    inference(resolution,[],[f378,f293]) ).

fof(f1174,plain,
    ( spl0_145
    | ~ spl0_50
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f520,f517,f453,f1172]) ).

fof(f520,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_50
    | ~ spl0_60 ),
    inference(superposition,[],[f518,f454]) ).

fof(f1170,plain,
    ( spl0_144
    | ~ spl0_43
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f487,f449,f394,f1168]) ).

fof(f487,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_49 ),
    inference(superposition,[],[f450,f396]) ).

fof(f1166,plain,
    ( spl0_143
    | ~ spl0_41
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f486,f449,f385,f1164]) ).

fof(f486,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_41
    | ~ spl0_49 ),
    inference(superposition,[],[f450,f387]) ).

fof(f1162,plain,
    ( spl0_142
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f485,f449,f381,f1160]) ).

fof(f485,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(superposition,[],[f450,f382]) ).

fof(f1158,plain,
    ( spl0_141
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f437,f425,f373,f1156]) ).

fof(f437,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(resolution,[],[f426,f374]) ).

fof(f1111,plain,
    ( spl0_140
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f550,f544,f229,f1109]) ).

fof(f1109,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f550,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f230]) ).

fof(f1107,plain,
    ( ~ spl0_138
    | spl0_139
    | ~ spl0_10
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f908,f893,f245,f1104,f1100]) ).

fof(f1100,plain,
    ( spl0_138
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1104,plain,
    ( spl0_139
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f245,plain,
    ( spl0_10
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f908,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_10
    | ~ spl0_114 ),
    inference(resolution,[],[f894,f247]) ).

fof(f247,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f1098,plain,
    ( spl0_137
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f414,f377,f280,f1096]) ).

fof(f414,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f281]) ).

fof(f1094,plain,
    ( spl0_136
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f407,f377,f296,f1092]) ).

fof(f407,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f297]) ).

fof(f1090,plain,
    ( spl0_135
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f371,f340,f320,f1088]) ).

fof(f371,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(resolution,[],[f341,f321]) ).

fof(f1086,plain,
    ( spl0_134
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f368,f336,f320,f1084]) ).

fof(f368,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(resolution,[],[f337,f321]) ).

fof(f1027,plain,
    ( spl0_133
    | ~ spl0_57
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f547,f544,f504,f1025]) ).

fof(f1025,plain,
    ( spl0_133
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f547,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_57
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f505]) ).

fof(f1023,plain,
    ( spl0_132
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f404,f373,f332,f1021]) ).

fof(f404,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f333]) ).

fof(f1019,plain,
    ( spl0_131
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f403,f373,f328,f1017]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f329]) ).

fof(f1015,plain,
    ( spl0_130
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f402,f373,f320,f1013]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f321]) ).

fof(f1011,plain,
    ( spl0_129
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f370,f340,f300,f1009]) ).

fof(f370,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(resolution,[],[f341,f301]) ).

fof(f1007,plain,
    ( spl0_128
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f367,f336,f300,f1005]) ).

fof(f367,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(resolution,[],[f337,f301]) ).

fof(f988,plain,
    ( ~ spl0_127
    | ~ spl0_12
    | spl0_108 ),
    inference(avatar_split_clause,[],[f941,f811,f255,f985]) ).

fof(f985,plain,
    ( spl0_127
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f811,plain,
    ( spl0_108
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f941,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_12
    | spl0_108 ),
    inference(resolution,[],[f812,f256]) ).

fof(f812,plain,
    ( ~ member(null_class,element_relation)
    | spl0_108 ),
    inference(avatar_component_clause,[],[f811]) ).

fof(f966,plain,
    ( spl0_126
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f474,f445,f255,f964]) ).

fof(f474,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(resolution,[],[f446,f256]) ).

fof(f962,plain,
    ( spl0_125
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f423,f394,f336,f960]) ).

fof(f423,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(superposition,[],[f337,f396]) ).

fof(f958,plain,
    ( spl0_124
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f421,f385,f336,f956]) ).

