%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET201-6 : 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 : n015.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 03:17:48 EDT 2024

% Result   : Unsatisfiable 12.21s 2.09s
% Output   : Refutation 12.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1032
% Syntax   : Number of formulae    : 3062 ( 139 unt;   0 def)
%            Number of atoms       : 11387 (1158 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 14764 (6439   ~;7399   |;   0   &)
%                                         ( 926 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   27 (   3 avg)
%            Number of predicates  :  938 ( 936 usr; 927 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;  16 con; 0-3 aty)
%            Number of variables   : 4050 (4050   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f20562,plain,
    $false,
    inference(avatar_sat_refutation,[],[f209,f214,f219,f224,f229,f233,f238,f242,f246,f250,f254,f259,f264,f268,f272,f277,f281,f285,f289,f293,f297,f301,f305,f309,f313,f318,f323,f329,f333,f337,f341,f345,f349,f353,f357,f361,f365,f369,f373,f386,f390,f394,f398,f403,f408,f445,f449,f453,f457,f465,f469,f473,f477,f481,f485,f489,f516,f520,f524,f529,f537,f541,f550,f554,f559,f563,f572,f576,f580,f584,f588,f599,f603,f607,f611,f624,f628,f639,f643,f647,f655,f660,f664,f676,f681,f685,f689,f694,f699,f703,f708,f712,f718,f734,f739,f743,f747,f751,f757,f767,f771,f778,f783,f787,f791,f795,f813,f823,f836,f840,f849,f853,f857,f920,f924,f928,f942,f960,f964,f973,f982,f991,f995,f999,f1003,f1007,f1044,f1048,f1052,f1056,f1060,f1064,f1085,f1128,f1132,f1136,f1140,f1144,f1191,f1195,f1199,f1203,f1207,f1216,f1266,f1275,f1284,f1288,f1292,f1318,f1322,f1326,f1331,f1335,f1353,f1357,f1386,f1393,f1403,f1407,f1411,f1415,f1419,f1486,f1490,f1494,f1498,f1506,f1510,f1548,f1556,f1564,f1577,f1583,f1590,f1613,f1617,f1623,f1636,f1648,f1654,f1673,f1690,f1694,f1738,f1745,f1749,f1783,f1811,f1831,f1841,f1845,f1902,f1940,f1947,f1957,f1970,f1974,f1984,f2033,f2037,f2090,f2101,f2114,f2127,f2131,f2144,f2159,f2163,f2167,f2185,f2194,f2199,f2203,f2209,f2213,f2240,f2248,f2252,f2256,f2259,f2260,f2360,f2370,f2390,f2396,f2421,f2429,f2434,f2439,f2443,f2447,f2451,f2459,f2464,f2469,f2473,f2481,f2489,f2497,f2501,f2511,f2520,f2531,f2535,f2539,f2543,f2561,f2572,f2576,f2580,f2596,f2601,f2607,f2611,f2620,f2640,f2680,f2772,f2776,f2784,f2790,f2794,f2796,f2808,f2812,f2816,f2820,f2828,f2893,f2897,f2901,f2905,f2909,f2914,f2919,f2942,f2996,f3007,f3013,f3019,f3026,f3031,f3036,f3040,f3044,f3112,f3138,f3149,f3157,f3162,f3167,f3188,f3209,f3228,f3232,f3236,f3240,f3244,f3248,f3252,f3258,f3262,f3267,f3274,f3278,f3284,f3292,f3300,f3304,f3308,f3312,f3393,f3407,f3411,f3415,f3429,f3543,f3556,f3562,f3567,f3569,f3579,f3587,f3591,f3595,f3599,f3603,f3607,f3612,f3617,f3621,f3625,f3629,f3633,f3637,f3720,f3724,f3788,f3858,f3862,f3866,f3870,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3933,f3937,f3941,f3945,f3949,f3953,f3978,f4371,f4375,f4379,f4383,f4387,f4391,f4395,f4399,f4403,f4407,f4411,f4416,f4420,f4429,f4448,f4685,f4825,f4945,f4949,f4955,f4960,f4964,f4968,f4972,f4976,f4980,f4985,f4990,f4994,f4998,f5002,f5006,f5010,f5022,f5026,f5205,f5317,f5321,f5497,f5649,f5658,f5665,f5670,f5688,f5694,f5700,f5704,f5712,f5718,f5726,f5739,f5743,f5747,f5751,f5755,f5759,f5764,f5775,f6023,f6027,f6093,f6099,f6104,f6108,f6112,f6117,f6122,f6126,f6130,f6134,f6227,f6231,f6398,f6403,f6407,f6412,f6424,f6428,f6432,f6440,f6450,f6455,f6459,f6463,f6628,f6632,f6636,f6640,f6645,f6650,f6654,f6658,f6662,f6667,f6671,f6675,f6683,f6823,f6827,f6831,f7043,f7048,f7052,f7056,f7060,f7064,f7068,f7072,f7076,f7080,f7255,f7259,f7263,f7267,f7271,f7275,f7279,f7283,f7287,f7291,f7295,f7585,f7589,f7593,f7597,f7601,f7614,f7622,f7627,f7632,f7650,f7659,f7664,f7670,f7674,f7678,f7682,f7686,f7690,f7694,f7698,f8403,f8407,f8411,f8415,f8419,f8435,f8451,f8462,f8469,f8480,f8484,f8488,f8492,f8496,f8500,f8504,f8508,f8515,f8520,f8528,f8532,f8546,f8550,f8554,f8558,f8562,f8601,f8969,f8973,f8977,f8981,f8985,f8989,f9081,f9088,f9092,f9100,f9104,f9108,f9117,f9124,f9250,f9254,f9258,f9263,f9267,f9271,f9331,f9354,f9358,f9365,f9418,f9423,f9428,f9433,f9439,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9518,f9631,f9635,f9642,f9649,f9654,f9659,f9666,f9671,f9675,f9679,f9687,f9699,f9703,f9886,f9890,f9898,f9956,f10035,f10039,f10047,f10054,f10058,f10065,f10069,f10073,f10086,f10097,f10131,f10135,f10139,f10143,f10147,f10151,f10278,f10284,f10292,f10298,f10311,f10319,f10324,f10328,f10332,f10336,f10340,f10344,f10348,f10352,f10356,f10360,f10695,f10703,f10707,f10711,f10715,f10819,f10823,f10827,f10835,f10870,f10874,f10878,f11053,f11058,f11063,f11323,f11327,f11331,f11335,f11339,f11343,f11376,f11729,f11733,f11738,f11742,f11769,f11773,f11871,f11875,f11902,f11911,f11918,f11923,f11935,f11941,f11948,f11952,f11963,f11967,f11981,f11985,f12013,f12023,f12027,f12056,f12060,f12064,f12162,f12166,f12170,f12208,f12213,f12218,f12222,f12226,f12234,f12240,f12244,f12248,f12252,f12607,f12612,f12617,f12621,f12625,f12629,f12789,f12944,f12948,f12952,f12956,f12960,f12964,f12968,f12972,f12976,f12980,f13304,f13374,f13378,f13409,f13413,f13417,f13421,f13425,f13429,f13566,f13615,f13619,f13623,f13627,f13713,f13722,f13726,f13730,f13734,f13738,f13742,f13746,f13984,f14050,f14054,f14058,f14062,f14241,f14245,f14249,f14253,f14305,f14333,f14369,f14415,f14423,f14429,f14437,f14558,f14562,f14566,f14571,f14715,f14720,f14724,f14908,f14931,f14939,f14940,f14945,f14950,f14970,f14980,f14987,f14992,f14996,f15004,f15009,f15013,f15191,f15223,f15227,f15232,f15261,f15265,f15270,f15275,f15282,f15286,f15290,f15301,f15305,f15380,f15399,f15403,f15462,f15470,f15504,f15508,f15523,f15594,f15602,f15607,f15619,f15623,f15628,f15632,f15636,f15640,f15752,f15756,f15774,f15794,f15802,f15841,f15845,f15849,f15898,f15902,f15973,f15977,f15985,f16003,f16011,f16016,f16020,f16096,f16141,f16146,f16151,f16155,f16160,f16165,f16169,f16173,f16255,f16259,f16377,f16381,f16385,f16389,f16393,f16397,f16444,f16489,f16542,f16546,f16550,f16566,f16570,f16595,f16627,f16635,f16643,f16647,f16654,f16694,f16695,f16696,f17053,f17195,f17846,f19110,f19469,f20031,f20171,f20561]) ).

fof(f20561,plain,
    ( ~ spl0_235
    | spl0_926 ),
    inference(avatar_contradiction_clause,[],[f20560]) ).

fof(f20560,plain,
    ( $false
    | ~ spl0_235
    | spl0_926 ),
    inference(resolution,[],[f20030,f2208]) ).

fof(f2208,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2207]) ).

fof(f2207,plain,
    ( spl0_235
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f20030,plain,
    ( ~ subclass(intersection(x,z),x)
    | spl0_926 ),
    inference(avatar_component_clause,[],[f20028]) ).

fof(f20028,plain,
    ( spl0_926
  <=> subclass(intersection(x,z),x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f20171,plain,
    ( ~ spl0_723
    | spl0_925 ),
    inference(avatar_contradiction_clause,[],[f20170]) ).

fof(f20170,plain,
    ( $false
    | ~ spl0_723
    | spl0_925 ),
    inference(resolution,[],[f20026,f11951]) ).

fof(f11951,plain,
    ( ! [X0] : subclass(intersection(X0,z),w)
    | ~ spl0_723 ),
    inference(avatar_component_clause,[],[f11950]) ).

fof(f11950,plain,
    ( spl0_723
  <=> ! [X0] : subclass(intersection(X0,z),w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f20026,plain,
    ( ~ subclass(intersection(x,z),w)
    | spl0_925 ),
    inference(avatar_component_clause,[],[f20024]) ).

fof(f20024,plain,
    ( spl0_925
  <=> subclass(intersection(x,z),w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f20031,plain,
    ( ~ spl0_925
    | ~ spl0_926
    | spl0_3
    | ~ spl0_923 ),
    inference(avatar_split_clause,[],[f19733,f19108,f216,f20028,f20024]) ).

fof(f216,plain,
    ( spl0_3
  <=> subclass(intersection(x,z),intersection(y,w)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f19108,plain,
    ( spl0_923
  <=> ! [X0,X1] :
        ( ~ subclass(X0,x)
        | subclass(X0,intersection(y,X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f19733,plain,
    ( ~ subclass(intersection(x,z),x)
    | ~ subclass(intersection(x,z),w)
    | spl0_3
    | ~ spl0_923 ),
    inference(resolution,[],[f19109,f218]) ).

fof(f218,plain,
    ( ~ subclass(intersection(x,z),intersection(y,w))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f19109,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(y,X1))
        | ~ subclass(X0,x)
        | ~ subclass(X0,X1) )
    | ~ spl0_923 ),
    inference(avatar_component_clause,[],[f19108]) ).

fof(f19469,plain,
    ( spl0_924
    | ~ spl0_412
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f11086,f7046,f4446,f19467]) ).

fof(f19467,plain,
    ( spl0_924
  <=> ! [X0,X1] :
        ( ~ subclass(X0,z)
        | subclass(X0,intersection(w,X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f4446,plain,
    ( spl0_412
  <=> ! [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_412])]) ).

fof(f7046,plain,
    ( spl0_511
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,z)
        | member(not_subclass_element(X0,X1),w) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f11086,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,z)
        | subclass(X0,intersection(w,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_412
    | ~ spl0_511 ),
    inference(duplicate_literal_removal,[],[f11075]) ).

fof(f11075,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,z)
        | subclass(X0,intersection(w,X1))
        | subclass(X0,intersection(w,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_412
    | ~ spl0_511 ),
    inference(resolution,[],[f7047,f4447]) ).

fof(f4447,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_412 ),
    inference(avatar_component_clause,[],[f4446]) ).

fof(f7047,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),w)
        | ~ subclass(X0,z)
        | subclass(X0,X1) )
    | ~ spl0_511 ),
    inference(avatar_component_clause,[],[f7046]) ).

fof(f19110,plain,
    ( spl0_923
    | ~ spl0_412
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f7104,f6829,f4446,f19108]) ).

fof(f6829,plain,
    ( spl0_509
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,x)
        | member(not_subclass_element(X0,X1),y) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f7104,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,x)
        | subclass(X0,intersection(y,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_412
    | ~ spl0_509 ),
    inference(duplicate_literal_removal,[],[f7096]) ).

fof(f7096,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,x)
        | subclass(X0,intersection(y,X1))
        | subclass(X0,intersection(y,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_412
    | ~ spl0_509 ),
    inference(resolution,[],[f6830,f4447]) ).

fof(f6830,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),y)
        | ~ subclass(X0,x)
        | subclass(X0,X1) )
    | ~ spl0_509 ),
    inference(avatar_component_clause,[],[f6829]) ).

fof(f17846,plain,
    ( spl0_920
    | spl0_921
    | ~ spl0_922
    | ~ spl0_43
    | ~ spl0_918 ),
    inference(avatar_split_clause,[],[f17520,f17051,f396,f17843,f17839,f17835]) ).

fof(f17835,plain,
    ( spl0_920
  <=> null_class = z ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f17839,plain,
    ( spl0_921
  <=> null_class = w ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f17843,plain,
    ( spl0_922
  <=> subclass(w,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f396,plain,
    ( spl0_43
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f17051,plain,
    ( spl0_918
  <=> ! [X0] :
        ( ~ subclass(w,intersection(z,X0))
        | w = intersection(z,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f17520,plain,
    ( ~ subclass(w,null_class)
    | null_class = w
    | null_class = z
    | ~ spl0_43
    | ~ spl0_918 ),
    inference(superposition,[],[f17052,f397]) ).

fof(f397,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f396]) ).

fof(f17052,plain,
    ( ! [X0] :
        ( ~ subclass(w,intersection(z,X0))
        | w = intersection(z,X0) )
    | ~ spl0_918 ),
    inference(avatar_component_clause,[],[f17051]) ).

fof(f17195,plain,
    ( spl0_919
    | ~ spl0_42
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f12085,f11950,f392,f17193]) ).

fof(f17193,plain,
    ( spl0_919
  <=> ! [X0] :
        ( ~ subclass(w,intersection(X0,z))
        | w = intersection(X0,z) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f392,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f12085,plain,
    ( ! [X0] :
        ( ~ subclass(w,intersection(X0,z))
        | w = intersection(X0,z) )
    | ~ spl0_42
    | ~ spl0_723 ),
    inference(resolution,[],[f11951,f393]) ).

fof(f393,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f392]) ).

fof(f17053,plain,
    ( spl0_918
    | ~ spl0_42
    | ~ spl0_714 ),
    inference(avatar_split_clause,[],[f12018,f11900,f392,f17051]) ).

fof(f11900,plain,
    ( spl0_714
  <=> ! [X0] : subclass(intersection(z,X0),w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f12018,plain,
    ( ! [X0] :
        ( ~ subclass(w,intersection(z,X0))
        | w = intersection(z,X0) )
    | ~ spl0_42
    | ~ spl0_714 ),
    inference(resolution,[],[f11901,f393]) ).

fof(f11901,plain,
    ( ! [X0] : subclass(intersection(z,X0),w)
    | ~ spl0_714 ),
    inference(avatar_component_clause,[],[f11900]) ).

fof(f16696,plain,
    ( ~ spl0_11
    | ~ spl0_916 ),
    inference(avatar_contradiction_clause,[],[f16655]) ).

fof(f16655,plain,
    ( $false
    | ~ spl0_11
    | ~ spl0_916 ),
    inference(resolution,[],[f16650,f253]) ).

fof(f253,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f252,plain,
    ( spl0_11
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f16650,plain,
    ( ! [X2] : ~ member(X2,universal_class)
    | ~ spl0_916 ),
    inference(avatar_component_clause,[],[f16649]) ).

fof(f16649,plain,
    ( spl0_916
  <=> ! [X2] : ~ member(X2,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f16695,plain,
    ( ~ spl0_102
    | ~ spl0_916 ),
    inference(avatar_contradiction_clause,[],[f16656]) ).

fof(f16656,plain,
    ( $false
    | ~ spl0_102
    | ~ spl0_916 ),
    inference(resolution,[],[f16650,f761]) ).

fof(f761,plain,
    ( member(null_class,universal_class)
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f760]) ).

fof(f760,plain,
    ( spl0_102
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f16694,plain,
    ( ~ spl0_7
    | ~ spl0_916 ),
    inference(avatar_contradiction_clause,[],[f16657]) ).

fof(f16657,plain,
    ( $false
    | ~ spl0_7
    | ~ spl0_916 ),
    inference(resolution,[],[f16650,f237]) ).

fof(f237,plain,
    ( member(omega,universal_class)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f235,plain,
    ( spl0_7
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f16654,plain,
    ( spl0_916
    | spl0_917
    | ~ spl0_79
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2091,f2088,f626,f16652,f16649]) ).

fof(f16652,plain,
    ( spl0_917
  <=> ! [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_917])]) ).

fof(f626,plain,
    ( spl0_79
  <=> ! [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_79])]) ).

fof(f2088,plain,
    ( spl0_219
  <=> ! [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_219])]) ).

fof(f2091,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_79
    | ~ spl0_219 ),
    inference(resolution,[],[f2089,f627]) ).

fof(f627,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_79 ),
    inference(avatar_component_clause,[],[f626]) ).

fof(f2089,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_219 ),
    inference(avatar_component_clause,[],[f2088]) ).

fof(f16647,plain,
    ( spl0_915
    | ~ spl0_97
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1458,f1409,f737,f16645]) ).

fof(f16645,plain,
    ( spl0_915
  <=> ! [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_915])]) ).

fof(f737,plain,
    ( spl0_97
  <=> ! [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_97])]) ).

fof(f1409,plain,
    ( spl0_172
  <=> ! [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_172])]) ).

fof(f1458,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_97
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f738]) ).

fof(f738,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_97 ),
    inference(avatar_component_clause,[],[f737]) ).

fof(f1410,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_172 ),
    inference(avatar_component_clause,[],[f1409]) ).

fof(f16643,plain,
    ( ~ spl0_913
    | spl0_914
    | ~ spl0_92
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1248,f1201,f701,f16641,f16637]) ).

fof(f16637,plain,
    ( spl0_913
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f16641,plain,
    ( spl0_914
  <=> ! [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_914])]) ).

fof(f701,plain,
    ( spl0_92
  <=> ! [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_92])]) ).

fof(f1201,plain,
    ( spl0_150
  <=> ! [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_150])]) ).

fof(f1248,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_92
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f702]) ).

fof(f702,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_92 ),
    inference(avatar_component_clause,[],[f701]) ).

fof(f1202,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1201]) ).

fof(f16635,plain,
    ( spl0_911
    | ~ spl0_912
    | ~ spl0_101
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f870,f834,f755,f16632,f16629]) ).

fof(f16629,plain,
    ( spl0_911
  <=> ! [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_911])]) ).

fof(f16632,plain,
    ( spl0_912
  <=> subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f755,plain,
    ( spl0_101
  <=> ! [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_101])]) ).

fof(f834,plain,
    ( spl0_112
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f870,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_101
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f756]) ).

fof(f756,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_101 ),
    inference(avatar_component_clause,[],[f755]) ).

fof(f835,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f834]) ).

fof(f16627,plain,
    ( spl0_909
    | ~ spl0_910
    | ~ spl0_190
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1925,f1900,f1588,f16624,f16621]) ).

fof(f16621,plain,
    ( spl0_909
  <=> ! [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_909])]) ).

fof(f16624,plain,
    ( spl0_910
  <=> 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_910])]) ).

fof(f1588,plain,
    ( spl0_190
  <=> ! [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_190])]) ).

fof(f1900,plain,
    ( spl0_210
  <=> ! [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_210])]) ).

fof(f1925,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_190
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f1589]) ).

fof(f1589,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_190 ),
    inference(avatar_component_clause,[],[f1588]) ).

fof(f1901,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_210 ),
    inference(avatar_component_clause,[],[f1900]) ).

fof(f16595,plain,
    ( spl0_908
    | ~ spl0_113
    | ~ spl0_770 ),
    inference(avatar_split_clause,[],[f13575,f13411,f838,f16593]) ).

fof(f16593,plain,
    ( spl0_908
  <=> ! [X0] :
        ( ~ subclass(X0,z)
        | member(null_class,intersection(w,X0))
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f838,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f13411,plain,
    ( spl0_770
  <=> ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,intersection(w,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f13575,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | member(null_class,intersection(w,X0))
        | ~ inductive(X0) )
    | ~ spl0_113
    | ~ spl0_770 ),
    inference(resolution,[],[f13412,f839]) ).

fof(f839,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f838]) ).

fof(f13412,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(w,X0))
        | ~ subclass(X0,z) )
    | ~ spl0_770 ),
    inference(avatar_component_clause,[],[f13411]) ).

fof(f16570,plain,
    ( spl0_907
    | ~ spl0_169
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2071,f2035,f1391,f16568]) ).

fof(f16568,plain,
    ( spl0_907
  <=> ! [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_907])]) ).

fof(f1391,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

fof(f2035,plain,
    ( spl0_218
  <=> ! [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_218])]) ).

fof(f2071,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_169
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f1392]) ).

fof(f1392,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_169 ),
    inference(avatar_component_clause,[],[f1391]) ).

fof(f2036,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_218 ),
    inference(avatar_component_clause,[],[f2035]) ).

fof(f16566,plain,
    ( spl0_906
    | ~ spl0_169
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2048,f2031,f1391,f16564]) ).

fof(f16564,plain,
    ( spl0_906
  <=> ! [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_906])]) ).

fof(f2031,plain,
    ( spl0_217
  <=> ! [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_217])]) ).