fof(f421,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(superposition,[],[f337,f387]) ).

fof(f954,plain,
    ( spl0_123
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f418,f381,f340,f952]) ).

fof(f418,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(superposition,[],[f341,f382]) ).

fof(f950,plain,
    ( spl0_121
    | ~ spl0_122
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f416,f377,f263,f947,f943]) ).

fof(f943,plain,
    ( spl0_121
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f416,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f265]) ).

fof(f940,plain,
    ( spl0_119
    | ~ spl0_120
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f411,f377,f250,f937,f933]) ).

fof(f933,plain,
    ( spl0_119
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f411,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f252]) ).

fof(f931,plain,
    ( spl0_117
    | ~ spl0_118
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f408,f377,f245,f928,f924]) ).

fof(f924,plain,
    ( spl0_117
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f408,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f247]) ).

fof(f922,plain,
    ( spl0_116
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f401,f373,f300,f920]) ).

fof(f401,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f301]) ).

fof(f918,plain,
    ( spl0_115
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f363,f320,f288,f916]) ).

fof(f363,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(resolution,[],[f321,f289]) ).

fof(f895,plain,
    ( spl0_114
    | ~ spl0_51
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f580,f565,f457,f893]) ).

fof(f565,plain,
    ( spl0_69
  <=> ! [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_69])]) ).

fof(f580,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_69 ),
    inference(resolution,[],[f566,f458]) ).

fof(f566,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_69 ),
    inference(avatar_component_clause,[],[f565]) ).

fof(f891,plain,
    ( spl0_113
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f419,f381,f336,f889]) ).

fof(f419,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(superposition,[],[f337,f382]) ).

fof(f887,plain,
    ( spl0_112
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f318,f300,f288,f885]) ).

fof(f318,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(resolution,[],[f301,f289]) ).

fof(f826,plain,
    ( spl0_111
    | ~ spl0_31
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f620,f609,f336,f824]) ).

fof(f620,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_31
    | ~ spl0_76 ),
    inference(superposition,[],[f337,f611]) ).

fof(f822,plain,
    ( spl0_110
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f412,f377,f259,f820]) ).

fof(f259,plain,
    ( spl0_13
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f412,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f260]) ).

fof(f260,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f259]) ).

fof(f818,plain,
    ( spl0_109
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f400,f373,f255,f816]) ).

fof(f400,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f256]) ).

fof(f814,plain,
    ( ~ spl0_107
    | spl0_108
    | ~ spl0_12
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f772,f732,f255,f811,f807]) ).

fof(f807,plain,
    ( spl0_107
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f772,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_12
    | ~ spl0_97 ),
    inference(resolution,[],[f733,f256]) ).

fof(f805,plain,
    ( spl0_106
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f399,f373,f241,f803]) ).

fof(f399,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f242]) ).

fof(f792,plain,
    ( spl0_105
    | ~ spl0_4
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f549,f544,f220,f790]) ).

fof(f790,plain,
    ( spl0_105
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f549,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_4
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f221]) ).

fof(f782,plain,
    ( spl0_104
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f369,f340,f255,f780]) ).

fof(f780,plain,
    ( spl0_104
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f369,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(resolution,[],[f341,f256]) ).

fof(f764,plain,
    ( spl0_103
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f422,f394,f340,f762]) ).

fof(f422,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f341,f396]) ).

fof(f760,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f203,f758]) ).

fof(f758,plain,
    ( spl0_102
  <=> ! [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_102])]) ).

fof(f203,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,[],[f202,f129]) ).

fof(f129,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(f202,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,[],[f201,f129]) ).

fof(f201,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,[],[f200,f129]) ).

fof(f200,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,[],[f199,f129]) ).

fof(f199,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,[],[f198,f129]) ).

fof(f198,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,[],[f197,f129]) ).

fof(f197,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,[],[f196,f129]) ).

fof(f196,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,[],[f195,f129]) ).

fof(f195,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,[],[f194,f129]) ).

fof(f194,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,[],[f176,f129]) ).

fof(f176,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,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f118,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(f117,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,f114,f116,f12]) ).

fof(f116,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,f115,f29]) ).

fof(f115,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(f114,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(f753,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f193,f751]) ).

fof(f193,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,[],[f192,f129]) ).

fof(f192,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,[],[f191,f129]) ).

fof(f191,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,[],[f190,f129]) ).

fof(f190,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,[],[f189,f129]) ).

fof(f189,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,[],[f168,f129]) ).

fof(f168,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,f118,f117,f118,f117,f117,f117,f117,f118]) ).

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(f748,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f188,f746]) ).

fof(f188,plain,
    ! [X0,X1,X4] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class)))))))))),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(cross_product(unordered_pair(X1,X1),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(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
      | ~ member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(forward_demodulation,[],[f167,f129]) ).

fof(f167,plain,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,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),X0),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),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,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),X0),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),X0),universal_class))))),element_relation)))))))),application_function)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(definition_unfolding,[],[f108,f118,f118,f117,f118,f118]) ).

fof(f108,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).

fof(f742,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f172,f740]) ).

fof(f172,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,f118,f118,f118,f118,f118,f118]) ).

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(f738,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f171,f736]) ).

fof(f171,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,f118,f118,f118,f118,f118,f118]) ).

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(f734,plain,
    ( spl0_97
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f420,f385,f340,f732]) ).

fof(f420,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(superposition,[],[f341,f387]) ).

fof(f730,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f156,f728]) ).

fof(f156,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,f118,f118,f118,f118]) ).

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(f726,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f155,f724]) ).

fof(f155,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,f118,f118,f118,f118]) ).

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(f721,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f179,f719]) ).

fof(f179,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,[],[f166]) ).

fof(f166,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,f124,f118,f118]) ).

fof(f124,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(f705,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f170,f703]) ).

fof(f170,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,f118,f118,f116,f116,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(f699,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f153,f697]) ).

fof(f153,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(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
    inference(definition_unfolding,[],[f97,f118,f118,f118]) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).

fof(f694,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f184,f692]) ).

fof(f184,plain,
    ! [X0,X1,X4] :
      ( 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),X0),universal_class))))))) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(forward_demodulation,[],[f150,f129]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f107,f117,f118,f118]) ).

fof(f107,axiom,
    ! [X0,X1,X4] :
      ( apply(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).

fof(f689,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f175,f687]) ).

fof(f175,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,f118]) ).

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(f685,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f154,f683]) ).

fof(f154,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,f118,f116,f116,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(f680,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f180,f678]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f169]) ).

fof(f169,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f94,f118,f118]) ).

fof(f94,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(ordered_pair(X1,X4),compose_class(X0))
      | ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).

fof(f676,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f152,f674]) ).

fof(f152,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
    inference(definition_unfolding,[],[f96,f118,f118]) ).

fof(f96,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).

fof(f672,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f148,f670]) ).

fof(f148,plain,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f106,f118,f118]) ).

fof(f106,axiom,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).

fof(f667,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f163,f665]) ).

fof(f163,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,f118,f118]) ).

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(f657,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f187,f655]) ).

fof(f187,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,[],[f186,f129]) ).

fof(f186,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,[],[f164,f129]) ).

fof(f164,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,f117]) ).

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(f653,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f173,f651]) ).

fof(f651,plain,
    ( spl0_83
  <=> ! [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_83])]) ).

fof(f173,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,f115]) ).

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(f648,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f174,f646]) ).

fof(f174,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,f115]) ).

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(f644,plain,
    ( ~ spl0_80
    | spl0_81
    | ~ spl0_4
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f606,f597,f220,f641,f637]) ).

fof(f641,plain,
    ( spl0_81
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f606,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_4
    | ~ spl0_75 ),
    inference(resolution,[],[f598,f221]) ).

fof(f631,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f149,f629]) ).

fof(f149,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,f118]) ).

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(f627,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f146,f625]) ).

fof(f146,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,f124,f118]) ).

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(f616,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f162,f614]) ).

fof(f162,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,f118]) ).