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(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_169
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f1392]) ).

fof(f2032,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_217 ),
    inference(avatar_component_clause,[],[f2031]) ).

fof(f16550,plain,
    ( spl0_905
    | ~ spl0_178
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1884,f1843,f1496,f16548]) ).

fof(f16548,plain,
    ( spl0_905
  <=> ! [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_905])]) ).

fof(f1496,plain,
    ( spl0_178
  <=> ! [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_178])]) ).

fof(f1843,plain,
    ( spl0_209
  <=> ! [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_209])]) ).

fof(f1884,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_178
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f1497]) ).

fof(f1497,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_178 ),
    inference(avatar_component_clause,[],[f1496]) ).

fof(f1844,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_209 ),
    inference(avatar_component_clause,[],[f1843]) ).

fof(f16546,plain,
    ( spl0_904
    | ~ spl0_178
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1858,f1839,f1496,f16544]) ).

fof(f16544,plain,
    ( spl0_904
  <=> ! [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_904])]) ).

fof(f1839,plain,
    ( spl0_208
  <=> ! [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_208])]) ).

fof(f1858,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_178
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f1497]) ).

fof(f1840,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_208 ),
    inference(avatar_component_clause,[],[f1839]) ).

fof(f16542,plain,
    ( spl0_903
    | ~ spl0_95
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1537,f1496,f716,f16540]) ).

fof(f16540,plain,
    ( spl0_903
  <=> ! [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_903])]) ).

fof(f716,plain,
    ( spl0_95
  <=> ! [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_95])]) ).

fof(f1537,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_95
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f717]) ).

fof(f717,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_95 ),
    inference(avatar_component_clause,[],[f716]) ).

fof(f16489,plain,
    ( spl0_902
    | ~ spl0_192
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2084,f2035,f1615,f16487]) ).

fof(f16487,plain,
    ( spl0_902
  <=> ! [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_902])]) ).

fof(f1615,plain,
    ( spl0_192
  <=> ! [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_192])]) ).

fof(f2084,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_192
    | ~ spl0_218 ),
    inference(duplicate_literal_removal,[],[f2080]) ).

fof(f2080,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_192
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f1616]) ).

fof(f1616,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_192 ),
    inference(avatar_component_clause,[],[f1615]) ).

fof(f16444,plain,
    ( spl0_901
    | ~ spl0_172
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2061,f2035,f1409,f16442]) ).

fof(f16442,plain,
    ( spl0_901
  <=> ! [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_901])]) ).

fof(f2061,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_172
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f1410]) ).

fof(f16397,plain,
    ( spl0_900
    | ~ spl0_43
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2122,f2112,f396,f16395]) ).

fof(f16395,plain,
    ( spl0_900
  <=> ! [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_900])]) ).

fof(f2112,plain,
    ( spl0_221
  <=> ! [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_221])]) ).

fof(f2122,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_43
    | ~ spl0_221 ),
    inference(superposition,[],[f2113,f397]) ).

fof(f2113,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_221 ),
    inference(avatar_component_clause,[],[f2112]) ).

fof(f16393,plain,
    ( spl0_899
    | ~ spl0_205
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1963,f1955,f1781,f16391]) ).

fof(f16391,plain,
    ( spl0_899
  <=> ! [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_899])]) ).

fof(f1781,plain,
    ( spl0_205
  <=> ! [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_205])]) ).

fof(f1955,plain,
    ( spl0_213
  <=> ! [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_213])]) ).

fof(f1963,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_205
    | ~ spl0_213 ),
    inference(resolution,[],[f1956,f1782]) ).

fof(f1782,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_205 ),
    inference(avatar_component_clause,[],[f1781]) ).

fof(f1956,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_213 ),
    inference(avatar_component_clause,[],[f1955]) ).

fof(f16389,plain,
    ( spl0_898
    | ~ spl0_329
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f11093,f7046,f3238,f16387]) ).

fof(f16387,plain,
    ( spl0_898
  <=> ! [X0,X1] :
        ( ~ subclass(X0,z)
        | subclass(X0,X1)
        | ~ subclass(X0,complement(w)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f3238,plain,
    ( spl0_329
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f11093,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,z)
        | subclass(X0,X1)
        | ~ subclass(X0,complement(w)) )
    | ~ spl0_329
    | ~ spl0_511 ),
    inference(duplicate_literal_removal,[],[f11068]) ).

fof(f11068,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,z)
        | subclass(X0,X1)
        | subclass(X0,X1)
        | ~ subclass(X0,complement(w)) )
    | ~ spl0_329
    | ~ spl0_511 ),
    inference(resolution,[],[f7047,f3239]) ).

fof(f3239,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_329 ),
    inference(avatar_component_clause,[],[f3238]) ).

fof(f16385,plain,
    ( spl0_897
    | ~ spl0_172
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1883,f1843,f1409,f16383]) ).

fof(f16383,plain,
    ( spl0_897
  <=> ! [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_897])]) ).

fof(f1883,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_172
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f1410]) ).

fof(f16381,plain,
    ( spl0_896
    | ~ spl0_172
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1857,f1839,f1409,f16379]) ).

fof(f16379,plain,
    ( spl0_896
  <=> ! [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_896])]) ).

fof(f1857,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_172
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f1410]) ).

fof(f16377,plain,
    ( spl0_895
    | ~ spl0_95
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1470,f1409,f716,f16375]) ).

fof(f16375,plain,
    ( spl0_895
  <=> ! [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_895])]) ).

fof(f1470,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_95
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f717]) ).

fof(f16259,plain,
    ( spl0_894
    | ~ spl0_248
    | ~ spl0_889 ),
    inference(avatar_split_clause,[],[f16161,f16158,f2393,f16257]) ).

fof(f16257,plain,
    ( spl0_894
  <=> ! [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_894])]) ).

fof(f2393,plain,
    ( spl0_248
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f16158,plain,
    ( spl0_889
  <=> ! [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_889])]) ).

fof(f16161,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_248
    | ~ spl0_889 ),
    inference(forward_demodulation,[],[f16159,f2395]) ).

fof(f2395,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f2393]) ).

fof(f16159,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_889 ),
    inference(avatar_component_clause,[],[f16158]) ).

fof(f16255,plain,
    ( spl0_893
    | ~ spl0_248
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f16156,f16153,f2393,f16253]) ).

fof(f16253,plain,
    ( spl0_893
  <=> ! [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_893])]) ).

fof(f16153,plain,
    ( spl0_888
  <=> ! [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_888])]) ).

fof(f16156,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_248
    | ~ spl0_888 ),
    inference(forward_demodulation,[],[f16154,f2395]) ).

fof(f16154,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_888 ),
    inference(avatar_component_clause,[],[f16153]) ).

fof(f16173,plain,
    ( spl0_892
    | ~ spl0_248
    | ~ spl0_886 ),
    inference(avatar_split_clause,[],[f16147,f16144,f2393,f16171]) ).

fof(f16171,plain,
    ( spl0_892
  <=> ! [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_892])]) ).

fof(f16144,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(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_886])]) ).

fof(f16147,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_248
    | ~ spl0_886 ),
    inference(forward_demodulation,[],[f16145,f2395]) ).

fof(f16145,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_886 ),
    inference(avatar_component_clause,[],[f16144]) ).

fof(f16169,plain,
    ( spl0_891
    | ~ spl0_248
    | ~ spl0_885 ),
    inference(avatar_split_clause,[],[f16142,f16139,f2393,f16167]) ).

fof(f16167,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(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_891])]) ).

fof(f16139,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(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_885])]) ).

fof(f16142,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_248
    | ~ spl0_885 ),
    inference(forward_demodulation,[],[f16140,f2395]) ).

fof(f16140,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_885 ),
    inference(avatar_component_clause,[],[f16139]) ).

fof(f16165,plain,
    ( spl0_890
    | ~ spl0_131
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2079,f2035,f993,f16163]) ).

fof(f16163,plain,
    ( spl0_890
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_890])]) ).

fof(f993,plain,
    ( spl0_131
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f2079,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_131
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f994]) ).

fof(f994,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,null_class)
        | null_class = X0 )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f993]) ).

fof(f16160,plain,
    ( spl0_889
    | ~ spl0_133
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2075,f2035,f1001,f16158]) ).

fof(f1001,plain,
    ( spl0_133
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f2075,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_133
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f1002]) ).

fof(f1002,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1001]) ).

fof(f16155,plain,
    ( spl0_888
    | ~ spl0_132
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2073,f2035,f997,f16153]) ).

fof(f997,plain,
    ( spl0_132
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f2073,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_132
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f998]) ).

fof(f998,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f997]) ).

fof(f16151,plain,
    ( spl0_887
    | ~ spl0_131
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2056,f2031,f993,f16149]) ).

fof(f16149,plain,
    ( spl0_887
  <=> ! [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_887])]) ).

fof(f2056,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_131
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f994]) ).

fof(f16146,plain,
    ( spl0_886
    | ~ spl0_133
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2052,f2031,f1001,f16144]) ).

fof(f2052,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_133
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f1002]) ).

fof(f16141,plain,
    ( spl0_885
    | ~ spl0_132
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2050,f2031,f997,f16139]) ).

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))),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_132
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f998]) ).

fof(f16096,plain,
    ( spl0_884
    | ~ spl0_159
    | ~ spl0_714 ),
    inference(avatar_split_clause,[],[f12014,f11900,f1286,f16094]) ).

fof(f16094,plain,
    ( spl0_884
  <=> ! [X0,X1] :
        ( ~ member(X0,z)
        | ~ member(X0,X1)
        | member(X0,w) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f1286,plain,
    ( spl0_159
  <=> ! [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_159])]) ).

fof(f12014,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,z)
        | ~ member(X0,X1)
        | member(X0,w) )
    | ~ spl0_159
    | ~ spl0_714 ),
    inference(resolution,[],[f11901,f1287]) ).

fof(f1287,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1286]) ).

fof(f16020,plain,
    ( spl0_883
    | ~ spl0_69
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2082,f2035,f570,f16018]) ).

fof(f16018,plain,
    ( spl0_883
  <=> ! [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_883])]) ).

fof(f570,plain,
    ( spl0_69
  <=> ! [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_69])]) ).

fof(f2082,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_69
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f571]) ).

fof(f571,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_69 ),
    inference(avatar_component_clause,[],[f570]) ).

fof(f16016,plain,
    ( spl0_882
    | ~ spl0_148
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1935,f1900,f1193,f16014]) ).

fof(f16014,plain,
    ( spl0_882
  <=> ! [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_882])]) ).

fof(f1193,plain,
    ( spl0_148
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1935,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_148
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f1194]) ).

fof(f1194,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,null_class)
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_148 ),
    inference(avatar_component_clause,[],[f1193]) ).

fof(f16011,plain,
    ( spl0_880
    | ~ spl0_881
    | ~ spl0_150
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1932,f1900,f1201,f16008,f16005]) ).

fof(f16005,plain,
    ( spl0_880
  <=> ! [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_880])]) ).

fof(f16008,plain,
    ( spl0_881
  <=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).

fof(f1932,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_150
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f1202]) ).

fof(f16003,plain,
    ( ~ spl0_879
    | ~ spl0_248
    | spl0_878 ),
    inference(avatar_split_clause,[],[f15986,f15982,f2393,f16000]) ).

fof(f16000,plain,
    ( spl0_879
  <=> subclass(composition_function,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f15982,plain,
    ( spl0_878
  <=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f15986,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_248
    | spl0_878 ),
    inference(forward_demodulation,[],[f15984,f2395]) ).

fof(f15984,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
    | spl0_878 ),
    inference(avatar_component_clause,[],[f15982]) ).

fof(f15985,plain,
    ( spl0_877
    | ~ spl0_878
    | ~ spl0_149
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1927,f1900,f1197,f15982,f15979]) ).

fof(f15979,plain,
    ( spl0_877
  <=> ! [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_877])]) ).

fof(f1197,plain,
    ( spl0_149
  <=> ! [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_149])]) ).

fof(f1927,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_149
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f1198]) ).

fof(f1198,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1197]) ).

fof(f15977,plain,
    ( spl0_876
    | ~ spl0_177
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1892,f1843,f1492,f15975]) ).

fof(f15975,plain,
    ( spl0_876
  <=> ! [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_876])]) ).

fof(f1492,plain,
    ( spl0_177
  <=> ! [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_177])]) ).

fof(f1892,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_177
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f1493]) ).

fof(f1493,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_177 ),
    inference(avatar_component_clause,[],[f1492]) ).

fof(f15973,plain,
    ( spl0_875
    | ~ spl0_177
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1866,f1839,f1492,f15971]) ).

fof(f15971,plain,
    ( spl0_875
  <=> ! [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_875])]) ).

fof(f1866,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_177
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f1493]) ).

fof(f15902,plain,
    ( spl0_874
    | spl0_644
    | ~ spl0_82
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1531,f1496,f645,f9954,f15900]) ).

fof(f15900,plain,
    ( spl0_874
  <=> ! [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_874])]) ).

fof(f9954,plain,
    ( spl0_644
  <=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f645,plain,
    ( spl0_82
  <=> ! [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_82])]) ).

fof(f1531,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_82
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f646]) ).

fof(f646,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_82 ),
    inference(avatar_component_clause,[],[f645]) ).

fof(f15898,plain,
    ( spl0_873
    | ~ spl0_95
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1519,f1492,f716,f15896]) ).

fof(f15896,plain,
    ( spl0_873
  <=> ! [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_873])]) ).

fof(f1519,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_95
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f717]) ).

fof(f15849,plain,
    ( spl0_872
    | ~ spl0_117
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2068,f2035,f855,f15847]) ).

fof(f15847,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(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_872])]) ).

fof(f855,plain,
    ( spl0_117
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f2068,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_117
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f856]) ).

fof(f856,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f855]) ).

fof(f15845,plain,
    ( spl0_871
    | ~ spl0_117
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2045,f2031,f855,f15843]) ).

fof(f15843,plain,
    ( spl0_871
  <=> ! [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_871])]) ).

fof(f2045,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_117
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f856]) ).

fof(f15841,plain,
    ( spl0_122
    | spl0_870
    | ~ spl0_33
    | ~ spl0_633 ),
    inference(avatar_split_clause,[],[f9878,f9673,f347,f15839,f939]) ).

fof(f939,plain,
    ( spl0_122
  <=> member(null_class,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f15839,plain,
    ( spl0_870
  <=> ! [X0] :
        ( ~ subclass(X0,x)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f347,plain,
    ( spl0_33
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f9673,plain,
    ( spl0_633
  <=> ! [X0] :
        ( ~ subclass(X0,x)
        | member(null_class,intersection(y,X0))
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f9878,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | ~ inductive(X0)
        | member(null_class,y) )
    | ~ spl0_33
    | ~ spl0_633 ),
    inference(resolution,[],[f9674,f348]) ).

fof(f348,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f9674,plain,
    ( ! [X0] :
        ( member(null_class,intersection(y,X0))
        | ~ subclass(X0,x)
        | ~ inductive(X0) )
    | ~ spl0_633 ),
    inference(avatar_component_clause,[],[f9673]) ).

fof(f15802,plain,
    ( spl0_868
    | spl0_869
    | ~ spl0_43
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2109,f2099,f396,f15800,f15796]) ).

fof(f15796,plain,
    ( spl0_868
  <=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f15800,plain,
    ( spl0_869
  <=> ! [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_869])]) ).

fof(f2099,plain,
    ( spl0_220
  <=> ! [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_220])]) ).

fof(f2109,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_43
    | ~ spl0_220 ),
    inference(superposition,[],[f2100,f397]) ).

fof(f2100,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_220 ),
    inference(avatar_component_clause,[],[f2099]) ).

fof(f15794,plain,
    ( spl0_867
    | ~ spl0_51
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1921,f1900,f463,f15792]) ).

fof(f15792,plain,
    ( spl0_867
  <=> ! [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_867])]) ).

fof(f463,plain,
    ( spl0_51
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f1921,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_51
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f464]) ).

fof(f464,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f463]) ).

fof(f15774,plain,
    ( spl0_866
    | ~ spl0_164
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1666,f1652,f1329,f15772]) ).

fof(f15772,plain,
    ( spl0_866
  <=> ! [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_866])]) ).

fof(f1329,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

fof(f1652,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

fof(f1666,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_164
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f1330]) ).

fof(f1330,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_164 ),
    inference(avatar_component_clause,[],[f1329]) ).

fof(f1653,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_198 ),
    inference(avatar_component_clause,[],[f1652]) ).

fof(f15756,plain,
    ( spl0_865
    | ~ spl0_190
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1798,f1781,f1588,f15754]) ).

fof(f15754,plain,
    ( spl0_865
  <=> ! [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_865])]) ).

fof(f1798,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_190
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f1589]) ).

fof(f15752,plain,
    ( spl0_864
    | ~ spl0_53
    | ~ spl0_73
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1686,f1671,f586,f471,f15750]) ).

fof(f15750,plain,
    ( spl0_864
  <=> ! [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_864])]) ).

fof(f471,plain,
    ( spl0_53
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f586,plain,
    ( spl0_73
  <=> ! [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_73])]) ).

fof(f1671,plain,
    ( spl0_199
  <=> ! [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_199])]) ).

fof(f1686,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_53
    | ~ spl0_73
    | ~ spl0_199 ),
    inference(forward_demodulation,[],[f1682,f472]) ).

fof(f472,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f471]) ).

fof(f1682,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_73
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f587]) ).

fof(f587,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_73 ),
    inference(avatar_component_clause,[],[f586]) ).

fof(f1672,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_199 ),
    inference(avatar_component_clause,[],[f1671]) ).

fof(f15640,plain,
    ( spl0_863
    | ~ spl0_248
    | ~ spl0_859 ),
    inference(avatar_split_clause,[],[f15624,f15621,f2393,f15638]) ).

fof(f15638,plain,
    ( spl0_863
  <=> ! [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_863])]) ).

fof(f15621,plain,
    ( spl0_859
  <=> ! [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_859])]) ).

fof(f15624,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_248
    | ~ spl0_859 ),
    inference(forward_demodulation,[],[f15622,f2395]) ).

fof(f15622,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_859 ),
    inference(avatar_component_clause,[],[f15621]) ).

fof(f15636,plain,
    ( spl0_862
    | ~ spl0_248
    | ~ spl0_856 ),
    inference(avatar_split_clause,[],[f15611,f15605,f2393,f15634]) ).

fof(f15634,plain,
    ( spl0_862
  <=> ! [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_862])]) ).

fof(f15605,plain,
    ( spl0_856
  <=> ! [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_856])]) ).

fof(f15611,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_248
    | ~ spl0_856 ),
    inference(forward_demodulation,[],[f15610,f2395]) ).

fof(f15610,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_248
    | ~ spl0_856 ),
    inference(forward_demodulation,[],[f15609,f2395]) ).

fof(f15609,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_248
    | ~ spl0_856 ),
    inference(forward_demodulation,[],[f15608,f2395]) ).

fof(f15608,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_248
    | ~ spl0_856 ),
    inference(forward_demodulation,[],[f15606,f2395]) ).

fof(f15606,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_856 ),
    inference(avatar_component_clause,[],[f15605]) ).

fof(f15632,plain,
    ( spl0_861
    | ~ spl0_248
    | ~ spl0_855 ),
    inference(avatar_split_clause,[],[f15603,f15600,f2393,f15630]) ).

fof(f15630,plain,
    ( spl0_861
  <=> ! [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_861])]) ).

fof(f15600,plain,
    ( spl0_855
  <=> ! [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_855])]) ).

fof(f15603,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_248
    | ~ spl0_855 ),
    inference(forward_demodulation,[],[f15601,f2395]) ).

fof(f15601,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_855 ),
    inference(avatar_component_clause,[],[f15600]) ).

fof(f15628,plain,
    ( spl0_860
    | ~ spl0_248
    | ~ spl0_854 ),
    inference(avatar_split_clause,[],[f15598,f15592,f2393,f15626]) ).

fof(f15626,plain,
    ( spl0_860
  <=> ! [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_860])]) ).

fof(f15592,plain,
    ( spl0_854
  <=> ! [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_854])]) ).

fof(f15598,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_248
    | ~ spl0_854 ),
    inference(forward_demodulation,[],[f15597,f2395]) ).

fof(f15597,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_248
    | ~ spl0_854 ),
    inference(forward_demodulation,[],[f15596,f2395]) ).

fof(f15596,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_248
    | ~ spl0_854 ),
    inference(forward_demodulation,[],[f15595,f2395]) ).

fof(f15595,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_248
    | ~ spl0_854 ),
    inference(forward_demodulation,[],[f15593,f2395]) ).

fof(f15593,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_854 ),
    inference(avatar_component_clause,[],[f15592]) ).

fof(f15623,plain,
    ( spl0_859
    | ~ spl0_150
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1725,f1692,f1201,f15621]) ).

fof(f1692,plain,
    ( spl0_201
  <=> ! [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_201])]) ).

fof(f1725,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_150
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f1202]) ).

fof(f1693,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_201 ),
    inference(avatar_component_clause,[],[f1692]) ).

fof(f15619,plain,
    ( spl0_857
    | ~ spl0_858
    | ~ spl0_291
    | ~ spl0_770 ),
    inference(avatar_split_clause,[],[f13578,f13411,f2774,f15616,f15613]) ).

fof(f15613,plain,
    ( spl0_857
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f15616,plain,
    ( spl0_858
  <=> subclass(universal_class,z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f2774,plain,
    ( spl0_291
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f13578,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,z)
        | member(unordered_pair(X0,X1),w) )
    | ~ spl0_291
    | ~ spl0_770 ),
    inference(resolution,[],[f13412,f2775]) ).

fof(f2775,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f2774]) ).

fof(f15607,plain,
    ( spl0_856
    | ~ spl0_149
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1722,f1692,f1197,f15605]) ).

fof(f1722,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_149
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f1198]) ).

fof(f15602,plain,
    ( spl0_855
    | ~ spl0_150
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1705,f1688,f1201,f15600]) ).

fof(f1688,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

fof(f1705,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_150
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f1202]) ).

fof(f1689,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_200 ),
    inference(avatar_component_clause,[],[f1688]) ).

fof(f15594,plain,
    ( spl0_854
    | ~ spl0_149
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1702,f1688,f1197,f15592]) ).

fof(f1702,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_149
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f1198]) ).

fof(f15523,plain,
    ( spl0_644
    | spl0_853
    | ~ spl0_82
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1513,f1492,f645,f15521,f9954]) ).

fof(f15521,plain,
    ( spl0_853
  <=> ! [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_853])]) ).

fof(f1513,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_82
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f646]) ).

fof(f15508,plain,
    ( spl0_852
    | ~ spl0_204
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1977,f1972,f1747,f15506]) ).

fof(f15506,plain,
    ( spl0_852
  <=> ! [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_852])]) ).

fof(f1747,plain,
    ( spl0_204
  <=> ! [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_204])]) ).

fof(f1972,plain,
    ( spl0_215
  <=> ! [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_215])]) ).

fof(f1977,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_204
    | ~ spl0_215 ),
    inference(superposition,[],[f1973,f1748]) ).

fof(f1748,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_204 ),
    inference(avatar_component_clause,[],[f1747]) ).

fof(f1973,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_215 ),
    inference(avatar_component_clause,[],[f1972]) ).

fof(f15504,plain,
    ( spl0_850
    | ~ spl0_851
    | ~ spl0_100
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f875,f834,f749,f15501,f15498]) ).

fof(f15498,plain,
    ( spl0_850
  <=> ! [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_850])]) ).

fof(f15501,plain,
    ( spl0_851
  <=> subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f749,plain,
    ( spl0_100
  <=> ! [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_100])]) ).

fof(f875,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_100
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f750]) ).

fof(f750,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_100 ),
    inference(avatar_component_clause,[],[f749]) ).

fof(f15470,plain,
    ( spl0_849
    | ~ spl0_181
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2046,f2031,f1508,f15468]) ).

fof(f15468,plain,
    ( spl0_849
  <=> ! [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_849])]) ).

fof(f1508,plain,
    ( spl0_181
  <=> ! [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_181])]) ).

fof(f2046,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_181
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f1509]) ).

fof(f1509,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_181 ),
    inference(avatar_component_clause,[],[f1508]) ).

fof(f15462,plain,
    ( ~ spl0_847
    | ~ spl0_848
    | spl0_645
    | ~ spl0_169
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1679,f1671,f1391,f10028,f15459,f15455]) ).

fof(f15455,plain,
    ( spl0_847
  <=> 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_847])]) ).

fof(f15459,plain,
    ( spl0_848
  <=> 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_848])]) ).

fof(f10028,plain,
    ( spl0_645
  <=> 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_645])]) ).

fof(f1679,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_169
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f1392]) ).

fof(f15403,plain,
    ( spl0_846
    | ~ spl0_181
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2086,f2035,f1508,f15401]) ).

fof(f15401,plain,
    ( spl0_846
  <=> ! [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_846])]) ).

fof(f2086,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_181
    | ~ spl0_218 ),
    inference(duplicate_literal_removal,[],[f2069]) ).

fof(f2069,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_181
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f1509]) ).

fof(f15399,plain,
    ( spl0_845
    | ~ spl0_90
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1975,f1972,f692,f15397]) ).