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(f612,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f130,f609]) ).

fof(f130,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(f599,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f185,f597]) ).

fof(f185,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,[],[f160,f129]) ).

fof(f160,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,f116]) ).

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(f595,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f182,f593]) ).

fof(f182,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,[],[f137,f129]) ).

fof(f137,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,f125]) ).

fof(f125,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,f116]) ).

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(f591,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f158,f589]) ).

fof(f158,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,f116]) ).

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(f587,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f151,f585]) ).

fof(f151,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
    inference(definition_unfolding,[],[f93,f118]) ).

fof(f93,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).

fof(f578,plain,
    ( spl0_71
    | ~ spl0_2
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f537,f512,f210,f575]) ).

fof(f575,plain,
    ( spl0_71
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f537,plain,
    ( single_valued_class(choice)
    | ~ spl0_2
    | ~ spl0_59 ),
    inference(resolution,[],[f513,f212]) ).

fof(f571,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f165,f569]) ).

fof(f165,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(f567,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f161,f565]) ).

fof(f161,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(f563,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f142,f561]) ).

fof(f142,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,f118]) ).

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(f559,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f141,f557]) ).

fof(f141,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,f118]) ).

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(f555,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f139,f553]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
    inference(definition_unfolding,[],[f100,f118]) ).

fof(f100,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).

fof(f546,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f159,f544]) ).

fof(f159,plain,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
      | maps(X8,domain_of(X8),X1) ),
    inference(definition_unfolding,[],[f112,f115]) ).

fof(f112,axiom,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(range_of(X8),X1)
      | maps(X8,domain_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).

fof(f542,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f147,f540]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
    inference(definition_unfolding,[],[f99,f118]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(ordered_pair(X0,X1),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).

fof(f535,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f181,f533]) ).

fof(f181,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,[],[f133,f129]) ).

fof(f133,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,f116]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).

fof(f531,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f145,f529]) ).

fof(f529,plain,
    ( spl0_62
  <=> ! [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_62])]) ).

fof(f145,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,f115]) ).

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(f527,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f140,f525]) ).

fof(f140,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,f118]) ).

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(f519,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f143,f517]) ).

fof(f143,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(f514,plain,
    ( spl0_59
    | ~ spl0_52
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f496,f465,f461,f512]) ).

fof(f465,plain,
    ( spl0_53
  <=> ! [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_53])]) ).

fof(f496,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_53 ),
    inference(resolution,[],[f466,f462]) ).

fof(f466,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f465]) ).

fof(f510,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f144,f508]) ).

fof(f508,plain,
    ( spl0_58
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f144,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f115]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).

fof(f506,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f134,f504]) ).

fof(f134,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f115]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).

fof(f502,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f79,f500]) ).

fof(f500,plain,
    ( spl0_56
  <=> ! [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_56])]) ).

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(f480,plain,
    ( spl0_55
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f405,f377,f220,f478]) ).

fof(f405,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f221]) ).

fof(f471,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f183,f469]) ).

fof(f183,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f138,f129]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f114]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).

fof(f467,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f136,f465]) ).

fof(f136,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(f463,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f135,f461]) ).

fof(f135,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(f459,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f131,f457]) ).

fof(f131,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(f455,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f129,f453]) ).

fof(f451,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f23,f449]) ).

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(f447,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f8,f445]) ).

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(f442,plain,
    ( spl0_47
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f398,f373,f224,f440]) ).

fof(f224,plain,
    ( spl0_5
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f398,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f226]) ).

fof(f226,plain,
    ( member(omega,universal_class)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f435,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f157,f433]) ).

fof(f433,plain,
    ( spl0_46
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f157,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(f431,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f83,f429]) ).

fof(f429,plain,
    ( spl0_45
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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(f427,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f25,f425]) ).

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(f397,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f128,f394]) ).

fof(f128,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(f392,plain,
    ( spl0_42
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f366,f336,f255,f390]) ).

fof(f366,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(resolution,[],[f337,f256]) ).

fof(f388,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f104,f385]) ).

fof(f104,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).

fof(f383,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f67,f381]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f379,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f7,f377]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f375,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1,f373]) ).