fof(f15397,plain,
    ( spl0_845
  <=> ! [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_845])]) ).

fof(f692,plain,
    ( spl0_90
  <=> ! [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_90])]) ).

fof(f1975,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_90
    | ~ spl0_215 ),
    inference(resolution,[],[f1973,f693]) ).

fof(f693,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_90 ),
    inference(avatar_component_clause,[],[f692]) ).

fof(f15380,plain,
    ( ~ spl0_844
    | ~ spl0_24
    | spl0_828 ),
    inference(avatar_split_clause,[],[f15005,f15001,f307,f15377]) ).

fof(f15377,plain,
    ( spl0_844
  <=> function(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f307,plain,
    ( spl0_24
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f15001,plain,
    ( spl0_828
  <=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f15005,plain,
    ( ~ function(composition_function)
    | ~ spl0_24
    | spl0_828 ),
    inference(resolution,[],[f15003,f308]) ).

fof(f308,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f307]) ).

fof(f15003,plain,
    ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
    | spl0_828 ),
    inference(avatar_component_clause,[],[f15001]) ).

fof(f15305,plain,
    ( spl0_843
    | ~ spl0_248
    | ~ spl0_837 ),
    inference(avatar_split_clause,[],[f15271,f15268,f2393,f15303]) ).

fof(f15303,plain,
    ( spl0_843
  <=> ! [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_843])]) ).

fof(f15268,plain,
    ( spl0_837
  <=> ! [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_837])]) ).

fof(f15271,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_248
    | ~ spl0_837 ),
    inference(forward_demodulation,[],[f15269,f2395]) ).

fof(f15269,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_837 ),
    inference(avatar_component_clause,[],[f15268]) ).

fof(f15301,plain,
    ( spl0_842
    | ~ spl0_248
    | ~ spl0_836 ),
    inference(avatar_split_clause,[],[f15266,f15263,f2393,f15299]) ).

fof(f15299,plain,
    ( spl0_842
  <=> ! [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_842])]) ).

fof(f15263,plain,
    ( spl0_836
  <=> ! [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_836])]) ).

fof(f15266,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_248
    | ~ spl0_836 ),
    inference(forward_demodulation,[],[f15264,f2395]) ).

fof(f15264,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_836 ),
    inference(avatar_component_clause,[],[f15263]) ).

fof(f15290,plain,
    ( spl0_841
    | ~ spl0_204
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1964,f1955,f1747,f15288]) ).

fof(f15288,plain,
    ( spl0_841
  <=> ! [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_841])]) ).

fof(f1964,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_204
    | ~ spl0_213 ),
    inference(superposition,[],[f1956,f1748]) ).

fof(f15286,plain,
    ( spl0_840
    | ~ spl0_160
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1885,f1843,f1290,f15284]) ).

fof(f15284,plain,
    ( spl0_840
  <=> ! [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_840])]) ).

fof(f1290,plain,
    ( spl0_160
  <=> ! [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_160])]) ).

fof(f1885,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_160
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f1291]) ).

fof(f1291,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1290]) ).

fof(f15282,plain,
    ( spl0_839
    | ~ spl0_160
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1859,f1839,f1290,f15280]) ).

fof(f15280,plain,
    ( spl0_839
  <=> ! [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_839])]) ).

fof(f1859,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_160
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f1291]) ).

fof(f15275,plain,
    ( spl0_838
    | ~ spl0_148
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1806,f1781,f1193,f15273]) ).

fof(f15273,plain,
    ( spl0_838
  <=> ! [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_838])]) ).

fof(f1806,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_148
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f1194]) ).

fof(f15270,plain,
    ( spl0_837
    | ~ spl0_150
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1803,f1781,f1201,f15268]) ).

fof(f1803,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_150
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f1202]) ).

fof(f15265,plain,
    ( spl0_836
    | ~ spl0_149
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1800,f1781,f1197,f15263]) ).

fof(f1800,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_149
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f1198]) ).

fof(f15261,plain,
    ( spl0_835
    | ~ spl0_95
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1310,f1290,f716,f15259]) ).

fof(f15259,plain,
    ( spl0_835
  <=> ! [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_835])]) ).

fof(f1310,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_95
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f717]) ).

fof(f15232,plain,
    ( spl0_834
    | ~ spl0_805
    | ~ spl0_833 ),
    inference(avatar_split_clause,[],[f15228,f15225,f14431,f15230]) ).

fof(f15230,plain,
    ( spl0_834
  <=> ! [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_834])]) ).

fof(f14431,plain,
    ( spl0_805
  <=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f15225,plain,
    ( spl0_833
  <=> ! [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_833])]) ).

fof(f15228,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_805
    | ~ spl0_833 ),
    inference(forward_demodulation,[],[f15226,f14433]) ).

fof(f14433,plain,
    ( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_805 ),
    inference(avatar_component_clause,[],[f14431]) ).

fof(f15226,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_833 ),
    inference(avatar_component_clause,[],[f15225]) ).

fof(f15227,plain,
    ( spl0_833
    | ~ spl0_204
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1943,f1938,f1747,f15225]) ).

fof(f1938,plain,
    ( spl0_211
  <=> ! [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_211])]) ).

fof(f1943,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_204
    | ~ spl0_211 ),
    inference(superposition,[],[f1939,f1748]) ).

fof(f1939,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_211 ),
    inference(avatar_component_clause,[],[f1938]) ).

fof(f15223,plain,
    ( spl0_832
    | ~ spl0_51
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1794,f1781,f463,f15221]) ).

fof(f15221,plain,
    ( spl0_832
  <=> ! [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_832])]) ).

fof(f1794,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_51
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f464]) ).

fof(f15191,plain,
    ( spl0_831
    | spl0_122
    | ~ spl0_113
    | ~ spl0_545 ),
    inference(avatar_split_clause,[],[f8389,f7657,f838,f939,f15189]) ).

fof(f15189,plain,
    ( spl0_831
  <=> ! [X0] : ~ inductive(intersection(X0,x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f7657,plain,
    ( spl0_545
  <=> ! [X0] : subclass(intersection(X0,x),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f8389,plain,
    ( ! [X0] :
        ( member(null_class,y)
        | ~ inductive(intersection(X0,x)) )
    | ~ spl0_113
    | ~ spl0_545 ),
    inference(resolution,[],[f7658,f839]) ).

fof(f7658,plain,
    ( ! [X0] : subclass(intersection(X0,x),y)
    | ~ spl0_545 ),
    inference(avatar_component_clause,[],[f7657]) ).

fof(f15013,plain,
    ( spl0_830
    | ~ spl0_79
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2067,f2035,f626,f15011]) ).

fof(f15011,plain,
    ( spl0_830
  <=> ! [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_830])]) ).

fof(f2067,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_79
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f627]) ).

fof(f15009,plain,
    ( spl0_829
    | ~ spl0_79
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2044,f2031,f626,f15007]) ).

fof(f15007,plain,
    ( spl0_829
  <=> ! [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_829])]) ).

fof(f2044,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_79
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f627]) ).

fof(f15004,plain,
    ( spl0_827
    | ~ spl0_828
    | ~ spl0_86
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1909,f1900,f674,f15001,f14998]) ).

fof(f14998,plain,
    ( spl0_827
  <=> ! [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_827])]) ).

fof(f674,plain,
    ( spl0_86
  <=> ! [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_86])]) ).

fof(f1909,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_86
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f675]) ).

fof(f675,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_86 ),
    inference(avatar_component_clause,[],[f674]) ).

fof(f14996,plain,
    ( spl0_826
    | ~ spl0_51
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1716,f1692,f463,f14994]) ).

fof(f14994,plain,
    ( spl0_826
  <=> ! [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_826])]) ).

fof(f1716,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_51
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f464]) ).

fof(f14992,plain,
    ( spl0_825
    | ~ spl0_51
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1696,f1688,f463,f14990]) ).

fof(f14990,plain,
    ( spl0_825
  <=> ! [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_825])]) ).

fof(f1696,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_51
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f464]) ).

fof(f14987,plain,
    ( spl0_824
    | ~ spl0_98
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1459,f1409,f741,f14985]) ).

fof(f14985,plain,
    ( spl0_824
  <=> ! [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_824])]) ).

fof(f741,plain,
    ( spl0_98
  <=> ! [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_98])]) ).

fof(f1459,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_98
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f742]) ).

fof(f742,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_98 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f14980,plain,
    ( ~ spl0_823
    | ~ spl0_248
    | spl0_821 ),
    inference(avatar_split_clause,[],[f14971,f14963,f2393,f14977]) ).

fof(f14977,plain,
    ( spl0_823
  <=> 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_823])]) ).

fof(f14963,plain,
    ( spl0_821
  <=> 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_821])]) ).

fof(f14971,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_248
    | spl0_821 ),
    inference(forward_demodulation,[],[f14964,f2395]) ).

fof(f14964,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_821 ),
    inference(avatar_component_clause,[],[f14963]) ).

fof(f14970,plain,
    ( spl0_542
    | ~ spl0_820
    | spl0_821
    | ~ spl0_822
    | ~ spl0_85
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1252,f1201,f662,f14967,f14963,f14959,f7639]) ).

fof(f7639,plain,
    ( spl0_542
  <=> null_class = domain_of(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f14959,plain,
    ( spl0_820
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f14967,plain,
    ( spl0_822
  <=> 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_822])]) ).

fof(f662,plain,
    ( spl0_85
  <=> ! [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_85])]) ).

fof(f1252,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_85
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f663]) ).

fof(f663,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_85 ),
    inference(avatar_component_clause,[],[f662]) ).

fof(f14950,plain,
    ( ~ spl0_819
    | ~ spl0_248
    | spl0_815 ),
    inference(avatar_split_clause,[],[f14933,f14924,f2393,f14947]) ).

fof(f14947,plain,
    ( spl0_819
  <=> 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_819])]) ).

fof(f14924,plain,
    ( spl0_815
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_815])]) ).

fof(f14933,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_248
    | spl0_815 ),
    inference(forward_demodulation,[],[f14925,f2395]) ).

fof(f14925,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_815 ),
    inference(avatar_component_clause,[],[f14924]) ).

fof(f14945,plain,
    ( ~ spl0_818
    | ~ spl0_248
    | spl0_816 ),
    inference(avatar_split_clause,[],[f14932,f14928,f2393,f14942]) ).

fof(f14942,plain,
    ( spl0_818
  <=> 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_818])]) ).

fof(f14928,plain,
    ( spl0_816
  <=> 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_816])]) ).

fof(f14932,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_248
    | spl0_816 ),
    inference(forward_demodulation,[],[f14930,f2395]) ).

fof(f14930,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_816 ),
    inference(avatar_component_clause,[],[f14928]) ).

fof(f14940,plain,
    ( spl0_122
    | ~ spl0_8
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f8521,f8482,f240,f939]) ).

fof(f240,plain,
    ( spl0_8
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f8482,plain,
    ( spl0_568
  <=> ! [X0] :
        ( ~ subclass(y,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f8521,plain,
    ( member(null_class,y)
    | ~ spl0_8
    | ~ spl0_568 ),
    inference(resolution,[],[f8483,f241]) ).

fof(f241,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f8483,plain,
    ( ! [X0] :
        ( ~ subclass(y,X0)
        | member(null_class,X0) )
    | ~ spl0_568 ),
    inference(avatar_component_clause,[],[f8482]) ).

fof(f14939,plain,
    ( ~ spl0_817
    | ~ spl0_248
    | spl0_814 ),
    inference(avatar_split_clause,[],[f14934,f14920,f2393,f14936]) ).

fof(f14936,plain,
    ( spl0_817
  <=> member(complement(compose(element_relation,complement(singleton_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f14920,plain,
    ( spl0_814
  <=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f14934,plain,
    ( ~ member(complement(compose(element_relation,complement(singleton_relation))),universal_class)
    | ~ spl0_248
    | spl0_814 ),
    inference(forward_demodulation,[],[f14922,f2395]) ).

fof(f14922,plain,
    ( ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | spl0_814 ),
    inference(avatar_component_clause,[],[f14920]) ).

fof(f14931,plain,
    ( spl0_536
    | ~ spl0_814
    | spl0_815
    | ~ spl0_816
    | ~ spl0_85
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1238,f1197,f662,f14928,f14924,f14920,f7603]) ).

fof(f7603,plain,
    ( spl0_536
  <=> null_class = complement(compose(element_relation,complement(identity_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1238,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_85
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f663]) ).

fof(f14908,plain,
    ( spl0_813
    | ~ spl0_41
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1976,f1972,f388,f14906]) ).

fof(f14906,plain,
    ( spl0_813
  <=> ! [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_813])]) ).

fof(f388,plain,
    ( spl0_41
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1976,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_41
    | ~ spl0_215 ),
    inference(resolution,[],[f1973,f389]) ).

fof(f389,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f388]) ).

fof(f14724,plain,
    ( spl0_812
    | ~ spl0_162
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1821,f1809,f1320,f14722]) ).

fof(f14722,plain,
    ( spl0_812
  <=> ! [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_812])]) ).

fof(f1320,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

fof(f1809,plain,
    ( spl0_206
  <=> ! [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_206])]) ).

fof(f1821,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_162
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1321]) ).

fof(f1321,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_162 ),
    inference(avatar_component_clause,[],[f1320]) ).

fof(f1810,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_206 ),
    inference(avatar_component_clause,[],[f1809]) ).

fof(f14720,plain,
    ( spl0_811
    | ~ spl0_161
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1820,f1809,f1316,f14718]) ).

fof(f14718,plain,
    ( spl0_811
  <=> ! [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_811])]) ).

fof(f1316,plain,
    ( spl0_161
  <=> ! [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_161])]) ).

fof(f1820,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_161
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1317]) ).

fof(f1317,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_161 ),
    inference(avatar_component_clause,[],[f1316]) ).

fof(f14715,plain,
    ( ~ spl0_122
    | ~ spl0_153
    | ~ spl0_52
    | spl0_782 ),
    inference(avatar_split_clause,[],[f14106,f13719,f467,f1213,f939]) ).

fof(f1213,plain,
    ( spl0_153
  <=> member(null_class,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f467,plain,
    ( spl0_52
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f13719,plain,
    ( spl0_782
  <=> member(null_class,intersection(y,w)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f14106,plain,
    ( ~ member(null_class,w)
    | ~ member(null_class,y)
    | ~ spl0_52
    | spl0_782 ),
    inference(resolution,[],[f13720,f468]) ).

fof(f468,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f467]) ).

fof(f13720,plain,
    ( ~ member(null_class,intersection(y,w))
    | spl0_782 ),
    inference(avatar_component_clause,[],[f13719]) ).

fof(f14571,plain,
    ( spl0_810
    | ~ spl0_805
    | ~ spl0_809 ),
    inference(avatar_split_clause,[],[f14567,f14564,f14431,f14569]) ).

fof(f14569,plain,
    ( spl0_810
  <=> ! [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_810])]) ).

fof(f14564,plain,
    ( spl0_809
  <=> ! [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_809])]) ).

fof(f14567,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_805
    | ~ spl0_809 ),
    inference(forward_demodulation,[],[f14565,f14433]) ).

fof(f14565,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_809 ),
    inference(avatar_component_clause,[],[f14564]) ).

fof(f14566,plain,
    ( spl0_809
    | ~ spl0_90
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1941,f1938,f692,f14564]) ).

fof(f1941,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_90
    | ~ spl0_211 ),
    inference(resolution,[],[f1939,f693]) ).

fof(f14562,plain,
    ( spl0_808
    | ~ spl0_148
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1727,f1692,f1193,f14560]) ).

fof(f14560,plain,
    ( spl0_808
  <=> ! [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_808])]) ).

fof(f1727,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_148
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f1194]) ).

fof(f14558,plain,
    ( spl0_807
    | ~ spl0_148
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1707,f1688,f1193,f14556]) ).

fof(f14556,plain,
    ( spl0_807
  <=> ! [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_807])]) ).

fof(f1707,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_148
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f1194]) ).

fof(f14437,plain,
    ( spl0_805
    | spl0_806
    | ~ spl0_43
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1979,f1972,f396,f14435,f14431]) ).

fof(f14435,plain,
    ( spl0_806
  <=> ! [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_806])]) ).

fof(f1979,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_43
    | ~ spl0_215 ),
    inference(superposition,[],[f1973,f397]) ).

fof(f14429,plain,
    ( spl0_804
    | ~ spl0_43
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1871,f1839,f396,f14427]) ).

fof(f14427,plain,
    ( spl0_804
  <=> ! [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_804])]) ).

fof(f1871,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_43
    | ~ spl0_208 ),
    inference(superposition,[],[f1840,f397]) ).

fof(f14423,plain,
    ( spl0_802
    | ~ spl0_803
    | ~ spl0_43
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1836,f1829,f396,f14420,f14417]) ).

fof(f14417,plain,
    ( spl0_802
  <=> ! [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_802])]) ).

fof(f14420,plain,
    ( spl0_803
  <=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f1829,plain,
    ( spl0_207
  <=> ! [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_207])]) ).

fof(f1836,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_43
    | ~ spl0_207 ),
    inference(superposition,[],[f1830,f397]) ).

fof(f1830,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_207 ),
    inference(avatar_component_clause,[],[f1829]) ).

fof(f14415,plain,
    ( spl0_801
    | ~ spl0_164
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1539,f1496,f1329,f14413]) ).

fof(f14413,plain,
    ( spl0_801
  <=> ! [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_801])]) ).

fof(f1539,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_164
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f1330]) ).

fof(f14369,plain,
    ( spl0_800
    | ~ spl0_52
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1678,f1671,f467,f14367]) ).

fof(f14367,plain,
    ( spl0_800
  <=> ! [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_800])]) ).

fof(f1678,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_52
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f468]) ).

fof(f14333,plain,
    ( spl0_799
    | ~ spl0_190
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1660,f1652,f1588,f14331]) ).

fof(f14331,plain,
    ( spl0_799
  <=> ! [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_799])]) ).

fof(f1660,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_190
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f1589]) ).

fof(f14305,plain,
    ( ~ spl0_798
    | ~ spl0_14
    | spl0_782 ),
    inference(avatar_split_clause,[],[f14107,f13719,f266,f14302]) ).

fof(f14302,plain,
    ( spl0_798
  <=> inductive(intersection(y,w)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f266,plain,
    ( spl0_14
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f14107,plain,
    ( ~ inductive(intersection(y,w))
    | ~ spl0_14
    | spl0_782 ),
    inference(resolution,[],[f13720,f267]) ).

fof(f267,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f14253,plain,
    ( spl0_797
    | ~ spl0_137
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1891,f1843,f1050,f14251]) ).

fof(f14251,plain,
    ( spl0_797
  <=> ! [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_797])]) ).

fof(f1050,plain,
    ( spl0_137
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1891,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_137
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f1051]) ).

fof(f1051,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1050]) ).

fof(f14249,plain,
    ( spl0_796
    | ~ spl0_137
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1865,f1839,f1050,f14247]) ).

fof(f14247,plain,
    ( spl0_796
  <=> ! [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_796])]) ).

fof(f1865,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_137
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f1051]) ).

fof(f14245,plain,
    ( spl0_795
    | ~ spl0_120
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1825,f1809,f926,f14243]) ).

fof(f14243,plain,
    ( spl0_795
  <=> ! [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_795])]) ).

fof(f926,plain,
    ( spl0_120
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1825,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_120
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f927]) ).

fof(f927,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_120 ),
    inference(avatar_component_clause,[],[f926]) ).

fof(f14241,plain,
    ( spl0_794
    | ~ spl0_95
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1111,f1050,f716,f14239]) ).

fof(f14239,plain,
    ( spl0_794
  <=> ! [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_794])]) ).

fof(f1111,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_95
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f717]) ).

fof(f14062,plain,
    ( spl0_793
    | ~ spl0_154
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1815,f1809,f1264,f14060]) ).

fof(f14060,plain,
    ( spl0_793
  <=> ! [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_793])]) ).

fof(f1264,plain,
    ( spl0_154
  <=> ! [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_154])]) ).

fof(f1815,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_154
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1265]) ).

fof(f1265,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1264]) ).

fof(f14058,plain,
    ( spl0_792
    | ~ spl0_164
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1472,f1409,f1329,f14056]) ).

fof(f14056,plain,
    ( spl0_792
  <=> ! [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_792])]) ).

fof(f1472,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_164
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f1330]) ).

fof(f14054,plain,
    ( spl0_791
    | ~ spl0_82
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1166,f1130,f645,f14052]) ).

fof(f14052,plain,
    ( spl0_791
  <=> ! [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_791])]) ).

fof(f1130,plain,
    ( spl0_143
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1166,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_82
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f646]) ).

fof(f1131,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1130]) ).

fof(f14050,plain,
    ( spl0_790
    | ~ spl0_82
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1148,f1126,f645,f14048]) ).

fof(f14048,plain,
    ( spl0_790
  <=> ! [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_790])]) ).

fof(f1126,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1148,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_82
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f646]) ).

fof(f1127,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1126]) ).

fof(f13984,plain,
    ( spl0_789
    | ~ spl0_41
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1942,f1938,f388,f13982]) ).

fof(f13982,plain,
    ( spl0_789
  <=> ! [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_789])]) ).

fof(f1942,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_41
    | ~ spl0_211 ),
    inference(resolution,[],[f1939,f389]) ).

fof(f13746,plain,
    ( spl0_788
    | ~ spl0_112
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1890,f1843,f834,f13744]) ).

fof(f13744,plain,
    ( spl0_788
  <=> ! [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_788])]) ).

fof(f1890,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_112
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f835]) ).

fof(f13742,plain,
    ( spl0_787
    | ~ spl0_73
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1873,f1843,f586,f13740]) ).

fof(f13740,plain,
    ( spl0_787
  <=> ! [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_787])]) ).

fof(f1873,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_73
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f587]) ).

fof(f13738,plain,
    ( spl0_786
    | ~ spl0_112
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1864,f1839,f834,f13736]) ).

fof(f13736,plain,
    ( spl0_786
  <=> ! [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_786])]) ).

fof(f1864,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_112
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f835]) ).

fof(f13734,plain,
    ( spl0_785
    | ~ spl0_73
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1847,f1839,f586,f13732]) ).

fof(f13732,plain,
    ( spl0_785
  <=> ! [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_785])]) ).

fof(f1847,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_73
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f587]) ).

fof(f13730,plain,
    ( spl0_784
    | ~ spl0_189
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1822,f1809,f1581,f13728]) ).

fof(f13728,plain,
    ( spl0_784
  <=> ! [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_784])]) ).

fof(f1581,plain,
    ( spl0_189
  <=> ! [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_189])]) ).

fof(f1822,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_189
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1582]) ).

fof(f1582,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_189 ),
    inference(avatar_component_clause,[],[f1581]) ).

fof(f13726,plain,
    ( spl0_783
    | ~ spl0_164
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1521,f1492,f1329,f13724]) ).

fof(f13724,plain,
    ( spl0_783
  <=> ! [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_783])]) ).

fof(f1521,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_164
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f1330]) ).

fof(f13722,plain,
    ( ~ spl0_781
    | spl0_782
    | ~ spl0_584
    | ~ spl0_761 ),
    inference(avatar_split_clause,[],[f13242,f12962,f8599,f13719,f13715]) ).

fof(f13715,plain,
    ( spl0_781
  <=> subclass(w,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f8599,plain,
    ( spl0_584
  <=> ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,intersection(y,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f12962,plain,
    ( spl0_761
  <=> ! [X0] :
        ( ~ subclass(w,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f13242,plain,
    ( member(null_class,intersection(y,w))
    | ~ subclass(w,x)
    | ~ spl0_584
    | ~ spl0_761 ),
    inference(resolution,[],[f12963,f8600]) ).

fof(f8600,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(y,X0))
        | ~ subclass(X0,x) )
    | ~ spl0_584 ),
    inference(avatar_component_clause,[],[f8599]) ).

fof(f12963,plain,
    ( ! [X0] :
        ( ~ subclass(w,X0)
        | member(null_class,X0) )
    | ~ spl0_761 ),
    inference(avatar_component_clause,[],[f12962]) ).

fof(f13713,plain,
    ( spl0_780
    | ~ spl0_95
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f883,f834,f716,f13711]) ).

fof(f13711,plain,
    ( spl0_780
  <=> ! [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_780])]) ).

fof(f883,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_95
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f717]) ).

fof(f13627,plain,
    ( spl0_779
    | ~ spl0_124
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1888,f1843,f962,f13625]) ).

fof(f13625,plain,
    ( spl0_779
  <=> ! [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_779])]) ).

fof(f962,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1888,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_124
    | ~ spl0_209 ),
    inference(resolution,[],[f1844,f963]) ).

fof(f963,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f962]) ).

fof(f13623,plain,
    ( spl0_778
    | ~ spl0_124
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1862,f1839,f962,f13621]) ).

fof(f13621,plain,
    ( spl0_778
  <=> ! [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_778])]) ).

fof(f1862,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_124
    | ~ spl0_208 ),
    inference(resolution,[],[f1840,f963]) ).

fof(f13619,plain,
    ( spl0_777
    | ~ spl0_48
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1680,f1671,f447,f13617]) ).

fof(f13617,plain,
    ( spl0_777
  <=> ! [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_777])]) ).

fof(f447,plain,
    ( spl0_48
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1680,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_48
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f448]) ).

fof(f448,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f447]) ).

fof(f13615,plain,
    ( spl0_776
    | ~ spl0_170
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1649,f1646,f1401,f13613]) ).

fof(f13613,plain,
    ( spl0_776
  <=> ! [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_776])]) ).

fof(f1401,plain,
    ( spl0_170
  <=> ! [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_170])]) ).

fof(f1646,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

fof(f1649,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_170
    | ~ spl0_197 ),
    inference(resolution,[],[f1647,f1402]) ).

fof(f1402,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_170 ),
    inference(avatar_component_clause,[],[f1401]) ).

fof(f1647,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_197 ),
    inference(avatar_component_clause,[],[f1646]) ).

fof(f13566,plain,
    ( spl0_775
    | ~ spl0_95
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1021,f962,f716,f13564]) ).

fof(f13564,plain,
    ( spl0_775
  <=> ! [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_775])]) ).

fof(f1021,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_95
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f717]) ).

fof(f13429,plain,
    ( spl0_774
    | ~ spl0_112
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2063,f2035,f834,f13427]) ).

fof(f13427,plain,
    ( spl0_774
  <=> ! [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_774])]) ).

fof(f2063,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_112
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f835]) ).

fof(f13425,plain,
    ( spl0_773
    | ~ spl0_112
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2040,f2031,f834,f13423]) ).

fof(f13423,plain,
    ( spl0_773
  <=> ! [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_773])]) ).

fof(f2040,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_112
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f835]) ).

fof(f13421,plain,
    ( spl0_772
    | ~ spl0_117
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1959,f1955,f855,f13419]) ).

fof(f13419,plain,
    ( spl0_772
  <=> ! [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_772])]) ).

fof(f1959,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_117
    | ~ spl0_213 ),
    inference(resolution,[],[f1956,f856]) ).

fof(f13417,plain,
    ( spl0_771
    | ~ spl0_43
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1895,f1843,f396,f13415]) ).

fof(f13415,plain,
    ( spl0_771
  <=> ! [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_771])]) ).

fof(f1895,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_43
    | ~ spl0_209 ),
    inference(superposition,[],[f1844,f397]) ).

fof(f13413,plain,
    ( spl0_770
    | ~ spl0_341
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f11087,f7046,f3298,f13411]) ).

fof(f3298,plain,
    ( spl0_341
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f11087,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,intersection(w,X0)) )
    | ~ spl0_341
    | ~ spl0_511 ),
    inference(duplicate_literal_removal,[],[f11074]) ).

fof(f11074,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,intersection(w,X0))
        | subclass(X0,intersection(w,X0)) )
    | ~ spl0_341
    | ~ spl0_511 ),
    inference(resolution,[],[f7047,f3299]) ).

fof(f3299,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f3298]) ).

fof(f13409,plain,
    ( spl0_769
    | ~ spl0_169
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1432,f1405,f1391,f13407]) ).

fof(f13407,plain,
    ( spl0_769
  <=> ! [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_769])]) ).

fof(f1405,plain,
    ( spl0_171
  <=> ! [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_171])]) ).

fof(f1432,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_169
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f1392]) ).

fof(f1406,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_171 ),
    inference(avatar_component_clause,[],[f1405]) ).

fof(f13378,plain,
    ( spl0_768
    | ~ spl0_41
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1920,f1900,f388,f13376]) ).

fof(f13376,plain,
    ( spl0_768
  <=> ! [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_768])]) ).

fof(f1920,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_41
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f389]) ).

fof(f13374,plain,
    ( spl0_767
    | ~ spl0_43
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1833,f1829,f396,f13372]) ).

fof(f13372,plain,
    ( spl0_767
  <=> ! [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_767])]) ).

fof(f1833,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_43
    | ~ spl0_207 ),
    inference(superposition,[],[f1830,f397]) ).

fof(f13304,plain,
    ( spl0_766
    | spl0_644
    | ~ spl0_82
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1304,f1290,f645,f9954,f13302]) ).

fof(f13302,plain,
    ( spl0_766
  <=> ! [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_766])]) ).

fof(f1304,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_82
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f646]) ).

fof(f12980,plain,
    ( spl0_765
    | ~ spl0_33
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1924,f1900,f347,f12978]) ).

fof(f12978,plain,
    ( spl0_765
  <=> ! [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_765])]) ).

fof(f1924,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_33
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f348]) ).

fof(f12976,plain,
    ( spl0_764
    | ~ spl0_34
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1923,f1900,f351,f12974]) ).

fof(f12974,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f351,plain,
    ( spl0_34
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f1923,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_34
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f352]) ).

fof(f352,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f12972,plain,
    ( spl0_763
    | ~ spl0_90
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1913,f1900,f692,f12970]) ).

fof(f12970,plain,
    ( spl0_763
  <=> ! [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_763])]) ).

fof(f1913,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_90
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f693]) ).

fof(f12968,plain,
    ( spl0_762
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1786,f1781,f674,f12966]) ).

fof(f12966,plain,
    ( spl0_762
  <=> ! [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_762])]) ).

fof(f1786,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_86
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f675]) ).

fof(f12964,plain,
    ( spl0_761
    | ~ spl0_41
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f12791,f1213,f388,f12962]) ).

fof(f12791,plain,
    ( ! [X0] :
        ( ~ subclass(w,X0)
        | member(null_class,X0) )
    | ~ spl0_41
    | ~ spl0_153 ),
    inference(resolution,[],[f1215,f389]) ).

fof(f1215,plain,
    ( member(null_class,w)
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1213]) ).

fof(f12960,plain,
    ( spl0_760
    | ~ spl0_170
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1779,f1747,f1401,f12958]) ).

fof(f12958,plain,
    ( spl0_760
  <=> ! [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_760])]) ).

fof(f1779,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_170
    | ~ spl0_204 ),
    inference(superposition,[],[f1402,f1748]) ).

fof(f12956,plain,
    ( spl0_759
    | ~ spl0_93
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1761,f1747,f706,f12954]) ).

fof(f12954,plain,
    ( spl0_759
  <=> ! [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_759])]) ).

fof(f706,plain,
    ( spl0_93
  <=> ! [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_93])]) ).

fof(f1761,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_93
    | ~ spl0_204 ),
    inference(superposition,[],[f707,f1748]) ).

fof(f707,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_93 ),
    inference(avatar_component_clause,[],[f706]) ).

fof(f12952,plain,
    ( spl0_758
    | ~ spl0_85
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1224,f1193,f662,f12950]) ).

fof(f12950,plain,
    ( spl0_758
  <=> ! [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_758])]) ).

fof(f1224,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_85
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f663]) ).

fof(f12948,plain,
    ( spl0_757
    | ~ spl0_82
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1088,f1046,f645,f12946]) ).

fof(f12946,plain,
    ( spl0_757
  <=> ! [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_757])]) ).

fof(f1046,plain,
    ( spl0_136
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1088,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_82
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f646]) ).

fof(f1047,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1046]) ).

fof(f12944,plain,
    ( spl0_756
    | ~ spl0_82
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1067,f1042,f645,f12942]) ).

fof(f12942,plain,
    ( spl0_756
  <=> ! [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_756])]) ).

fof(f1042,plain,
    ( spl0_135
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1067,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_82
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f646]) ).

fof(f1043,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1042]) ).

fof(f12789,plain,
    ( spl0_755
    | spl0_153
    | ~ spl0_113
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f12084,f11950,f838,f1213,f12787]) ).

fof(f12787,plain,
    ( spl0_755
  <=> ! [X0] : ~ inductive(intersection(X0,z)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f12084,plain,
    ( ! [X0] :
        ( member(null_class,w)
        | ~ inductive(intersection(X0,z)) )
    | ~ spl0_113
    | ~ spl0_723 ),
    inference(resolution,[],[f11951,f839]) ).

fof(f12629,plain,
    ( spl0_754
    | ~ spl0_11
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2064,f2035,f252,f12627]) ).

fof(f12627,plain,
    ( spl0_754
  <=> ! [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_754])]) ).

fof(f2064,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_218 ),
    inference(resolution,[],[f2036,f253]) ).

fof(f12625,plain,
    ( spl0_753
    | ~ spl0_11
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2041,f2031,f252,f12623]) ).

fof(f12623,plain,
    ( spl0_753
  <=> ! [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_753])]) ).

fof(f2041,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_217 ),
    inference(resolution,[],[f2032,f253]) ).

fof(f12621,plain,
    ( spl0_752
    | ~ spl0_22
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1926,f1900,f299,f12619]) ).

fof(f12619,plain,
    ( spl0_752
  <=> ! [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_752])]) ).

fof(f299,plain,
    ( spl0_22
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1926,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_22
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f300]) ).

fof(f300,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f299]) ).

fof(f12617,plain,
    ( spl0_751
    | spl0_158
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1819,f1809,f1281,f12614]) ).

fof(f12614,plain,
    ( spl0_751
  <=> 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_751])]) ).

fof(f1281,plain,
    ( spl0_158
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1819,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_158
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1283]) ).

fof(f1283,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | spl0_158 ),
    inference(avatar_component_clause,[],[f1281]) ).

fof(f12612,plain,
    ( spl0_750
    | spl0_156
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1818,f1809,f1272,f12609]) ).

fof(f12609,plain,
    ( spl0_750
  <=> 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_750])]) ).

fof(f1272,plain,
    ( spl0_156
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f1818,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_156
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1274]) ).

fof(f1274,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | spl0_156 ),
    inference(avatar_component_clause,[],[f1272]) ).

fof(f12607,plain,
    ( spl0_749
    | ~ spl0_145
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1816,f1809,f1138,f12605]) ).

fof(f12605,plain,
    ( spl0_749
  <=> ! [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_749])]) ).

fof(f1138,plain,
    ( spl0_145
  <=> ! [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_145])]) ).

fof(f1816,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_145
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1139]) ).

fof(f1139,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1138]) ).

fof(f12252,plain,
    ( spl0_748
    | ~ spl0_248
    | ~ spl0_739 ),
    inference(avatar_split_clause,[],[f12214,f12211,f2393,f12250]) ).

fof(f12250,plain,
    ( spl0_748
  <=> ! [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_748])]) ).

fof(f12211,plain,
    ( spl0_739
  <=> ! [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_739])]) ).

fof(f12214,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_248
    | ~ spl0_739 ),
    inference(forward_demodulation,[],[f12212,f2395]) ).

fof(f12212,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_739 ),
    inference(avatar_component_clause,[],[f12211]) ).

fof(f12248,plain,
    ( spl0_747
    | ~ spl0_248
    | ~ spl0_738 ),
    inference(avatar_split_clause,[],[f12209,f12206,f2393,f12246]) ).

fof(f12246,plain,
    ( spl0_747
  <=> ! [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_747])]) ).

fof(f12206,plain,
    ( spl0_738
  <=> ! [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_738])]) ).

fof(f12209,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_248
    | ~ spl0_738 ),
    inference(forward_demodulation,[],[f12207,f2395]) ).

fof(f12207,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_738 ),
    inference(avatar_component_clause,[],[f12206]) ).

fof(f12244,plain,
    ( spl0_746
    | ~ spl0_11
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1948,f1945,f252,f12242]) ).

fof(f12242,plain,
    ( spl0_746
  <=> ! [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_746])]) ).

fof(f1945,plain,
    ( spl0_212
  <=> ! [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_212])]) ).

fof(f1948,plain,
    ( ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_11
    | ~ spl0_212 ),
    inference(resolution,[],[f1946,f253]) ).

fof(f1946,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_212 ),
    inference(avatar_component_clause,[],[f1945]) ).

fof(f12240,plain,
    ( ~ spl0_745
    | ~ spl0_248
    | spl0_744 ),
    inference(avatar_split_clause,[],[f12235,f12231,f2393,f12237]) ).

fof(f12237,plain,
    ( spl0_745
  <=> subclass(composition_function,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f12231,plain,
    ( spl0_744
  <=> subclass(composition_function,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f12235,plain,
    ( ~ subclass(composition_function,singleton_relation)
    | ~ spl0_248
    | spl0_744 ),
    inference(forward_demodulation,[],[f12233,f2395]) ).

fof(f12233,plain,
    ( ~ subclass(composition_function,identity_relation)
    | spl0_744 ),
    inference(avatar_component_clause,[],[f12231]) ).

fof(f12234,plain,
    ( spl0_743
    | ~ spl0_744
    | ~ spl0_109
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1934,f1900,f793,f12231,f12228]) ).

fof(f12228,plain,
    ( spl0_743
  <=> ! [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_743])]) ).

fof(f793,plain,
    ( spl0_109
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1934,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_109
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f794]) ).

fof(f794,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f793]) ).

fof(f12226,plain,
    ( spl0_742
    | ~ spl0_166
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1777,f1747,f1351,f12224]) ).

fof(f12224,plain,
    ( spl0_742
  <=> ! [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_742])]) ).

fof(f1351,plain,
    ( spl0_166
  <=> ! [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_166])]) ).

fof(f1777,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_166
    | ~ spl0_204 ),
    inference(superposition,[],[f1352,f1748]) ).

fof(f1352,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1351]) ).

fof(f12222,plain,
    ( spl0_741
    | spl0_153
    | ~ spl0_113
    | ~ spl0_714 ),
    inference(avatar_split_clause,[],[f12017,f11900,f838,f1213,f12220]) ).

fof(f12220,plain,
    ( spl0_741
  <=> ! [X0] : ~ inductive(intersection(z,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f12017,plain,
    ( ! [X0] :
        ( member(null_class,w)
        | ~ inductive(intersection(z,X0)) )
    | ~ spl0_113
    | ~ spl0_714 ),
    inference(resolution,[],[f11901,f839]) ).

fof(f12218,plain,
    ( spl0_740
    | ~ spl0_148
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1668,f1652,f1193,f12216]) ).

fof(f12216,plain,
    ( spl0_740
  <=> ! [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_740])]) ).

fof(f1668,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_148
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f1194]) ).

fof(f12213,plain,
    ( spl0_739
    | ~ spl0_150
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1665,f1652,f1201,f12211]) ).

fof(f1665,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_150
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f1202]) ).

fof(f12208,plain,
    ( spl0_738
    | ~ spl0_149
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1662,f1652,f1197,f12206]) ).

fof(f1662,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_149
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f1198]) ).

fof(f12170,plain,
    ( spl0_737
    | ~ spl0_42
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1824,f1809,f392,f12168]) ).

fof(f12168,plain,
    ( spl0_737
  <=> ! [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_737])]) ).

fof(f1824,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_42
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f393]) ).

fof(f12166,plain,
    ( spl0_736
    | ~ spl0_90
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1790,f1781,f692,f12164]) ).

fof(f12164,plain,
    ( spl0_736
  <=> ! [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_736])]) ).

fof(f1790,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_90
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f693]) ).

fof(f12162,plain,
    ( spl0_735
    | ~ spl0_96
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f915,f855,f732,f12160]) ).

fof(f12160,plain,
    ( spl0_735
  <=> ! [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_735])]) ).

fof(f732,plain,
    ( spl0_96
  <=> ! [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_96])]) ).

fof(f915,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_96
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f733]) ).

fof(f733,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_96 ),
    inference(avatar_component_clause,[],[f732]) ).

fof(f12064,plain,
    ( spl0_734
    | ~ spl0_53
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1870,f1839,f471,f12062]) ).

fof(f12062,plain,
    ( spl0_734
  <=> ! [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_734])]) ).

fof(f1870,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_53
    | ~ spl0_208 ),
    inference(superposition,[],[f1840,f472]) ).

fof(f12060,plain,
    ( spl0_733
    | ~ spl0_139
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1776,f1747,f1058,f12058]) ).

fof(f12058,plain,
    ( spl0_733
  <=> ! [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_733])]) ).

fof(f1058,plain,
    ( spl0_139
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f1776,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_139
    | ~ spl0_204 ),
    inference(superposition,[],[f1059,f1748]) ).

fof(f1059,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1058]) ).

fof(f12056,plain,
    ( spl0_732
    | ~ spl0_51
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1656,f1652,f463,f12054]) ).

fof(f12054,plain,
    ( spl0_732
  <=> ! [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_732])]) ).

fof(f1656,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_51
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f464]) ).

fof(f12027,plain,
    ( spl0_731
    | ~ spl0_53
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1835,f1829,f471,f12025]) ).

fof(f12025,plain,
    ( spl0_731
  <=> ! [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_731])]) ).

fof(f1835,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_53
    | ~ spl0_207 ),
    inference(superposition,[],[f1830,f472]) ).

fof(f12023,plain,
    ( spl0_730
    | ~ spl0_53
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1832,f1829,f471,f12021]) ).

fof(f12021,plain,
    ( spl0_730
  <=> ! [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_730])]) ).

fof(f1832,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_53
    | ~ spl0_207 ),
    inference(superposition,[],[f1830,f472]) ).

fof(f12013,plain,
    ( spl0_729
    | ~ spl0_90
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1760,f1747,f692,f12011]) ).

fof(f12011,plain,
    ( spl0_729
  <=> ! [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_729])]) ).

fof(f1760,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_90
    | ~ spl0_204 ),
    inference(superposition,[],[f693,f1748]) ).

fof(f11985,plain,
    ( spl0_728
    | ~ spl0_79
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1965,f1955,f626,f11983]) ).

fof(f11983,plain,
    ( spl0_728
  <=> ! [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_728])]) ).

fof(f1965,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_79
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f1958]) ).

fof(f1958,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_79
    | ~ spl0_213 ),
    inference(resolution,[],[f1956,f627]) ).

fof(f11981,plain,
    ( spl0_727
    | ~ spl0_144
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1812,f1809,f1134,f11979]) ).

fof(f11979,plain,
    ( spl0_727
  <=> ! [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_727])]) ).

fof(f1134,plain,
    ( spl0_144
  <=> ! [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_144])]) ).

fof(f1812,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_144
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f1135]) ).

fof(f1135,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1134]) ).

fof(f11967,plain,
    ( spl0_726
    | ~ spl0_32
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1771,f1747,f343,f11965]) ).

fof(f11965,plain,
    ( spl0_726
  <=> ! [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_726])]) ).

fof(f343,plain,
    ( spl0_32
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f1771,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_32
    | ~ spl0_204 ),
    inference(superposition,[],[f344,f1748]) ).

fof(f344,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f11963,plain,
    ( ~ spl0_724
    | spl0_725
    | ~ spl0_172
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1600,f1588,f1409,f11961,f11957]) ).

fof(f11957,plain,
    ( spl0_724
  <=> 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_724])]) ).

fof(f11961,plain,
    ( spl0_725
  <=> ! [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_725])]) ).

fof(f1600,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_172
    | ~ spl0_190 ),
    inference(resolution,[],[f1589,f1410]) ).

fof(f11952,plain,
    ( spl0_723
    | ~ spl0_236
    | ~ spl0_705 ),
    inference(avatar_split_clause,[],[f11747,f11374,f2211,f11950]) ).

fof(f2211,plain,
    ( spl0_236
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f11374,plain,
    ( spl0_705
  <=> ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,w) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f11747,plain,
    ( ! [X0] : subclass(intersection(X0,z),w)
    | ~ spl0_236
    | ~ spl0_705 ),
    inference(resolution,[],[f11375,f2212]) ).

fof(f2212,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f2211]) ).

fof(f11375,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,w) )
    | ~ spl0_705 ),
    inference(avatar_component_clause,[],[f11374]) ).

fof(f11948,plain,
    ( spl0_722
    | ~ spl0_41
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1793,f1781,f388,f11946]) ).

fof(f11946,plain,
    ( spl0_722
  <=> ! [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_722])]) ).

fof(f1793,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_41
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f389]) ).

fof(f11941,plain,
    ( ~ spl0_721
    | ~ spl0_248
    | spl0_719 ),
    inference(avatar_split_clause,[],[f11936,f11928,f2393,f11938]) ).

fof(f11938,plain,
    ( spl0_721
  <=> 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_721])]) ).

fof(f11928,plain,
    ( spl0_719
  <=> 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_719])]) ).

fof(f11936,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_248
    | spl0_719 ),
    inference(forward_demodulation,[],[f11930,f2395]) ).

fof(f11930,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_719 ),
    inference(avatar_component_clause,[],[f11928]) ).

fof(f11935,plain,
    ( ~ spl0_719
    | ~ spl0_720
    | spl0_443
    | ~ spl0_133
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1683,f1671,f1001,f5681,f11932,f11928]) ).

fof(f11932,plain,
    ( spl0_720
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f5681,plain,
    ( spl0_443
  <=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f1683,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_133
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f1002]) ).

fof(f11923,plain,
    ( ~ spl0_718
    | ~ spl0_248
    | spl0_715 ),
    inference(avatar_split_clause,[],[f11913,f11904,f2393,f11920]) ).

fof(f11920,plain,
    ( spl0_718
  <=> 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_718])]) ).

fof(f11904,plain,
    ( spl0_715
  <=> 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_715])]) ).

fof(f11913,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_248
    | spl0_715 ),
    inference(forward_demodulation,[],[f11906,f2395]) ).

fof(f11906,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_715 ),
    inference(avatar_component_clause,[],[f11904]) ).

fof(f11918,plain,
    ( ~ spl0_717
    | ~ spl0_248
    | spl0_716 ),
    inference(avatar_split_clause,[],[f11912,f11908,f2393,f11915]) ).

fof(f11915,plain,
    ( spl0_717
  <=> member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f11908,plain,
    ( spl0_716
  <=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f11912,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class)
    | ~ spl0_248
    | spl0_716 ),
    inference(forward_demodulation,[],[f11910,f2395]) ).

fof(f11910,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | spl0_716 ),
    inference(avatar_component_clause,[],[f11908]) ).