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(f362,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f132,f360]) ).

fof(f132,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(f358,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f110,f356]) ).

fof(f356,plain,
    ( spl0_36
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).

fof(f354,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f88,f352]) ).

fof(f352,plain,
    ( spl0_35
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f350,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f35,f348]) ).

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(f346,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f32,f344]) ).

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(f342,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f22,f340]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f338,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f21,f336]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f334,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f10,f332]) ).

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(f330,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f9,f328]) ).

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(f326,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f3,f324]) ).

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(f322,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f2,f320]) ).

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(f317,plain,
    ( spl0_26
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f313,f288,f255,f315]) ).

fof(f315,plain,
    ( spl0_26
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f313,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(resolution,[],[f289,f256]) ).

fof(f312,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f105,f309]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f307,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f95,f304]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f302,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f66,f300]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f298,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f62,f296]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f294,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f57,f292]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f290,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f24,f288]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f286,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f109,f284]) ).

fof(f284,plain,
    ( spl0_19
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).

fof(f282,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f92,f280]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f278,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f87,f276]) ).

fof(f276,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f274,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f86,f272]) ).

fof(f272,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f270,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f82,f268]) ).

fof(f268,plain,
    ( spl0_15
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f266,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f98,f263]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f261,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f51,f259]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f257,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f47,f255]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

fof(f253,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f44,f250]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f248,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f18,f245]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f243,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f11,f241]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f239,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f78,f237]) ).

fof(f237,plain,
    ( spl0_8
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f235,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f71,f233]) ).

fof(f233,plain,
    ( spl0_7
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f231,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f177,f229]) ).

fof(f177,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(f227,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f52,f224]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f222,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f4,f220]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f218,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f127,f215]) ).

fof(f127,plain,
    universal_class != complement(intersection(complement(complement(x)),complement(x))),
    inference(definition_unfolding,[],[f113,f26]) ).

fof(f113,axiom,
    universal_class != union(complement(x),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_with_complement_1) ).

fof(f213,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f69,f210]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f208,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f50,f205]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET154-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.00/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n013.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 11:32:38 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  % (15889)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33  % (15896)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)
% 0.11/0.33  % (15892)WARNING: value z3 for option sas not known
% 0.11/0.33  % (15890)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33  % (15894)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)
% 0.11/0.33  % (15892)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)
% 0.11/0.34  % (15895)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)
% 0.11/0.34  % (15893)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.34  % (15891)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.36  TRYING [1]
% 0.15/0.36  TRYING [2]
% 0.15/0.40  TRYING [3]
% 0.15/0.48  TRYING [1]
% 0.15/0.49  TRYING [2]
% 0.15/0.55  TRYING [4]
% 1.71/0.58  TRYING [1]
% 1.71/0.58  TRYING [2]
% 1.86/0.59  TRYING [3]
% 1.86/0.60  TRYING [3]
% 2.29/0.66  TRYING [4]
% 3.13/0.83  TRYING [5]
% 4.85/1.03  TRYING [5]
% 8.05/1.49  TRYING [6]
% 8.51/1.57  TRYING [4]
% 13.96/2.31  % (15894)First to succeed.
% 13.96/2.37  % (15894)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15889"
% 13.96/2.38  % (15894)Refutation found. Thanks to Tanya!
% 13.96/2.38  % SZS status Unsatisfiable for theBenchmark
% 13.96/2.38  % SZS output start Proof for theBenchmark
% See solution above
% 14.51/2.41  % (15894)------------------------------
% 14.51/2.41  % (15894)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 14.51/2.41  % (15894)Termination reason: Refutation
% 14.51/2.41  
% 14.51/2.41  % (15894)Memory used [KB]: 18969
% 14.51/2.41  % (15894)Time elapsed: 2.042 s
% 14.51/2.41  % (15894)Instructions burned: 4235 (million)
% 14.51/2.41  % (15889)Success in time 2.084 s
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