fof(f11911,plain,
    ( ~ spl0_715
    | ~ spl0_716
    | spl0_439
    | ~ spl0_132
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1681,f1671,f997,f5651,f11908,f11904]) ).

fof(f5651,plain,
    ( spl0_439
  <=> null_class = complement(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f1681,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_132
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f998]) ).

fof(f11902,plain,
    ( spl0_714
    | ~ spl0_235
    | ~ spl0_705 ),
    inference(avatar_split_clause,[],[f11746,f11374,f2207,f11900]) ).

fof(f11746,plain,
    ( ! [X0] : subclass(intersection(z,X0),w)
    | ~ spl0_235
    | ~ spl0_705 ),
    inference(resolution,[],[f11375,f2208]) ).

fof(f11875,plain,
    ( spl0_713
    | ~ spl0_33
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1797,f1781,f347,f11873]) ).

fof(f11873,plain,
    ( spl0_713
  <=> ! [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_713])]) ).

fof(f1797,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_33
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f348]) ).

fof(f11871,plain,
    ( spl0_712
    | ~ spl0_34
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1796,f1781,f351,f11869]) ).

fof(f11869,plain,
    ( spl0_712
  <=> ! [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_712])]) ).

fof(f1796,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_34
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f352]) ).

fof(f11773,plain,
    ( spl0_711
    | ~ spl0_22
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1799,f1781,f299,f11771]) ).

fof(f11771,plain,
    ( spl0_711
  <=> ! [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_711])]) ).

fof(f1799,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_22
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f300]) ).

fof(f11769,plain,
    ( spl0_710
    | ~ spl0_51
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1772,f1747,f463,f11767]) ).

fof(f11767,plain,
    ( spl0_710
  <=> ! [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_710])]) ).

fof(f1772,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_51
    | ~ spl0_204 ),
    inference(superposition,[],[f464,f1748]) ).

fof(f11742,plain,
    ( spl0_709
    | ~ spl0_248
    | ~ spl0_707 ),
    inference(avatar_split_clause,[],[f11734,f11731,f2393,f11740]) ).

fof(f11740,plain,
    ( spl0_709
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),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)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f11731,plain,
    ( spl0_707
  <=> ! [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_707])]) ).

fof(f11734,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),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)))),subset_relation) )
    | ~ spl0_248
    | ~ spl0_707 ),
    inference(forward_demodulation,[],[f11732,f2395]) ).

fof(f11732,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_707 ),
    inference(avatar_component_clause,[],[f11731]) ).

fof(f11738,plain,
    ( spl0_708
    | ~ spl0_108
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1807,f1781,f789,f11736]) ).

fof(f11736,plain,
    ( spl0_708
  <=> ! [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_708])]) ).

fof(f789,plain,
    ( spl0_108
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1807,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_108
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f790]) ).

fof(f790,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f789]) ).

fof(f11733,plain,
    ( spl0_707
    | ~ spl0_109
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1805,f1781,f793,f11731]) ).

fof(f1805,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_109
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f794]) ).

fof(f11729,plain,
    ( spl0_706
    | ~ spl0_134
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1774,f1747,f1005,f11727]) ).

fof(f11727,plain,
    ( spl0_706
  <=> ! [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_706])]) ).

fof(f1005,plain,
    ( spl0_134
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1774,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_134
    | ~ spl0_204 ),
    inference(superposition,[],[f1006,f1748]) ).

fof(f1006,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | null_class = X1
        | null_class = X0 )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1005]) ).

fof(f11376,plain,
    ( spl0_705
    | ~ spl0_29
    | ~ spl0_511 ),
    inference(avatar_split_clause,[],[f11095,f7046,f331,f11374]) ).

fof(f331,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f11095,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,w) )
    | ~ spl0_29
    | ~ spl0_511 ),
    inference(duplicate_literal_removal,[],[f11066]) ).

fof(f11066,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | subclass(X0,w)
        | subclass(X0,w) )
    | ~ spl0_29
    | ~ spl0_511 ),
    inference(resolution,[],[f7047,f332]) ).

fof(f332,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f331]) ).

fof(f11343,plain,
    ( spl0_704
    | ~ spl0_41
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1740,f1736,f388,f11341]) ).

fof(f11341,plain,
    ( spl0_704
  <=> ! [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_704])]) ).

fof(f1736,plain,
    ( spl0_202
  <=> ! [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_202])]) ).

fof(f1740,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_41
    | ~ spl0_202 ),
    inference(resolution,[],[f1737,f389]) ).

fof(f1737,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_202 ),
    inference(avatar_component_clause,[],[f1736]) ).

fof(f11339,plain,
    ( spl0_703
    | ~ spl0_33
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1719,f1692,f347,f11337]) ).

fof(f11337,plain,
    ( spl0_703
  <=> ! [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_703])]) ).

fof(f1719,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_33
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f348]) ).

fof(f11335,plain,
    ( spl0_702
    | ~ spl0_34
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1718,f1692,f351,f11333]) ).

fof(f11333,plain,
    ( spl0_702
  <=> ! [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_702])]) ).

fof(f1718,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_34
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f352]) ).

fof(f11331,plain,
    ( spl0_701
    | ~ spl0_33
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1699,f1688,f347,f11329]) ).

fof(f11329,plain,
    ( spl0_701
  <=> ! [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_701])]) ).

fof(f1699,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_33
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f348]) ).

fof(f11327,plain,
    ( spl0_700
    | ~ spl0_34
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1698,f1688,f351,f11325]) ).

fof(f11325,plain,
    ( spl0_700
  <=> ! [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_700])]) ).

fof(f1698,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_34
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f352]) ).

fof(f11323,plain,
    ( spl0_699
    | ~ spl0_53
    | ~ spl0_73
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1448,f1405,f586,f471,f11321]) ).

fof(f11321,plain,
    ( spl0_699
  <=> ! [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_699])]) ).

fof(f1448,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_53
    | ~ spl0_73
    | ~ spl0_171 ),
    inference(forward_demodulation,[],[f1435,f472]) ).

fof(f1435,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_73
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f587]) ).

fof(f11063,plain,
    ( spl0_698
    | spl0_130
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1817,f1809,f988,f11060]) ).

fof(f11060,plain,
    ( spl0_698
  <=> 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_698])]) ).

fof(f988,plain,
    ( spl0_130
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f1817,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_130
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f990]) ).

fof(f990,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | spl0_130 ),
    inference(avatar_component_clause,[],[f988]) ).

fof(f11058,plain,
    ( spl0_697
    | spl0_128
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1814,f1809,f979,f11055]) ).

fof(f11055,plain,
    ( spl0_697
  <=> 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_697])]) ).

fof(f979,plain,
    ( spl0_128
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1814,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_128
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f981]) ).

fof(f981,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_128 ),
    inference(avatar_component_clause,[],[f979]) ).

fof(f11053,plain,
    ( spl0_696
    | spl0_126
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1813,f1809,f970,f11050]) ).

fof(f11050,plain,
    ( spl0_696
  <=> 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_696])]) ).

fof(f970,plain,
    ( spl0_126
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1813,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_126
    | ~ spl0_206 ),
    inference(resolution,[],[f1810,f972]) ).

fof(f972,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_126 ),
    inference(avatar_component_clause,[],[f970]) ).

fof(f10878,plain,
    ( spl0_695
    | ~ spl0_160
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1347,f1329,f1290,f10876]) ).

fof(f10876,plain,
    ( spl0_695
  <=> ! [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_695])]) ).

fof(f1347,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_160
    | ~ spl0_164 ),
    inference(resolution,[],[f1330,f1291]) ).

fof(f10874,plain,
    ( spl0_694
    | ~ spl0_98
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f874,f834,f741,f10872]) ).

fof(f10872,plain,
    ( spl0_694
  <=> ! [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_694])]) ).

fof(f874,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_98
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f742]) ).

fof(f10870,plain,
    ( spl0_693
    | ~ spl0_97
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f873,f834,f737,f10868]) ).

fof(f10868,plain,
    ( spl0_693
  <=> ! [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_693])]) ).

fof(f873,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_97
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f738]) ).

fof(f10835,plain,
    ( spl0_691
    | ~ spl0_692
    | ~ spl0_81
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1912,f1900,f641,f10832,f10829]) ).

fof(f10829,plain,
    ( spl0_691
  <=> ! [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_691])]) ).

fof(f10832,plain,
    ( spl0_692
  <=> subclass(composition_function,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f641,plain,
    ( spl0_81
  <=> ! [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_81])]) ).

fof(f1912,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_81
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f642]) ).

fof(f642,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_81 ),
    inference(avatar_component_clause,[],[f641]) ).

fof(f10827,plain,
    ( spl0_690
    | ~ spl0_81
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1789,f1781,f641,f10825]) ).

fof(f10825,plain,
    ( spl0_690
  <=> ! [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_690])]) ).

fof(f1789,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_81
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f642]) ).

fof(f10823,plain,
    ( spl0_689
    | ~ spl0_148
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1541,f1496,f1193,f10821]) ).

fof(f10821,plain,
    ( spl0_689
  <=> ! [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_689])]) ).

fof(f1541,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_148
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f1194]) ).

fof(f10819,plain,
    ( spl0_688
    | ~ spl0_448
    | ~ spl0_149
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1535,f1496,f1197,f5706,f10817]) ).

fof(f10817,plain,
    ( spl0_688
  <=> ! [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_688])]) ).

fof(f5706,plain,
    ( spl0_448
  <=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f1535,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_149
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f1198]) ).

fof(f10715,plain,
    ( spl0_687
    | ~ spl0_138
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1775,f1747,f1054,f10713]) ).

fof(f10713,plain,
    ( spl0_687
  <=> ! [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_687])]) ).

fof(f1054,plain,
    ( spl0_138
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1775,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_138
    | ~ spl0_204 ),
    inference(superposition,[],[f1055,f1748]) ).

fof(f1055,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1054]) ).

fof(f10711,plain,
    ( spl0_686
    | ~ spl0_81
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1756,f1747,f641,f10709]) ).

fof(f10709,plain,
    ( spl0_686
  <=> ! [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_686])]) ).

fof(f1756,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_81
    | ~ spl0_204 ),
    inference(superposition,[],[f642,f1748]) ).

fof(f10707,plain,
    ( spl0_685
    | ~ spl0_22
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1721,f1692,f299,f10705]) ).

fof(f10705,plain,
    ( spl0_685
  <=> ! [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_685])]) ).

fof(f1721,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_22
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f300]) ).

fof(f10703,plain,
    ( spl0_684
    | ~ spl0_22
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1701,f1688,f299,f10701]) ).

fof(f10701,plain,
    ( spl0_684
  <=> ! [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_684])]) ).

fof(f1701,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_22
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f300]) ).

fof(f10695,plain,
    ( ~ spl0_682
    | ~ spl0_683
    | spl0_357
    | ~ spl0_117
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1677,f1671,f855,f3576,f10692,f10688]) ).

fof(f10688,plain,
    ( spl0_682
  <=> 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_682])]) ).

fof(f10692,plain,
    ( spl0_683
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f3576,plain,
    ( spl0_357
  <=> null_class = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f1677,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_117
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f856]) ).

fof(f10360,plain,
    ( spl0_681
    | ~ spl0_181
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1768,f1747,f1508,f10358]) ).

fof(f10358,plain,
    ( spl0_681
  <=> ! [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_681])]) ).

fof(f1768,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_181
    | ~ spl0_204 ),
    inference(superposition,[],[f1509,f1748]) ).

fof(f10356,plain,
    ( spl0_680
    | ~ spl0_119
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1723,f1692,f922,f10354]) ).

fof(f10354,plain,
    ( spl0_680
  <=> ! [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_680])]) ).

fof(f922,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1723,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_119
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f923]) ).

fof(f923,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f922]) ).

fof(f10352,plain,
    ( spl0_679
    | ~ spl0_41
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1715,f1692,f388,f10350]) ).

fof(f10350,plain,
    ( spl0_679
  <=> ! [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_679])]) ).

fof(f1715,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_41
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f389]) ).

fof(f10348,plain,
    ( spl0_678
    | ~ spl0_119
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1703,f1688,f922,f10346]) ).

fof(f10346,plain,
    ( spl0_678
  <=> ! [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_678])]) ).

fof(f1703,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_119
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f923]) ).

fof(f10344,plain,
    ( spl0_677
    | ~ spl0_41
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1695,f1688,f388,f10342]) ).

fof(f10342,plain,
    ( spl0_677
  <=> ! [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_677])]) ).

fof(f1695,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_41
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f389]) ).

fof(f10340,plain,
    ( spl0_676
    | ~ spl0_131
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1684,f1671,f993,f10338]) ).

fof(f10338,plain,
    ( spl0_676
  <=> ! [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_676])]) ).

fof(f1684,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_131
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f994]) ).

fof(f10336,plain,
    ( spl0_675
    | ~ spl0_51
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1530,f1496,f463,f10334]) ).

fof(f10334,plain,
    ( spl0_675
  <=> ! [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_675])]) ).

fof(f1530,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_51
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f464]) ).

fof(f10332,plain,
    ( spl0_674
    | ~ spl0_148
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1523,f1492,f1193,f10330]) ).

fof(f10330,plain,
    ( spl0_674
  <=> ! [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_674])]) ).

fof(f1523,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_148
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f1194]) ).

fof(f10328,plain,
    ( ~ spl0_448
    | spl0_673
    | ~ spl0_149
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1517,f1492,f1197,f10326,f5706]) ).

fof(f10326,plain,
    ( spl0_673
  <=> ! [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_673])]) ).

fof(f1517,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_149
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f1198]) ).

fof(f10324,plain,
    ( spl0_672
    | ~ spl0_148
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1474,f1409,f1193,f10322]) ).

fof(f10322,plain,
    ( spl0_672
  <=> ! [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_672])]) ).

fof(f1474,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_148
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f1194]) ).

fof(f10319,plain,
    ( spl0_670
    | ~ spl0_671
    | ~ spl0_150
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1471,f1409,f1201,f10316,f10313]) ).

fof(f10313,plain,
    ( spl0_670
  <=> ! [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_670])]) ).

fof(f10316,plain,
    ( spl0_671
  <=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f1471,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_150
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f1202]) ).

fof(f10311,plain,
    ( spl0_667
    | spl0_668
    | ~ spl0_669
    | ~ spl0_43
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f10160,f10037,f396,f10308,f10304,f10300]) ).

fof(f10300,plain,
    ( spl0_667
  <=> null_class = x ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f10304,plain,
    ( spl0_668
  <=> null_class = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f10308,plain,
    ( spl0_669
  <=> subclass(y,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f10037,plain,
    ( spl0_647
  <=> ! [X0] :
        ( ~ subclass(y,intersection(x,X0))
        | y = intersection(x,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f10160,plain,
    ( ~ subclass(y,null_class)
    | null_class = y
    | null_class = x
    | ~ spl0_43
    | ~ spl0_647 ),
    inference(superposition,[],[f10038,f397]) ).

fof(f10038,plain,
    ( ! [X0] :
        ( ~ subclass(y,intersection(x,X0))
        | y = intersection(x,X0) )
    | ~ spl0_647 ),
    inference(avatar_component_clause,[],[f10037]) ).

fof(f10298,plain,
    ( ~ spl0_666
    | ~ spl0_248
    | spl0_665 ),
    inference(avatar_split_clause,[],[f10293,f10289,f2393,f10295]) ).

fof(f10295,plain,
    ( spl0_666
  <=> subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f10289,plain,
    ( spl0_665
  <=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f10293,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_248
    | spl0_665 ),
    inference(forward_demodulation,[],[f10291,f2395]) ).

fof(f10291,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
    | spl0_665 ),
    inference(avatar_component_clause,[],[f10289]) ).

fof(f10292,plain,
    ( spl0_664
    | ~ spl0_665
    | ~ spl0_149
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1468,f1409,f1197,f10289,f10286]) ).

fof(f10286,plain,
    ( spl0_664
  <=> ! [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_664])]) ).

fof(f1468,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_149
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f1198]) ).

fof(f10284,plain,
    ( spl0_663
    | ~ spl0_82
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1106,f1050,f645,f10282]) ).

fof(f10282,plain,
    ( spl0_663
  <=> ! [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_663])]) ).

fof(f1106,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_82
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f646]) ).

fof(f10278,plain,
    ( spl0_662
    | ~ spl0_88
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1759,f1747,f683,f10276]) ).

fof(f10276,plain,
    ( spl0_662
  <=> ! [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_662])]) ).

fof(f683,plain,
    ( spl0_88
  <=> ! [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_88])]) ).

fof(f1759,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_88
    | ~ spl0_204 ),
    inference(superposition,[],[f684,f1748]) ).

fof(f684,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_88 ),
    inference(avatar_component_clause,[],[f683]) ).

fof(f10151,plain,
    ( spl0_661
    | ~ spl0_74
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1914,f1900,f597,f10149]) ).

fof(f10149,plain,
    ( spl0_661
  <=> ! [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_661])]) ).

fof(f597,plain,
    ( spl0_74
  <=> ! [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_74])]) ).

fof(f1914,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_74
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f598]) ).

fof(f598,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_74 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f10147,plain,
    ( spl0_660
    | ~ spl0_31
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1770,f1747,f339,f10145]) ).

fof(f10145,plain,
    ( spl0_660
  <=> ! [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_660])]) ).

fof(f339,plain,
    ( spl0_31
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1770,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_31
    | ~ spl0_204 ),
    inference(superposition,[],[f340,f1748]) ).

fof(f340,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f339]) ).

fof(f10143,plain,
    ( spl0_659
    | ~ spl0_51
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1512,f1492,f463,f10141]) ).

fof(f10141,plain,
    ( spl0_659
  <=> ! [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_659])]) ).

fof(f1512,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_51
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f464]) ).

fof(f10139,plain,
    ( spl0_658
    | ~ spl0_51
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1463,f1409,f463,f10137]) ).

fof(f10137,plain,
    ( spl0_658
  <=> ! [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_658])]) ).

fof(f1463,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_51
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f464]) ).

fof(f10135,plain,
    ( spl0_657
    | ~ spl0_52
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1431,f1405,f467,f10133]) ).

fof(f10133,plain,
    ( spl0_657
  <=> ! [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_657])]) ).

fof(f1431,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_52
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f468]) ).

fof(f10131,plain,
    ( spl0_656
    | ~ spl0_123
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1398,f1391,f958,f10129]) ).

fof(f10129,plain,
    ( spl0_656
  <=> ! [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_656])]) ).

fof(f958,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1398,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_123
    | ~ spl0_169 ),
    inference(resolution,[],[f1392,f959]) ).

fof(f959,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f958]) ).

fof(f10097,plain,
    ( spl0_655
    | ~ spl0_42
    | ~ spl0_545 ),
    inference(avatar_split_clause,[],[f8390,f7657,f392,f10095]) ).

fof(f10095,plain,
    ( spl0_655
  <=> ! [X0] :
        ( ~ subclass(y,intersection(X0,x))
        | y = intersection(X0,x) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f8390,plain,
    ( ! [X0] :
        ( ~ subclass(y,intersection(X0,x))
        | y = intersection(X0,x) )
    | ~ spl0_42
    | ~ spl0_545 ),
    inference(resolution,[],[f7658,f393]) ).

fof(f10086,plain,
    ( spl0_654
    | ~ spl0_248
    | ~ spl0_650 ),
    inference(avatar_split_clause,[],[f10061,f10056,f2393,f10084]) ).

fof(f10084,plain,
    ( spl0_654
  <=> ! [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_654])]) ).

fof(f10056,plain,
    ( spl0_650
  <=> ! [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_650])]) ).

fof(f10061,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_248
    | ~ spl0_650 ),
    inference(forward_demodulation,[],[f10060,f2395]) ).

fof(f10060,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_248
    | ~ spl0_650 ),
    inference(forward_demodulation,[],[f10059,f2395]) ).

fof(f10059,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_248
    | ~ spl0_650 ),
    inference(forward_demodulation,[],[f10057,f2395]) ).

fof(f10057,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_650 ),
    inference(avatar_component_clause,[],[f10056]) ).

fof(f10073,plain,
    ( spl0_653
    | ~ spl0_248
    | ~ spl0_648 ),
    inference(avatar_split_clause,[],[f10050,f10045,f2393,f10071]) ).

fof(f10071,plain,
    ( spl0_653
  <=> ! [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_653])]) ).

fof(f10045,plain,
    ( spl0_648
  <=> ! [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_648])]) ).

fof(f10050,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_248
    | ~ spl0_648 ),
    inference(forward_demodulation,[],[f10049,f2395]) ).

fof(f10049,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_248
    | ~ spl0_648 ),
    inference(forward_demodulation,[],[f10048,f2395]) ).

fof(f10048,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_248
    | ~ spl0_648 ),
    inference(forward_demodulation,[],[f10046,f2395]) ).

fof(f10046,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_648 ),
    inference(avatar_component_clause,[],[f10045]) ).

fof(f10069,plain,
    ( spl0_652
    | ~ spl0_71
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1907,f1900,f578,f10067]) ).

fof(f10067,plain,
    ( spl0_652
  <=> ! [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_652])]) ).

fof(f578,plain,
    ( spl0_71
  <=> ! [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_71])]) ).

fof(f1907,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_71
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f579]) ).

fof(f579,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_71 ),
    inference(avatar_component_clause,[],[f578]) ).

fof(f10065,plain,
    ( spl0_651
    | ~ spl0_108
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1728,f1692,f789,f10063]) ).

fof(f10063,plain,
    ( spl0_651
  <=> ! [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_651])]) ).

fof(f1728,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_108
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f790]) ).

fof(f10058,plain,
    ( spl0_650
    | ~ spl0_109
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1726,f1692,f793,f10056]) ).

fof(f1726,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_109
    | ~ spl0_201 ),
    inference(resolution,[],[f1693,f794]) ).

fof(f10054,plain,
    ( spl0_649
    | ~ spl0_108
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1708,f1688,f789,f10052]) ).

fof(f10052,plain,
    ( spl0_649
  <=> ! [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_649])]) ).

fof(f1708,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_108
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f790]) ).

fof(f10047,plain,
    ( spl0_648
    | ~ spl0_109
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1706,f1688,f793,f10045]) ).

fof(f1706,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_109
    | ~ spl0_200 ),
    inference(resolution,[],[f1689,f794]) ).

fof(f10039,plain,
    ( spl0_647
    | ~ spl0_42
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f7703,f7599,f392,f10037]) ).

fof(f7599,plain,
    ( spl0_535
  <=> ! [X0] : subclass(intersection(x,X0),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f7703,plain,
    ( ! [X0] :
        ( ~ subclass(y,intersection(x,X0))
        | y = intersection(x,X0) )
    | ~ spl0_42
    | ~ spl0_535 ),
    inference(resolution,[],[f7600,f393]) ).

fof(f7600,plain,
    ( ! [X0] : subclass(intersection(x,X0),y)
    | ~ spl0_535 ),
    inference(avatar_component_clause,[],[f7599]) ).

fof(f10035,plain,
    ( spl0_645
    | ~ spl0_646
    | ~ spl0_118
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1399,f1391,f918,f10032,f10028]) ).

fof(f10032,plain,
    ( spl0_646
  <=> 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_646])]) ).

fof(f918,plain,
    ( spl0_118
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1399,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_118
    | ~ spl0_169 ),
    inference(resolution,[],[f1392,f919]) ).

fof(f919,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f918]) ).

fof(f9956,plain,
    ( spl0_643
    | spl0_644
    | ~ spl0_82
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f879,f834,f645,f9954,f9951]) ).

fof(f9951,plain,
    ( spl0_643
  <=> ! [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_643])]) ).

fof(f879,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_82
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f646]) ).

fof(f9898,plain,
    ( spl0_641
    | ~ spl0_642
    | ~ spl0_67
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1915,f1900,f557,f9895,f9892]) ).

fof(f9892,plain,
    ( spl0_641
  <=> ! [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_641])]) ).

fof(f9895,plain,
    ( spl0_642
  <=> subclass(composition_function,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f557,plain,
    ( spl0_67
  <=> ! [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_67])]) ).

fof(f1915,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_67
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f558]) ).

fof(f558,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f557]) ).

fof(f9890,plain,
    ( spl0_640
    | ~ spl0_90
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1455,f1409,f692,f9888]) ).

fof(f9888,plain,
    ( spl0_640
  <=> ! [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_640])]) ).

fof(f1455,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_90
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f693]) ).

fof(f9886,plain,
    ( spl0_639
    | ~ spl0_29
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1397,f1391,f331,f9884]) ).

fof(f9884,plain,
    ( spl0_639
  <=> ! [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_639])]) ).

fof(f1397,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_29
    | ~ spl0_169 ),
    inference(resolution,[],[f1392,f332]) ).

fof(f9703,plain,
    ( spl0_638
    | ~ spl0_248
    | ~ spl0_631 ),
    inference(avatar_split_clause,[],[f9667,f9664,f2393,f9701]) ).

fof(f9701,plain,
    ( spl0_638
  <=> ! [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_638])]) ).

fof(f9664,plain,
    ( spl0_631
  <=> ! [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_631])]) ).

fof(f9667,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_248
    | ~ spl0_631 ),
    inference(forward_demodulation,[],[f9665,f2395]) ).

fof(f9665,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_631 ),
    inference(avatar_component_clause,[],[f9664]) ).

fof(f9699,plain,
    ( spl0_637
    | ~ spl0_248
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9662,f9657,f2393,f9697]) ).

fof(f9697,plain,
    ( spl0_637
  <=> ! [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_637])]) ).

fof(f9657,plain,
    ( spl0_630
  <=> ! [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_630])]) ).

fof(f9662,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_248
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f9661,f2395]) ).

fof(f9661,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_248
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f9660,f2395]) ).

fof(f9660,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_248
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f9658,f2395]) ).

fof(f9658,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_630 ),
    inference(avatar_component_clause,[],[f9657]) ).

fof(f9687,plain,
    ( spl0_635
    | ~ spl0_636
    | ~ spl0_62
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1910,f1900,f535,f9684,f9681]) ).

fof(f9681,plain,
    ( spl0_635
  <=> ! [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_635])]) ).

fof(f9684,plain,
    ( spl0_636
  <=> subclass(composition_function,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f535,plain,
    ( spl0_62
  <=> ! [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_62])]) ).

fof(f1910,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_62
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f536]) ).

fof(f536,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f535]) ).

fof(f9679,plain,
    ( spl0_634
    | ~ spl0_119
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1663,f1652,f922,f9677]) ).

fof(f9677,plain,
    ( spl0_634
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,null_class)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f1663,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,null_class)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_119
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f923]) ).

fof(f9675,plain,
    ( spl0_633
    | ~ spl0_113
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f8932,f8599,f838,f9673]) ).

fof(f8932,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | member(null_class,intersection(y,X0))
        | ~ inductive(X0) )
    | ~ spl0_113
    | ~ spl0_584 ),
    inference(resolution,[],[f8600,f839]) ).

fof(f9671,plain,
    ( spl0_632
    | ~ spl0_41
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1655,f1652,f388,f9669]) ).

fof(f9669,plain,
    ( spl0_632
  <=> ! [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_632])]) ).

fof(f1655,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_41
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f389]) ).

fof(f9666,plain,
    ( spl0_631
    | ~ spl0_133
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1436,f1405,f1001,f9664]) ).

fof(f1436,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_133
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f1002]) ).

fof(f9659,plain,
    ( spl0_630
    | ~ spl0_132
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1434,f1405,f997,f9657]) ).

fof(f1434,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_132
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f998]) ).

fof(f9654,plain,
    ( spl0_629
    | ~ spl0_143
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1257,f1201,f1130,f9652]) ).

fof(f9652,plain,
    ( spl0_629
  <=> ! [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_629])]) ).

fof(f1257,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_143
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f1131]) ).

fof(f9649,plain,
    ( spl0_628
    | ~ spl0_142
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1250,f1201,f1126,f9647]) ).

fof(f9647,plain,
    ( spl0_628
  <=> ! [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_628])]) ).

fof(f1250,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_142
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f1127]) ).

fof(f9642,plain,
    ( spl0_627
    | ~ spl0_143
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1243,f1197,f1130,f9640]) ).

fof(f9640,plain,
    ( spl0_627
  <=> ! [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_627])]) ).

fof(f1243,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_143
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f1131]) ).

fof(f9635,plain,
    ( spl0_626
    | ~ spl0_142
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1236,f1197,f1126,f9633]) ).

fof(f9633,plain,
    ( spl0_626
  <=> ! [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_626])]) ).

fof(f1236,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_142
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f1127]) ).

fof(f9631,plain,
    ( spl0_625
    | ~ spl0_89
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f916,f855,f687,f9629]) ).

fof(f9629,plain,
    ( spl0_625
  <=> ! [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_625])]) ).

fof(f687,plain,
    ( spl0_89
  <=> ! [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_89])]) ).

fof(f916,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_89
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f688]) ).

fof(f688,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_89 ),
    inference(avatar_component_clause,[],[f687]) ).

fof(f9518,plain,
    ( spl0_624
    | ~ spl0_87
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1758,f1747,f679,f9516]) ).

fof(f9516,plain,
    ( spl0_624
  <=> ! [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_624])]) ).

fof(f679,plain,
    ( spl0_87
  <=> ! [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_87])]) ).

fof(f1758,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_87
    | ~ spl0_204 ),
    inference(superposition,[],[f680,f1748]) ).

fof(f680,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_87 ),
    inference(avatar_component_clause,[],[f679]) ).

fof(f9514,plain,
    ( spl0_623
    | ~ spl0_86
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1757,f1747,f674,f9512]) ).

fof(f9512,plain,
    ( spl0_623
  <=> ! [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_623])]) ).

fof(f1757,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_86
    | ~ spl0_204 ),
    inference(superposition,[],[f675,f1748]) ).

fof(f9510,plain,
    ( spl0_622
    | ~ spl0_33
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1659,f1652,f347,f9508]) ).

fof(f9508,plain,
    ( spl0_622
  <=> ! [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_622])]) ).

fof(f1659,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_33
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f348]) ).

fof(f9506,plain,
    ( spl0_621
    | ~ spl0_34
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1658,f1652,f351,f9504]) ).

fof(f9504,plain,
    ( spl0_621
  <=> ! [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_621])]) ).

fof(f1658,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_34
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f352]) ).

fof(f9502,plain,
    ( spl0_620
    | ~ spl0_137
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1606,f1588,f1050,f9500]) ).

fof(f9500,plain,
    ( spl0_620
  <=> ! [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_620])]) ).

fof(f1606,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_137
    | ~ spl0_190 ),
    inference(resolution,[],[f1589,f1051]) ).

fof(f9498,plain,
    ( spl0_619
    | ~ spl0_329
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f7109,f6829,f3238,f9496]) ).

fof(f9496,plain,
    ( spl0_619
  <=> ! [X0,X1] :
        ( ~ subclass(X0,x)
        | subclass(X0,X1)
        | ~ subclass(X0,complement(y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f7109,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,x)
        | subclass(X0,X1)
        | ~ subclass(X0,complement(y)) )
    | ~ spl0_329
    | ~ spl0_509 ),
    inference(duplicate_literal_removal,[],[f7091]) ).

fof(f7091,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,x)
        | subclass(X0,X1)
        | subclass(X0,X1)
        | ~ subclass(X0,complement(y)) )
    | ~ spl0_329
    | ~ spl0_509 ),
    inference(resolution,[],[f6830,f3239]) ).

fof(f9494,plain,
    ( spl0_618
    | ~ spl0_48
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1433,f1405,f447,f9492]) ).

fof(f9492,plain,
    ( spl0_618
  <=> ! [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_618])]) ).

fof(f1433,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_48
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f448]) ).

fof(f9490,plain,
    ( spl0_617
    | ~ spl0_82
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1016,f962,f645,f9488]) ).

fof(f9488,plain,
    ( spl0_617
  <=> ! [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_617])]) ).

fof(f1016,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_82
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f646]) ).

fof(f9439,plain,
    ( ~ spl0_616
    | ~ spl0_248
    | spl0_615 ),
    inference(avatar_split_clause,[],[f9434,f9430,f2393,f9436]) ).

fof(f9436,plain,
    ( spl0_616
  <=> 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_616])]) ).

fof(f9430,plain,
    ( spl0_615
  <=> 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_615])]) ).

fof(f9434,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_248
    | spl0_615 ),
    inference(forward_demodulation,[],[f9431,f2395]) ).

fof(f9431,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_615 ),
    inference(avatar_component_clause,[],[f9430]) ).

fof(f9433,plain,
    ( ~ spl0_563
    | spl0_246
    | spl0_615
    | ~ spl0_45
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1734,f1692,f405,f9430,f2383,f8455]) ).

fof(f8455,plain,
    ( spl0_563
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f2383,plain,
    ( spl0_246
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f405,plain,
    ( spl0_45
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1734,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_45
    | ~ spl0_201 ),
    inference(superposition,[],[f1693,f407]) ).

fof(f407,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f405]) ).

fof(f9428,plain,
    ( spl0_614
    | ~ spl0_22
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1661,f1652,f299,f9426]) ).

fof(f9426,plain,
    ( spl0_614
  <=> ! [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_614])]) ).

fof(f1661,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_22
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f300]) ).

fof(f9423,plain,
    ( spl0_613
    | ~ spl0_136
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1256,f1201,f1046,f9421]) ).

fof(f9421,plain,
    ( spl0_613
  <=> ! [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_613])]) ).

fof(f1256,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_136
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f1047]) ).

fof(f9418,plain,
    ( spl0_612
    | ~ spl0_135
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1254,f1201,f1042,f9416]) ).

fof(f9416,plain,
    ( spl0_612
  <=> ! [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_612])]) ).

fof(f1254,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_135
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f1043]) ).

fof(f9365,plain,
    ( spl0_611
    | ~ spl0_136
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1242,f1197,f1046,f9363]) ).

fof(f9363,plain,
    ( spl0_611
  <=> ! [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_611])]) ).

fof(f1242,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_136
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f1047]) ).

fof(f9358,plain,
    ( spl0_610
    | ~ spl0_135
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1240,f1197,f1042,f9356]) ).

fof(f9356,plain,
    ( spl0_610
  <=> ! [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_610])]) ).

fof(f1240,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_135
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f1043]) ).

fof(f9354,plain,
    ( spl0_609
    | ~ spl0_53
    | ~ spl0_73
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1012,f958,f586,f471,f9352]) ).

fof(f9352,plain,
    ( spl0_609
  <=> ! [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_609])]) ).

fof(f1012,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_53
    | ~ spl0_73
    | ~ spl0_123 ),
    inference(forward_demodulation,[],[f1011,f472]) ).

fof(f1011,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_73
    | ~ spl0_123 ),
    inference(resolution,[],[f959,f587]) ).

fof(f9331,plain,
    ( spl0_608
    | ~ spl0_248
    | ~ spl0_604 ),
    inference(avatar_split_clause,[],[f9259,f9256,f2393,f9329]) ).

fof(f9329,plain,
    ( spl0_608
  <=> ! [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_608])]) ).

fof(f9256,plain,
    ( spl0_604
  <=> ! [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_604])]) ).

fof(f9259,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_248
    | ~ spl0_604 ),
    inference(forward_demodulation,[],[f9257,f2395]) ).

fof(f9257,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_604 ),
    inference(avatar_component_clause,[],[f9256]) ).

fof(f9271,plain,
    ( spl0_607
    | ~ spl0_74
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1791,f1781,f597,f9269]) ).

fof(f9269,plain,
    ( spl0_607
  <=> ! [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_607])]) ).

fof(f1791,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_74
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f598]) ).

fof(f9267,plain,
    ( spl0_606
    | ~ spl0_159
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f7699,f7599,f1286,f9265]) ).

fof(f9265,plain,
    ( spl0_606
  <=> ! [X0,X1] :
        ( ~ member(X0,x)
        | ~ member(X0,X1)
        | member(X0,y) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f7699,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,x)
        | ~ member(X0,X1)
        | member(X0,y) )
    | ~ spl0_159
    | ~ spl0_535 ),
    inference(resolution,[],[f7600,f1287]) ).

fof(f9263,plain,
    ( spl0_605
    | ~ spl0_108
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1669,f1652,f789,f9261]) ).

fof(f9261,plain,
    ( spl0_605
  <=> ! [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_605])]) ).

fof(f1669,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_108
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f790]) ).

fof(f9258,plain,
    ( spl0_604
    | ~ spl0_109
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1667,f1652,f793,f9256]) ).

fof(f1667,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_109
    | ~ spl0_198 ),
    inference(resolution,[],[f1653,f794]) ).

fof(f9254,plain,
    ( spl0_603
    | ~ spl0_124
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1603,f1588,f962,f9252]) ).

fof(f9252,plain,
    ( spl0_603
  <=> ! [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_603])]) ).

fof(f1603,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_124
    | ~ spl0_190 ),
    inference(resolution,[],[f1589,f963]) ).

fof(f9250,plain,
    ( spl0_602
    | ~ spl0_90
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f864,f834,f692,f9248]) ).

fof(f9248,plain,
    ( spl0_602
  <=> ! [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_602])]) ).

fof(f864,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_90
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f693]) ).

fof(f9124,plain,
    ( spl0_601
    | ~ spl0_79
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1755,f1747,f626,f9122]) ).

fof(f9122,plain,
    ( spl0_601
  <=> ! [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_601])]) ).

fof(f1755,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_79
    | ~ spl0_204 ),
    inference(superposition,[],[f627,f1748]) ).

fof(f9117,plain,
    ( ~ spl0_599
    | spl0_286
    | spl0_600
    | ~ spl0_78
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1732,f1692,f621,f9114,f2613,f9110]) ).

fof(f9110,plain,
    ( spl0_599
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f2613,plain,
    ( spl0_286
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f9114,plain,
    ( spl0_600
  <=> 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_600])]) ).

fof(f621,plain,
    ( spl0_78
  <=> 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_78])]) ).

fof(f1732,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_78
    | ~ spl0_201 ),
    inference(superposition,[],[f1693,f623]) ).

fof(f623,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_78 ),
    inference(avatar_component_clause,[],[f621]) ).

fof(f9108,plain,
    ( spl0_598
    | ~ spl0_160
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1675,f1671,f1290,f9106]) ).

fof(f9106,plain,
    ( spl0_598
  <=> ! [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_598])]) ).

fof(f1675,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_160
    | ~ spl0_199 ),
    inference(resolution,[],[f1672,f1291]) ).

fof(f9104,plain,
    ( spl0_597
    | ~ spl0_41
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1619,f1615,f388,f9102]) ).

fof(f9102,plain,
    ( spl0_597
  <=> ! [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_597])]) ).

fof(f1619,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_41
    | ~ spl0_192 ),
    inference(resolution,[],[f1616,f389]) ).

fof(f9100,plain,
    ( ~ spl0_595
    | spl0_596
    | ~ spl0_112
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1605,f1588,f834,f9098,f9094]) ).

fof(f9094,plain,
    ( spl0_595
  <=> 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_595])]) ).

fof(f9098,plain,
    ( spl0_596
  <=> ! [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_596])]) ).

fof(f1605,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_112
    | ~ spl0_190 ),
    inference(resolution,[],[f1589,f835]) ).

fof(f9092,plain,
    ( spl0_594
    | ~ spl0_78
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1441,f1405,f621,f9090]) ).

fof(f9090,plain,
    ( spl0_594
  <=> ! [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_594])]) ).

fof(f1441,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_78
    | ~ spl0_171 ),
    inference(superposition,[],[f1406,f623]) ).

fof(f9088,plain,
    ( spl0_593
    | ~ spl0_137
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1349,f1329,f1050,f9086]) ).

fof(f9086,plain,
    ( spl0_593
  <=> ! [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_593])]) ).

fof(f1349,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_137
    | ~ spl0_164 ),
    inference(resolution,[],[f1330,f1051]) ).

fof(f9081,plain,
    ( spl0_591
    | ~ spl0_592
    | ~ spl0_291
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f8935,f8599,f2774,f9078,f9075]) ).

fof(f9075,plain,
    ( spl0_591
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f9078,plain,
    ( spl0_592
  <=> subclass(universal_class,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f8935,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,x)
        | member(unordered_pair(X0,X1),y) )
    | ~ spl0_291
    | ~ spl0_584 ),
    inference(resolution,[],[f8600,f2775]) ).

fof(f8989,plain,
    ( spl0_590
    | ~ spl0_67
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1792,f1781,f557,f8987]) ).

fof(f8987,plain,
    ( spl0_590
  <=> ! [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_590])]) ).

fof(f1792,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_67
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f558]) ).

fof(f8985,plain,
    ( spl0_589
    | ~ spl0_120
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1425,f1401,f926,f8983]) ).

fof(f8983,plain,
    ( spl0_589
  <=> ! [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_589])]) ).

fof(f1425,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_120
    | ~ spl0_170 ),
    inference(resolution,[],[f1402,f927]) ).

fof(f8981,plain,
    ( spl0_588
    | ~ spl0_148
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1313,f1290,f1193,f8979]) ).

fof(f8979,plain,
    ( spl0_588
  <=> ! [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_588])]) ).

fof(f1313,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_148
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f1194]) ).

fof(f8977,plain,
    ( spl0_587
    | ~ spl0_448
    | ~ spl0_149
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1308,f1290,f1197,f5706,f8975]) ).

fof(f8975,plain,
    ( spl0_587
  <=> ! [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_587])]) ).

fof(f1308,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_149
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f1198]) ).

fof(f8973,plain,
    ( spl0_586
    | ~ spl0_78
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1299,f1286,f621,f8971]) ).

fof(f8971,plain,
    ( spl0_586
  <=> ! [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_586])]) ).

fof(f1299,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_78
    | ~ spl0_159 ),
    inference(superposition,[],[f1287,f623]) ).

fof(f8969,plain,
    ( spl0_585
    | ~ spl0_53
    | ~ spl0_73
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f933,f918,f586,f471,f8967]) ).

fof(f8967,plain,
    ( spl0_585
  <=> ! [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_585])]) ).

fof(f933,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_53
    | ~ spl0_73
    | ~ spl0_118 ),
    inference(forward_demodulation,[],[f932,f472]) ).

fof(f932,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_73
    | ~ spl0_118 ),
    inference(resolution,[],[f919,f587]) ).

fof(f8601,plain,
    ( spl0_584
    | ~ spl0_341
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f7105,f6829,f3298,f8599]) ).

fof(f7105,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,intersection(y,X0)) )
    | ~ spl0_341
    | ~ spl0_509 ),
    inference(duplicate_literal_removal,[],[f7095]) ).

fof(f7095,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,intersection(y,X0))
        | subclass(X0,intersection(y,X0)) )
    | ~ spl0_341
    | ~ spl0_509 ),
    inference(resolution,[],[f6830,f3299]) ).

fof(f8562,plain,
    ( spl0_583
    | ~ spl0_62
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1787,f1781,f535,f8560]) ).

fof(f8560,plain,
    ( spl0_583
  <=> ! [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_583])]) ).

fof(f1787,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_62
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f536]) ).

fof(f8558,plain,
    ( spl0_582
    | ~ spl0_74
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1754,f1747,f597,f8556]) ).

fof(f8556,plain,
    ( spl0_582
  <=> ! [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_582])]) ).

fof(f1754,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_74
    | ~ spl0_204 ),
    inference(superposition,[],[f598,f1748]) ).

fof(f8554,plain,
    ( spl0_581
    | ~ spl0_142
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1643,f1621,f1126,f8552]) ).

fof(f8552,plain,
    ( spl0_581
  <=> ! [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_581])]) ).

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

fof(f1643,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_142
    | ~ spl0_193 ),
    inference(duplicate_literal_removal,[],[f1638]) ).

fof(f1638,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_142
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1127]) ).

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

fof(f8550,plain,
    ( spl0_580
    | ~ spl0_143
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1642,f1621,f1130,f8548]) ).

fof(f8548,plain,
    ( spl0_580
  <=> ! [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_580])]) ).

fof(f1642,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_143
    | ~ spl0_193 ),
    inference(duplicate_literal_removal,[],[f1639]) ).

fof(f1639,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_143
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1131]) ).

fof(f8546,plain,
    ( spl0_579
    | ~ spl0_66
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1477,f1413,f552,f8544]) ).

fof(f8544,plain,
    ( spl0_579
  <=> ! [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_579])]) ).

fof(f552,plain,
    ( spl0_66
  <=> ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1413,plain,
    ( spl0_173
  <=> ! [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_173])]) ).

fof(f1477,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_66
    | ~ spl0_173 ),
    inference(resolution,[],[f1414,f553]) ).

fof(f553,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f552]) ).

fof(f1414,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_173 ),
    inference(avatar_component_clause,[],[f1413]) ).

fof(f8532,plain,
    ( spl0_578
    | ~ spl0_16
    | ~ spl0_86
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1451,f1409,f674,f274,f8530]) ).

fof(f8530,plain,
    ( spl0_578
  <=> ! [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_578])]) ).

fof(f274,plain,
    ( spl0_16
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f1451,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_86
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f675]) ).

fof(f8528,plain,
    ( spl0_577
    | ~ spl0_131
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1437,f1405,f993,f8526]) ).

fof(f8526,plain,
    ( spl0_577
  <=> ! [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_577])]) ).

fof(f1437,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_131
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f994]) ).

fof(f8520,plain,
    ( spl0_576
    | ~ spl0_117
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1430,f1405,f855,f8518]) ).

fof(f8518,plain,
    ( spl0_576
  <=> ! [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_576])]) ).

fof(f1430,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_117
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f856]) ).

fof(f8515,plain,
    ( spl0_575
    | ~ spl0_28
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1249,f1201,f327,f8513]) ).

fof(f8513,plain,
    ( spl0_575
  <=> ! [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_575])]) ).

fof(f327,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1249,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_28
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f328]) ).

fof(f328,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f8508,plain,
    ( spl0_574
    | ~ spl0_28
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1235,f1197,f327,f8506]) ).

fof(f8506,plain,
    ( spl0_574
  <=> ! [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_574])]) ).

fof(f1235,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_28
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f328]) ).

fof(f8504,plain,
    ( spl0_573
    | ~ spl0_143
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1229,f1193,f1130,f8502]) ).

fof(f8502,plain,
    ( spl0_573
  <=> ! [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_573])]) ).

fof(f1229,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_143
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f1131]) ).

fof(f8500,plain,
    ( spl0_572
    | ~ spl0_142
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1222,f1193,f1126,f8498]) ).

fof(f8498,plain,
    ( spl0_572
  <=> ! [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_572])]) ).

fof(f1222,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_142
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f1127]) ).

fof(f8496,plain,
    ( spl0_571
    | ~ spl0_51
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1165,f1130,f463,f8494]) ).

fof(f8494,plain,
    ( spl0_571
  <=> ! [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_571])]) ).

fof(f1165,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_51
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f464]) ).

fof(f8492,plain,
    ( spl0_570
    | ~ spl0_51
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1147,f1126,f463,f8490]) ).

fof(f8490,plain,
    ( spl0_570
  <=> ! [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_570])]) ).

fof(f1147,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_51
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f464]) ).

fof(f8488,plain,
    ( spl0_569
    | ~ spl0_86
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f912,f855,f674,f8486]) ).

fof(f8486,plain,
    ( spl0_569
  <=> ! [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_569])]) ).

fof(f912,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_86
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f675]) ).

fof(f8484,plain,
    ( spl0_568
    | ~ spl0_41
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f8438,f939,f388,f8482]) ).

fof(f8438,plain,
    ( ! [X0] :
        ( ~ subclass(y,X0)
        | member(null_class,X0) )
    | ~ spl0_41
    | ~ spl0_122 ),
    inference(resolution,[],[f941,f389]) ).

fof(f941,plain,
    ( member(null_class,y)
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f939]) ).

fof(f8480,plain,
    ( ~ spl0_4
    | ~ spl0_566
    | spl0_567
    | ~ spl0_66
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f906,f851,f552,f8477,f8473,f221]) ).

fof(f221,plain,
    ( spl0_4
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f8473,plain,
    ( spl0_566
  <=> 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_566])]) ).

fof(f8477,plain,
    ( spl0_567
  <=> 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_567])]) ).

fof(f851,plain,
    ( spl0_116
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f906,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_66
    | ~ spl0_116 ),
    inference(resolution,[],[f852,f553]) ).

fof(f852,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f851]) ).

fof(f8469,plain,
    ( ~ spl0_565
    | ~ spl0_248
    | spl0_564 ),
    inference(avatar_split_clause,[],[f8463,f8459,f2393,f8466]) ).

fof(f8466,plain,
    ( spl0_565
  <=> 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_565])]) ).

fof(f8459,plain,
    ( spl0_564
  <=> 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_564])]) ).

fof(f8463,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_248
    | spl0_564 ),
    inference(forward_demodulation,[],[f8460,f2395]) ).

fof(f8460,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_564 ),
    inference(avatar_component_clause,[],[f8459]) ).

fof(f8462,plain,
    ( spl0_246
    | ~ spl0_563
    | spl0_564
    | ~ spl0_85
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f808,f793,f662,f8459,f8455,f2383]) ).

fof(f808,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_85
    | ~ spl0_109 ),
    inference(resolution,[],[f794,f663]) ).

fof(f8451,plain,
    ( spl0_244
    | ~ spl0_561
    | spl0_562
    | ~ spl0_85
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f804,f789,f662,f8448,f8444,f2363]) ).

fof(f2363,plain,
    ( spl0_244
  <=> null_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f8444,plain,
    ( spl0_561
  <=> member(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f8448,plain,
    ( spl0_562
  <=> 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_562])]) ).

fof(f804,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_85
    | ~ spl0_108 ),
    inference(resolution,[],[f790,f663]) ).

fof(f8435,plain,
    ( spl0_560
    | spl0_122
    | ~ spl0_113
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f7702,f7599,f838,f939,f8433]) ).

fof(f8433,plain,
    ( spl0_560
  <=> ! [X0] : ~ inductive(intersection(x,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f7702,plain,
    ( ! [X0] :
        ( member(null_class,y)
        | ~ inductive(intersection(x,X0)) )
    | ~ spl0_113
    | ~ spl0_535 ),
    inference(resolution,[],[f7600,f839]) ).

fof(f8419,plain,
    ( spl0_559
    | ~ spl0_70
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1785,f1781,f574,f8417]) ).

fof(f8417,plain,
    ( spl0_559
  <=> ! [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_559])]) ).

fof(f574,plain,
    ( spl0_70
  <=> ! [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_70])]) ).

fof(f1785,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_70
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f575]) ).

fof(f575,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_70 ),
    inference(avatar_component_clause,[],[f574]) ).

fof(f8415,plain,
    ( spl0_558
    | ~ spl0_71
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1784,f1781,f578,f8413]) ).

fof(f8413,plain,
    ( spl0_558
  <=> ! [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_558])]) ).

fof(f1784,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_71
    | ~ spl0_205 ),
    inference(resolution,[],[f1782,f579]) ).

fof(f8411,plain,
    ( spl0_557
    | ~ spl0_42
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1423,f1401,f392,f8409]) ).

fof(f8409,plain,
    ( spl0_557
  <=> ! [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_557])]) ).

fof(f1423,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_42
    | ~ spl0_170 ),
    inference(resolution,[],[f1402,f393]) ).

fof(f8407,plain,
    ( spl0_556
    | ~ spl0_112
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1348,f1329,f834,f8405]) ).

fof(f8405,plain,
    ( spl0_556
  <=> ! [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_556])]) ).

fof(f1348,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_112
    | ~ spl0_164 ),
    inference(resolution,[],[f1330,f835]) ).

fof(f8403,plain,
    ( spl0_555
    | ~ spl0_51
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1303,f1290,f463,f8401]) ).

fof(f8401,plain,
    ( spl0_555
  <=> ! [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_555])]) ).

fof(f1303,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_51
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f464]) ).

fof(f7698,plain,
    ( spl0_554
    | ~ spl0_67
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1751,f1747,f557,f7696]) ).

fof(f7696,plain,
    ( spl0_554
  <=> ! [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_554])]) ).

fof(f1751,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_67
    | ~ spl0_204 ),
    inference(superposition,[],[f558,f1748]) ).

fof(f7694,plain,
    ( spl0_553
    | ~ spl0_24
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1586,f1581,f307,f7692]) ).

fof(f7692,plain,
    ( spl0_553
  <=> ! [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_553])]) ).

fof(f1586,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_24
    | ~ spl0_189 ),
    inference(resolution,[],[f1582,f308]) ).

fof(f7690,plain,
    ( spl0_552
    | ~ spl0_41
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1544,f1508,f388,f7688]) ).

fof(f7688,plain,
    ( spl0_552
  <=> ! [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_552])]) ).

fof(f1544,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_41
    | ~ spl0_181 ),
    inference(resolution,[],[f1509,f389]) ).

fof(f7686,plain,
    ( spl0_551
    | ~ spl0_41
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1529,f1496,f388,f7684]) ).

fof(f7684,plain,
    ( spl0_551
  <=> ! [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_551])]) ).

fof(f1529,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_41
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f389]) ).

fof(f7682,plain,
    ( spl0_550
    | ~ spl0_41
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1511,f1492,f388,f7680]) ).

fof(f7680,plain,
    ( spl0_550
  <=> ! [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_550])]) ).

fof(f1511,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_41
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f389]) ).

fof(f7678,plain,
    ( spl0_549
    | ~ spl0_59
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1476,f1413,f518,f7676]) ).

fof(f7676,plain,
    ( spl0_549
  <=> ! [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_549])]) ).

fof(f518,plain,
    ( spl0_59
  <=> ! [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_59])]) ).

fof(f1476,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_59
    | ~ spl0_173 ),
    inference(resolution,[],[f1414,f519]) ).

fof(f519,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f518]) ).

fof(f7674,plain,
    ( spl0_548
    | ~ spl0_116
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1424,f1401,f851,f7672]) ).

fof(f7672,plain,
    ( spl0_548
  <=> ! [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_548])]) ).

fof(f1424,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_116
    | ~ spl0_170 ),
    inference(resolution,[],[f1402,f852]) ).

fof(f7670,plain,
    ( spl0_547
    | ~ spl0_124
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1346,f1329,f962,f7668]) ).

fof(f7668,plain,
    ( spl0_547
  <=> ! [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_547])]) ).

fof(f1346,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_124
    | ~ spl0_164 ),
    inference(resolution,[],[f1330,f963]) ).

fof(f7664,plain,
    ( ~ spl0_546
    | ~ spl0_248
    | spl0_543 ),
    inference(avatar_split_clause,[],[f7651,f7643,f2393,f7661]) ).

fof(f7661,plain,
    ( spl0_546
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f7643,plain,
    ( spl0_543
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f7651,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
    | ~ spl0_248
    | spl0_543 ),
    inference(forward_demodulation,[],[f7644,f2395]) ).

fof(f7644,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | spl0_543 ),
    inference(avatar_component_clause,[],[f7643]) ).

fof(f7659,plain,
    ( spl0_545
    | ~ spl0_236
    | ~ spl0_524 ),
    inference(avatar_split_clause,[],[f7511,f7269,f2211,f7657]) ).

fof(f7269,plain,
    ( spl0_524
  <=> ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,y) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f7511,plain,
    ( ! [X0] : subclass(intersection(X0,x),y)
    | ~ spl0_236
    | ~ spl0_524 ),
    inference(resolution,[],[f7270,f2212]) ).

fof(f7270,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,y) )
    | ~ spl0_524 ),
    inference(avatar_component_clause,[],[f7269]) ).

fof(f7650,plain,
    ( spl0_542
    | spl0_543
    | ~ spl0_544
    | ~ spl0_25
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1253,f1201,f311,f7647,f7643,f7639]) ).

fof(f7647,plain,
    ( spl0_544
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f311,plain,
    ( spl0_25
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1253,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_25
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f312]) ).

fof(f312,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f311]) ).

fof(f7632,plain,
    ( ~ spl0_541
    | ~ spl0_248
    | spl0_537 ),
    inference(avatar_split_clause,[],[f7616,f7607,f2393,f7629]) ).

fof(f7629,plain,
    ( spl0_541
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f7607,plain,
    ( spl0_537
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f7616,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
    | ~ spl0_248
    | spl0_537 ),
    inference(forward_demodulation,[],[f7608,f2395]) ).

fof(f7608,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | spl0_537 ),
    inference(avatar_component_clause,[],[f7607]) ).

fof(f7627,plain,
    ( ~ spl0_540
    | ~ spl0_248
    | spl0_538 ),
    inference(avatar_split_clause,[],[f7615,f7611,f2393,f7624]) ).

fof(f7624,plain,
    ( spl0_540
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f7611,plain,
    ( spl0_538
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f7615,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
    | ~ spl0_248
    | spl0_538 ),
    inference(forward_demodulation,[],[f7613,f2395]) ).

fof(f7613,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | spl0_538 ),
    inference(avatar_component_clause,[],[f7611]) ).

fof(f7622,plain,
    ( ~ spl0_539
    | ~ spl0_248
    | spl0_536 ),
    inference(avatar_split_clause,[],[f7617,f7603,f2393,f7619]) ).

fof(f7619,plain,
    ( spl0_539
  <=> null_class = complement(compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f7617,plain,
    ( null_class != complement(compose(element_relation,complement(singleton_relation)))
    | ~ spl0_248
    | spl0_536 ),
    inference(forward_demodulation,[],[f7604,f2395]) ).

fof(f7604,plain,
    ( null_class != complement(compose(element_relation,complement(identity_relation)))
    | spl0_536 ),
    inference(avatar_component_clause,[],[f7603]) ).

fof(f7614,plain,
    ( spl0_536
    | spl0_537
    | ~ spl0_538
    | ~ spl0_25
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1239,f1197,f311,f7611,f7607,f7603]) ).

fof(f1239,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_25
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f312]) ).

fof(f7601,plain,
    ( spl0_535
    | ~ spl0_235
    | ~ spl0_524 ),
    inference(avatar_split_clause,[],[f7510,f7269,f2207,f7599]) ).

fof(f7510,plain,
    ( ! [X0] : subclass(intersection(x,X0),y)
    | ~ spl0_235
    | ~ spl0_524 ),
    inference(resolution,[],[f7270,f2208]) ).

fof(f7597,plain,
    ( spl0_534
    | ~ spl0_136
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1228,f1193,f1046,f7595]) ).

fof(f7595,plain,
    ( spl0_534
  <=> ! [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_534])]) ).

fof(f1228,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_136
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f1047]) ).

fof(f7593,plain,
    ( spl0_533
    | ~ spl0_135
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1226,f1193,f1042,f7591]) ).

fof(f7591,plain,
    ( spl0_533
  <=> ! [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_533])]) ).

fof(f1226,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_135
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f1043]) ).

fof(f7589,plain,
    ( spl0_532
    | ~ spl0_51
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1087,f1046,f463,f7587]) ).

fof(f7587,plain,
    ( spl0_532
  <=> ! [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_532])]) ).

fof(f1087,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_51
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f464]) ).

fof(f7585,plain,
    ( spl0_531
    | ~ spl0_51
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1066,f1042,f463,f7583]) ).

fof(f7583,plain,
    ( spl0_531
  <=> ! [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_531])]) ).

fof(f1066,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_51
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f464]) ).

fof(f7295,plain,
    ( spl0_530
    | ~ spl0_62
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1750,f1747,f535,f7293]) ).

fof(f7293,plain,
    ( spl0_530
  <=> ! [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_530])]) ).

fof(f1750,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_62
    | ~ spl0_204 ),
    inference(superposition,[],[f536,f1748]) ).

fof(f7291,plain,
    ( spl0_529
    | ~ spl0_137
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1641,f1621,f1050,f7289]) ).

fof(f7289,plain,
    ( spl0_529
  <=> ! [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_529])]) ).

fof(f1641,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_137
    | ~ spl0_193 ),
    inference(duplicate_literal_removal,[],[f1640]) ).

fof(f1640,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_137
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1051]) ).

fof(f7287,plain,
    ( spl0_528
    | ~ spl0_33
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1533,f1496,f347,f7285]) ).

fof(f7285,plain,
    ( spl0_528
  <=> ! [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_528])]) ).

fof(f1533,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_33
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f348]) ).

fof(f7283,plain,
    ( spl0_527
    | ~ spl0_34
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1532,f1496,f351,f7281]) ).

fof(f7281,plain,
    ( spl0_527
  <=> ! [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_527])]) ).

fof(f1532,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_34
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f352]) ).

fof(f7279,plain,
    ( spl0_526
    | ~ spl0_33
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1515,f1492,f347,f7277]) ).

fof(f7277,plain,
    ( spl0_526
  <=> ! [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_526])]) ).

fof(f1515,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_33
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f348]) ).

fof(f7275,plain,
    ( spl0_525
    | ~ spl0_34
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1514,f1492,f351,f7273]) ).

fof(f7273,plain,
    ( spl0_525
  <=> ! [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_525])]) ).

fof(f1514,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_34
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f352]) ).

fof(f7271,plain,
    ( spl0_524
    | ~ spl0_29
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f7111,f6829,f331,f7269]) ).

fof(f7111,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,y) )
    | ~ spl0_29
    | ~ spl0_509 ),
    inference(duplicate_literal_removal,[],[f7089]) ).

fof(f7089,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | subclass(X0,y)
        | subclass(X0,y) )
    | ~ spl0_29
    | ~ spl0_509 ),
    inference(resolution,[],[f6830,f332]) ).

fof(f7267,plain,
    ( spl0_523
    | ~ spl0_41
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1462,f1409,f388,f7265]) ).

fof(f7265,plain,
    ( spl0_523
  <=> ! [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_523])]) ).

fof(f1462,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_41
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f389]) ).

fof(f7263,plain,
    ( spl0_522
    | ~ spl0_148
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1381,f1351,f1193,f7261]) ).

fof(f7261,plain,
    ( spl0_522
  <=> ! [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_522])]) ).

fof(f1381,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_148
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1360]) ).

fof(f1360,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_148
    | ~ spl0_166 ),
    inference(superposition,[],[f1194,f1352]) ).

fof(f7259,plain,
    ( spl0_521
    | ~ spl0_148
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1376,f1351,f1193,f7257]) ).

fof(f7257,plain,
    ( spl0_521
  <=> ! [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_521])]) ).

fof(f1376,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_148
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1365]) ).

fof(f1365,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_148
    | ~ spl0_166 ),
    inference(superposition,[],[f1194,f1352]) ).

fof(f7255,plain,
    ( spl0_520
    | ~ spl0_52
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1009,f958,f467,f7253]) ).

fof(f7253,plain,
    ( spl0_520
  <=> ! [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_520])]) ).

fof(f1009,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_52
    | ~ spl0_123 ),
    inference(resolution,[],[f959,f468]) ).

fof(f7080,plain,
    ( spl0_519
    | ~ spl0_248
    | ~ spl0_510 ),
    inference(avatar_split_clause,[],[f7044,f7041,f2393,f7078]) ).

fof(f7078,plain,
    ( spl0_519
  <=> ! [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_519])]) ).

fof(f7041,plain,
    ( spl0_510
  <=> ! [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_510])]) ).

fof(f7044,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_248
    | ~ spl0_510 ),
    inference(forward_demodulation,[],[f7042,f2395]) ).

fof(f7042,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_510 ),
    inference(avatar_component_clause,[],[f7041]) ).

fof(f7076,plain,
    ( spl0_518
    | ~ spl0_70
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1908,f1900,f574,f7074]) ).

fof(f7074,plain,
    ( spl0_518
  <=> ! [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_518])]) ).

fof(f1908,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_70
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f575]) ).

fof(f7072,plain,
    ( spl0_517
    | ~ spl0_22
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1534,f1496,f299,f7070]) ).

fof(f7070,plain,
    ( spl0_517
  <=> ! [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_517])]) ).

fof(f1534,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_22
    | ~ spl0_178 ),
    inference(resolution,[],[f1497,f300]) ).

fof(f7068,plain,
    ( spl0_516
    | ~ spl0_22
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1516,f1492,f299,f7066]) ).

fof(f7066,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f1516,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_22
    | ~ spl0_177 ),
    inference(resolution,[],[f1493,f300]) ).

fof(f7064,plain,
    ( spl0_515
    | ~ spl0_33
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1466,f1409,f347,f7062]) ).

fof(f7062,plain,
    ( spl0_515
  <=> ! [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_515])]) ).

fof(f1466,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_33
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f348]) ).

fof(f7060,plain,
    ( spl0_514
    | ~ spl0_34
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1465,f1409,f351,f7058]) ).

fof(f7058,plain,
    ( spl0_514
  <=> ! [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_514])]) ).

fof(f1465,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_34
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f352]) ).

fof(f7056,plain,
    ( spl0_513
    | ~ spl0_113
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1422,f1401,f838,f7054]) ).

fof(f7054,plain,
    ( spl0_513
  <=> ! [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_513])]) ).

fof(f1422,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_113
    | ~ spl0_170 ),
    inference(resolution,[],[f1402,f839]) ).

fof(f7052,plain,
    ( spl0_512
    | ~ spl0_41
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1396,f1391,f388,f7050]) ).

fof(f7050,plain,
    ( spl0_512
  <=> ! [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_512])]) ).

fof(f1396,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_41
    | ~ spl0_169 ),
    inference(resolution,[],[f1392,f389]) ).

fof(f7048,plain,
    ( spl0_511
    | ~ spl0_2
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f4143,f3896,f211,f7046]) ).

fof(f211,plain,
    ( spl0_2
  <=> subclass(z,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f3896,plain,
    ( spl0_384
  <=> ! [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_384])]) ).

fof(f4143,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,z)
        | member(not_subclass_element(X0,X1),w) )
    | ~ spl0_2
    | ~ spl0_384 ),
    inference(resolution,[],[f3897,f213]) ).

fof(f213,plain,
    ( subclass(z,w)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f3897,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X1,X3)
        | subclass(X0,X2)
        | ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_384 ),
    inference(avatar_component_clause,[],[f3896]) ).

fof(f7043,plain,
    ( spl0_510
    | ~ spl0_53
    | ~ spl0_73
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1260,f1201,f586,f471,f7041]) ).

fof(f1260,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_53
    | ~ spl0_73
    | ~ spl0_150 ),
    inference(forward_demodulation,[],[f1247,f472]) ).

fof(f1247,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_73
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f587]) ).

fof(f6831,plain,
    ( spl0_509
    | ~ spl0_1
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f4142,f3896,f206,f6829]) ).

fof(f206,plain,
    ( spl0_1
  <=> subclass(x,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f4142,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,x)
        | member(not_subclass_element(X0,X1),y) )
    | ~ spl0_1
    | ~ spl0_384 ),
    inference(resolution,[],[f3897,f208]) ).

fof(f208,plain,
    ( subclass(x,y)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f6827,plain,
    ( spl0_508
    | ~ spl0_248
    | ~ spl0_497 ),
    inference(avatar_split_clause,[],[f6646,f6643,f2393,f6825]) ).

fof(f6825,plain,
    ( spl0_508
  <=> ! [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_508])]) ).

fof(f6643,plain,
    ( spl0_497
  <=> ! [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_497])]) ).

fof(f6646,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_248
    | ~ spl0_497 ),
    inference(forward_demodulation,[],[f6644,f2395]) ).

fof(f6644,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_497 ),
    inference(avatar_component_clause,[],[f6643]) ).

fof(f6823,plain,
    ( spl0_507
    | ~ spl0_248
    | ~ spl0_496 ),
    inference(avatar_split_clause,[],[f6641,f6638,f2393,f6821]) ).

fof(f6821,plain,
    ( spl0_507
  <=> ! [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_507])]) ).

fof(f6638,plain,
    ( spl0_496
  <=> ! [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_496])]) ).

fof(f6641,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_248
    | ~ spl0_496 ),
    inference(forward_demodulation,[],[f6639,f2395]) ).

fof(f6639,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_496 ),
    inference(avatar_component_clause,[],[f6638]) ).

fof(f6683,plain,
    ( spl0_505
    | ~ spl0_506
    | ~ spl0_87
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1904,f1900,f679,f6680,f6677]) ).

fof(f6677,plain,
    ( spl0_505
  <=> ! [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_505])]) ).

fof(f6680,plain,
    ( spl0_506
  <=> subclass(composition_function,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f1904,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_87
    | ~ spl0_210 ),
    inference(resolution,[],[f1901,f680]) ).

fof(f6675,plain,
    ( spl0_504
    | ~ spl0_71
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1753,f1747,f578,f6673]) ).

fof(f6673,plain,
    ( spl0_504
  <=> ! [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_504])]) ).

fof(f1753,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_71
    | ~ spl0_204 ),
    inference(superposition,[],[f579,f1748]) ).

fof(f6671,plain,
    ( spl0_503
    | ~ spl0_70
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1752,f1747,f574,f6669]) ).

fof(f6669,plain,
    ( spl0_503
  <=> ! [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_503])]) ).

fof(f1752,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_70
    | ~ spl0_204 ),
    inference(superposition,[],[f575,f1748]) ).

fof(f6667,plain,
    ( spl0_502
    | ~ spl0_24
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f1480,f1413,f307,f6665]) ).

fof(f6665,plain,
    ( spl0_502
  <=> ! [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_502])]) ).

fof(f1480,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_24
    | ~ spl0_173 ),
    inference(resolution,[],[f1414,f308]) ).

fof(f6662,plain,
    ( spl0_501
    | ~ spl0_22
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1467,f1409,f299,f6660]) ).

fof(f6660,plain,
    ( spl0_501
  <=> ! [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_501])]) ).

fof(f1467,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_22
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f300]) ).

fof(f6658,plain,
    ( spl0_500
    | ~ spl0_138
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1421,f1401,f1054,f6656]) ).

fof(f6656,plain,
    ( spl0_500
  <=> ! [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_500])]) ).

fof(f1421,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_138
    | ~ spl0_170 ),
    inference(resolution,[],[f1402,f1055]) ).

fof(f6654,plain,
    ( spl0_499
    | ~ spl0_139
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1420,f1401,f1058,f6652]) ).

fof(f6652,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(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f1420,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_139
    | ~ spl0_170 ),
    inference(resolution,[],[f1402,f1059]) ).

fof(f6650,plain,
    ( spl0_498
    | ~ spl0_41
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1387,f1355,f388,f6648]) ).

fof(f6648,plain,
    ( spl0_498
  <=> ! [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_498])]) ).

fof(f1355,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

fof(f1387,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_41
    | ~ spl0_167 ),
    inference(resolution,[],[f1356,f389]) ).

fof(f1356,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_167 ),
    inference(avatar_component_clause,[],[f1355]) ).

fof(f6645,plain,
    ( spl0_497
    | ~ spl0_137
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1259,f1201,f1050,f6643]) ).

fof(f1259,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_137
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f1051]) ).

fof(f6640,plain,
    ( spl0_496
    | ~ spl0_137
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1245,f1197,f1050,f6638]) ).

fof(f1245,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_137
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f1051]) ).

fof(f6636,plain,
    ( spl0_495
    | ~ spl0_137
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1231,f1193,f1050,f6634]) ).

fof(f6634,plain,
    ( spl0_495
  <=> ! [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_495])]) ).

fof(f1231,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_137
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f1051]) ).

fof(f6632,plain,
    ( spl0_494
    | ~ spl0_78
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1177,f1130,f621,f6630]) ).

fof(f6630,plain,
    ( spl0_494
  <=> ! [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_494])]) ).

fof(f1177,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_78
    | ~ spl0_143 ),
    inference(superposition,[],[f1131,f623]) ).

fof(f6628,plain,
    ( spl0_493
    | ~ spl0_52
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f930,f918,f467,f6626]) ).

fof(f6626,plain,
    ( spl0_493
  <=> ! [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_493])]) ).

fof(f930,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_52
    | ~ spl0_118 ),
    inference(resolution,[],[f919,f468]) ).

fof(f6463,plain,
    ( spl0_492
    | ~ spl0_28
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1644,f1621,f327,f6461]) ).

fof(f6461,plain,
    ( spl0_492
  <=> ! [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_492])]) ).

fof(f1644,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_28
    | ~ spl0_193 ),
    inference(duplicate_literal_removal,[],[f1637]) ).

fof(f1637,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_28
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f328]) ).

fof(f6459,plain,
    ( spl0_491
    | ~ spl0_52
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1608,f1588,f467,f6457]) ).

fof(f6457,plain,
    ( spl0_491
  <=> ! [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_491])]) ).

fof(f1608,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_52
    | ~ spl0_190 ),
    inference(duplicate_literal_removal,[],[f1592]) ).

fof(f1592,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_52
    | ~ spl0_190 ),
    inference(resolution,[],[f1589,f468]) ).

fof(f6455,plain,
    ( ~ spl0_490
    | ~ spl0_248
    | spl0_487 ),
    inference(avatar_split_clause,[],[f6441,f6437,f2393,f6452]) ).

fof(f6452,plain,
    ( spl0_490
  <=> subclass(domain_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f6437,plain,
    ( spl0_487
  <=> subclass(domain_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f6441,plain,
    ( ~ subclass(domain_relation,singleton_relation)
    | ~ spl0_248
    | spl0_487 ),
    inference(forward_demodulation,[],[f6439,f2395]) ).

fof(f6439,plain,
    ( ~ subclass(domain_relation,identity_relation)
    | spl0_487 ),
    inference(avatar_component_clause,[],[f6437]) ).

fof(f6450,plain,
    ( ~ spl0_488
    | ~ spl0_489
    | spl0_455
    | ~ spl0_15
    | ~ spl0_437 ),
    inference(avatar_split_clause,[],[f6390,f5495,f270,f5736,f6447,f6443]) ).

fof(f6443,plain,
    ( spl0_488
  <=> inductive(complement(w)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f6447,plain,
    ( spl0_489
  <=> subclass(omega,z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f5736,plain,
    ( spl0_455
  <=> null_class = omega ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f270,plain,
    ( spl0_15
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f5495,plain,
    ( spl0_437
  <=> ! [X0] :
        ( ~ subclass(X0,z)
        | null_class = X0
        | ~ subclass(X0,complement(w)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f6390,plain,
    ( null_class = omega
    | ~ subclass(omega,z)
    | ~ inductive(complement(w))
    | ~ spl0_15
    | ~ spl0_437 ),
    inference(resolution,[],[f5496,f271]) ).

fof(f271,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f5496,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(w))
        | null_class = X0
        | ~ subclass(X0,z) )
    | ~ spl0_437 ),
    inference(avatar_component_clause,[],[f5495]) ).

fof(f6440,plain,
    ( spl0_486
    | ~ spl0_487
    | ~ spl0_109
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1473,f1409,f793,f6437,f6434]) ).

fof(f6434,plain,
    ( spl0_486
  <=> ! [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_486])]) ).

fof(f1473,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_109
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f794]) ).

fof(f6432,plain,
    ( spl0_485
    | ~ spl0_124
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1379,f1351,f962,f6430]) ).

fof(f6430,plain,
    ( spl0_485
  <=> ! [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_485])]) ).

fof(f1379,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_124
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1362]) ).

fof(f1362,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_124
    | ~ spl0_166 ),
    inference(superposition,[],[f963,f1352]) ).

fof(f6428,plain,
    ( spl0_484
    | ~ spl0_124
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1374,f1351,f962,f6426]) ).

fof(f6426,plain,
    ( spl0_484
  <=> ! [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_484])]) ).

fof(f1374,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_124
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1367]) ).

fof(f1367,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_124
    | ~ spl0_166 ),
    inference(superposition,[],[f963,f1352]) ).

fof(f6424,plain,
    ( spl0_483
    | ~ spl0_28
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1221,f1193,f327,f6422]) ).

fof(f6422,plain,
    ( spl0_483
  <=> ! [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_483])]) ).

fof(f1221,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_28
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f328]) ).

fof(f6412,plain,
    ( spl0_286
    | spl0_482
    | ~ spl0_78
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1099,f1046,f621,f6409,f2613]) ).

fof(f6409,plain,
    ( spl0_482
  <=> 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_482])]) ).

fof(f1099,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_78
    | ~ spl0_136 ),
    inference(superposition,[],[f1047,f623]) ).

fof(f6407,plain,
    ( spl0_481
    | ~ spl0_48
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1010,f958,f447,f6405]) ).

fof(f6405,plain,
    ( spl0_481
  <=> ! [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_481])]) ).

fof(f1010,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_48
    | ~ spl0_123 ),
    inference(resolution,[],[f959,f448]) ).

fof(f6403,plain,
    ( spl0_480
    | ~ spl0_82
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f909,f855,f645,f6401]) ).

fof(f6401,plain,
    ( spl0_480
  <=> ! [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_480])]) ).

fof(f909,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_82
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f646]) ).

fof(f6398,plain,
    ( spl0_478
    | ~ spl0_479
    | ~ spl0_86
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f860,f834,f674,f6395,f6392]) ).

fof(f6392,plain,
    ( spl0_478
  <=> ! [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_478])]) ).

fof(f6395,plain,
    ( spl0_479
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f860,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_86
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f675]) ).

fof(f6231,plain,
    ( spl0_477
    | ~ spl0_248
    | ~ spl0_471 ),
    inference(avatar_split_clause,[],[f6118,f6115,f2393,f6229]) ).

fof(f6229,plain,
    ( spl0_477
  <=> ! [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_477])]) ).

fof(f6115,plain,
    ( spl0_471
  <=> ! [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_471])]) ).

fof(f6118,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_248
    | ~ spl0_471 ),
    inference(forward_demodulation,[],[f6116,f2395]) ).

fof(f6116,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_471 ),
    inference(avatar_component_clause,[],[f6115]) ).

fof(f6227,plain,
    ( spl0_476
    | ~ spl0_248
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f6113,f6110,f2393,f6225]) ).

fof(f6225,plain,
    ( spl0_476
  <=> ! [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_476])]) ).

fof(f6110,plain,
    ( spl0_470
  <=> ! [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_470])]) ).

fof(f6113,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_248
    | ~ spl0_470 ),
    inference(forward_demodulation,[],[f6111,f2395]) ).

fof(f6111,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_470 ),
    inference(avatar_component_clause,[],[f6110]) ).

fof(f6134,plain,
    ( spl0_475
    | ~ spl0_248
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f6100,f6097,f2393,f6132]) ).

fof(f6132,plain,
    ( spl0_475
  <=> ! [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_475])]) ).

fof(f6097,plain,
    ( spl0_467
  <=> ! [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_467])]) ).

fof(f6100,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_248
    | ~ spl0_467 ),
    inference(forward_demodulation,[],[f6098,f2395]) ).

fof(f6098,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_467 ),
    inference(avatar_component_clause,[],[f6097]) ).

fof(f6130,plain,
    ( spl0_474
    | ~ spl0_248
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f6095,f6091,f2393,f6128]) ).

fof(f6128,plain,
    ( spl0_474
  <=> ! [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_474])]) ).

fof(f6091,plain,
    ( spl0_466
  <=> ! [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_466])]) ).

fof(f6095,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_248
    | ~ spl0_466 ),
    inference(forward_demodulation,[],[f6094,f2395]) ).

fof(f6094,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_248
    | ~ spl0_466 ),
    inference(forward_demodulation,[],[f6092,f2395]) ).

fof(f6092,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_466 ),
    inference(avatar_component_clause,[],[f6091]) ).

fof(f6126,plain,
    ( spl0_473
    | ~ spl0_43
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1378,f1351,f396,f6124]) ).

fof(f6124,plain,
    ( spl0_473
  <=> ! [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_473])]) ).

fof(f1378,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_43
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1363]) ).

fof(f1363,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_43
    | ~ spl0_166 ),
    inference(superposition,[],[f397,f1352]) ).

fof(f6122,plain,
    ( spl0_472
    | ~ spl0_43
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1373,f1351,f396,f6120]) ).

fof(f6120,plain,
    ( spl0_472
  <=> ! [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_472])]) ).

fof(f1373,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_43
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1368]) ).

fof(f1368,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_43
    | ~ spl0_166 ),
    inference(superposition,[],[f397,f1352]) ).

fof(f6117,plain,
    ( spl0_471
    | ~ spl0_124
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1255,f1201,f962,f6115]) ).

fof(f1255,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_124
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f963]) ).

fof(f6112,plain,
    ( spl0_470
    | ~ spl0_124
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1241,f1197,f962,f6110]) ).

fof(f1241,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_124
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f963]) ).

fof(f6108,plain,
    ( spl0_469
    | ~ spl0_124
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1227,f1193,f962,f6106]) ).

fof(f6106,plain,
    ( spl0_469
  <=> ! [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_469])]) ).

fof(f1227,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_124
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f963]) ).

fof(f6104,plain,
    ( spl0_468
    | ~ spl0_51
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1105,f1050,f463,f6102]) ).

fof(f6102,plain,
    ( spl0_468
  <=> ! [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_468])]) ).

fof(f1105,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_51
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f464]) ).

fof(f6099,plain,
    ( spl0_467
    | ~ spl0_123
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1037,f1001,f958,f6097]) ).

fof(f1037,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_123
    | ~ spl0_133 ),
    inference(resolution,[],[f1002,f959]) ).

fof(f6093,plain,
    ( spl0_466
    | ~ spl0_123
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1033,f997,f958,f6091]) ).

fof(f1033,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_123
    | ~ spl0_132 ),
    inference(resolution,[],[f998,f959]) ).

fof(f6027,plain,
    ( spl0_465
    | ~ spl0_248
    | ~ spl0_461 ),
    inference(avatar_split_clause,[],[f5767,f5762,f2393,f6025]) ).

fof(f6025,plain,
    ( spl0_465
  <=> ! [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_465])]) ).

fof(f5762,plain,
    ( spl0_461
  <=> ! [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_461])]) ).

fof(f5767,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_248
    | ~ spl0_461 ),
    inference(forward_demodulation,[],[f5766,f2395]) ).

fof(f5766,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_248
    | ~ spl0_461 ),
    inference(forward_demodulation,[],[f5765,f2395]) ).

fof(f5765,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_248
    | ~ spl0_461 ),
    inference(forward_demodulation,[],[f5763,f2395]) ).

fof(f5763,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_461 ),
    inference(avatar_component_clause,[],[f5762]) ).

fof(f6023,plain,
    ( spl0_464
    | ~ spl0_248
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f5760,f5757,f2393,f6021]) ).

fof(f6021,plain,
    ( spl0_464
  <=> ! [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_464])]) ).

fof(f5757,plain,
    ( spl0_460
  <=> ! [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_460])]) ).

fof(f5760,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_248
    | ~ spl0_460 ),
    inference(forward_demodulation,[],[f5758,f2395]) ).

fof(f5758,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_460 ),
    inference(avatar_component_clause,[],[f5757]) ).

fof(f5775,plain,
    ( spl0_462
    | ~ spl0_463
    | ~ spl0_81
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1454,f1409,f641,f5772,f5769]) ).

fof(f5769,plain,
    ( spl0_462
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f5772,plain,
    ( spl0_463
  <=> subclass(domain_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f1454,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,successor_relation)
        | ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
    | ~ spl0_81
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f642]) ).

fof(f5764,plain,
    ( spl0_461
    | ~ spl0_45
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1443,f1405,f405,f5762]) ).

fof(f1443,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_45
    | ~ spl0_171 ),
    inference(superposition,[],[f1406,f407]) ).

fof(f5759,plain,
    ( spl0_460
    | ~ spl0_44
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1442,f1405,f400,f5757]) ).

fof(f400,plain,
    ( spl0_44
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f1442,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_44
    | ~ spl0_171 ),
    inference(superposition,[],[f1406,f402]) ).

fof(f402,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f400]) ).

fof(f5755,plain,
    ( spl0_459
    | ~ spl0_43
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1438,f1405,f396,f5753]) ).

fof(f5753,plain,
    ( spl0_459
  <=> ! [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_459])]) ).

fof(f1438,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_43
    | ~ spl0_171 ),
    inference(superposition,[],[f1406,f397]) ).

fof(f5751,plain,
    ( spl0_458
    | ~ spl0_131
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1380,f1351,f993,f5749]) ).

fof(f5749,plain,
    ( spl0_458
  <=> ! [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_458])]) ).

fof(f1380,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_131
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1361]) ).

fof(f1361,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_131
    | ~ spl0_166 ),
    inference(superposition,[],[f994,f1352]) ).

fof(f5747,plain,
    ( spl0_457
    | ~ spl0_131
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1375,f1351,f993,f5745]) ).

fof(f5745,plain,
    ( spl0_457
  <=> ! [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_457])]) ).

fof(f1375,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_131
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1366]) ).

fof(f1366,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_131
    | ~ spl0_166 ),
    inference(superposition,[],[f994,f1352]) ).

fof(f5743,plain,
    ( spl0_456
    | ~ spl0_41
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1302,f1290,f388,f5741]) ).

fof(f5741,plain,
    ( spl0_456
  <=> ! [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_456])]) ).

fof(f1302,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_41
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f389]) ).

fof(f5739,plain,
    ( ~ spl0_453
    | ~ spl0_454
    | spl0_455
    | ~ spl0_15
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f5679,f5203,f270,f5736,f5732,f5728]) ).

fof(f5728,plain,
    ( spl0_453
  <=> inductive(complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f5732,plain,
    ( spl0_454
  <=> subclass(omega,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f5203,plain,
    ( spl0_434
  <=> ! [X0] :
        ( ~ subclass(X0,x)
        | null_class = X0
        | ~ subclass(X0,complement(y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f5679,plain,
    ( null_class = omega
    | ~ subclass(omega,x)
    | ~ inductive(complement(y))
    | ~ spl0_15
    | ~ spl0_434 ),
    inference(resolution,[],[f5204,f271]) ).

fof(f5204,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(y))
        | null_class = X0
        | ~ subclass(X0,x) )
    | ~ spl0_434 ),
    inference(avatar_component_clause,[],[f5203]) ).

fof(f5726,plain,
    ( ~ spl0_451
    | spl0_452
    | ~ spl0_112
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1258,f1201,f834,f5724,f5720]) ).

fof(f5720,plain,
    ( spl0_451
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f5724,plain,
    ( spl0_452
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f1258,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_112
    | ~ spl0_150 ),
    inference(resolution,[],[f1202,f835]) ).

fof(f5718,plain,
    ( ~ spl0_450
    | ~ spl0_248
    | spl0_448 ),
    inference(avatar_split_clause,[],[f5713,f5706,f2393,f5715]) ).

fof(f5715,plain,
    ( spl0_450
  <=> subclass(universal_class,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f5713,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_248
    | spl0_448 ),
    inference(forward_demodulation,[],[f5708,f2395]) ).

fof(f5708,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
    | spl0_448 ),
    inference(avatar_component_clause,[],[f5706]) ).

fof(f5712,plain,
    ( ~ spl0_448
    | spl0_449
    | ~ spl0_112
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1244,f1197,f834,f5710,f5706]) ).

fof(f5710,plain,
    ( spl0_449
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1244,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_112
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f835]) ).

fof(f5704,plain,
    ( spl0_447
    | ~ spl0_112
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1230,f1193,f834,f5702]) ).

fof(f5702,plain,
    ( spl0_447
  <=> ! [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_447])]) ).

fof(f1230,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_112
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f835]) ).

fof(f5700,plain,
    ( spl0_446
    | ~ spl0_25
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1225,f1193,f311,f5698]) ).

fof(f5698,plain,
    ( spl0_446
  <=> ! [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_446])]) ).

fof(f1225,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) )
    | ~ spl0_25
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f312]) ).

fof(f5694,plain,
    ( ~ spl0_445
    | ~ spl0_248
    | spl0_444 ),
    inference(avatar_split_clause,[],[f5689,f5685,f2393,f5691]) ).

fof(f5691,plain,
    ( spl0_445
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f5685,plain,
    ( spl0_444
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f5689,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
    | ~ spl0_248
    | spl0_444 ),
    inference(forward_demodulation,[],[f5687,f2395]) ).

fof(f5687,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | spl0_444 ),
    inference(avatar_component_clause,[],[f5685]) ).

fof(f5688,plain,
    ( spl0_443
    | ~ spl0_444
    | ~ spl0_118
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1039,f1001,f918,f5685,f5681]) ).

fof(f1039,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_118
    | ~ spl0_133 ),
    inference(resolution,[],[f1002,f919]) ).

fof(f5670,plain,
    ( ~ spl0_442
    | ~ spl0_248
    | spl0_440 ),
    inference(avatar_split_clause,[],[f5659,f5655,f2393,f5667]) ).

fof(f5667,plain,
    ( spl0_442
  <=> member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f5655,plain,
    ( spl0_440
  <=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f5659,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
    | ~ spl0_248
    | spl0_440 ),
    inference(forward_demodulation,[],[f5657,f2395]) ).

fof(f5657,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | spl0_440 ),
    inference(avatar_component_clause,[],[f5655]) ).

fof(f5665,plain,
    ( ~ spl0_441
    | ~ spl0_248
    | spl0_439 ),
    inference(avatar_split_clause,[],[f5660,f5651,f2393,f5662]) ).

fof(f5662,plain,
    ( spl0_441
  <=> null_class = complement(complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f5660,plain,
    ( null_class != complement(complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_248
    | spl0_439 ),
    inference(forward_demodulation,[],[f5652,f2395]) ).

fof(f5652,plain,
    ( null_class != complement(complement(compose(element_relation,complement(identity_relation))))
    | spl0_439 ),
    inference(avatar_component_clause,[],[f5651]) ).

fof(f5658,plain,
    ( spl0_439
    | ~ spl0_440
    | ~ spl0_118
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1034,f997,f918,f5655,f5651]) ).

fof(f1034,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_118
    | ~ spl0_132 ),
    inference(resolution,[],[f998,f919]) ).

fof(f5649,plain,
    ( spl0_438
    | ~ spl0_48
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f931,f918,f447,f5647]) ).

fof(f5647,plain,
    ( spl0_438
  <=> ! [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_438])]) ).

fof(f931,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_48
    | ~ spl0_118 ),
    inference(resolution,[],[f919,f448]) ).

fof(f5497,plain,
    ( spl0_437
    | ~ spl0_304
    | ~ spl0_378 ),
    inference(avatar_split_clause,[],[f4442,f3872,f2899,f5495]) ).

fof(f2899,plain,
    ( spl0_304
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f3872,plain,
    ( spl0_378
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,z)
        | member(regular(X0),w) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f4442,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | null_class = X0
        | ~ subclass(X0,complement(w)) )
    | ~ spl0_304
    | ~ spl0_378 ),
    inference(duplicate_literal_removal,[],[f4432]) ).

fof(f4432,plain,
    ( ! [X0] :
        ( ~ subclass(X0,z)
        | null_class = X0
        | null_class = X0
        | ~ subclass(X0,complement(w)) )
    | ~ spl0_304
    | ~ spl0_378 ),
    inference(resolution,[],[f3873,f2900]) ).

fof(f2900,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_304 ),
    inference(avatar_component_clause,[],[f2899]) ).

fof(f3873,plain,
    ( ! [X0] :
        ( member(regular(X0),w)
        | ~ subclass(X0,z)
        | null_class = X0 )
    | ~ spl0_378 ),
    inference(avatar_component_clause,[],[f3872]) ).

fof(f5321,plain,
    ( spl0_436
    | ~ spl0_248
    | ~ spl0_425 ),
    inference(avatar_split_clause,[],[f4986,f4983,f2393,f5319]) ).

fof(f5319,plain,
    ( spl0_436
  <=> ! [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_436])]) ).

fof(f4983,plain,
    ( spl0_425
  <=> ! [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_425])]) ).

fof(f4986,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_248
    | ~ spl0_425 ),
    inference(forward_demodulation,[],[f4984,f2395]) ).

fof(f4984,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_425 ),
    inference(avatar_component_clause,[],[f4983]) ).

fof(f5317,plain,
    ( spl0_435
    | ~ spl0_248
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f4981,f4978,f2393,f5315]) ).

fof(f5315,plain,
    ( spl0_435
  <=> ! [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_435])]) ).

fof(f4978,plain,
    ( spl0_424
  <=> ! [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_424])]) ).

fof(f4981,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_248
    | ~ spl0_424 ),
    inference(forward_demodulation,[],[f4979,f2395]) ).

fof(f4979,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_424 ),
    inference(avatar_component_clause,[],[f4978]) ).

fof(f5205,plain,
    ( spl0_434
    | ~ spl0_304
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f3927,f3786,f2899,f5203]) ).

fof(f3786,plain,
    ( spl0_373
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,x)
        | member(regular(X0),y) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f3927,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | null_class = X0
        | ~ subclass(X0,complement(y)) )
    | ~ spl0_304
    | ~ spl0_373 ),
    inference(duplicate_literal_removal,[],[f3917]) ).

fof(f3917,plain,
    ( ! [X0] :
        ( ~ subclass(X0,x)
        | null_class = X0
        | null_class = X0
        | ~ subclass(X0,complement(y)) )
    | ~ spl0_304
    | ~ spl0_373 ),
    inference(resolution,[],[f3787,f2900]) ).

fof(f3787,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | ~ subclass(X0,x)
        | null_class = X0 )
    | ~ spl0_373 ),
    inference(avatar_component_clause,[],[f3786]) ).

fof(f5026,plain,
    ( spl0_433
    | ~ spl0_248
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f4956,f4953,f2393,f5024]) ).

fof(f5024,plain,
    ( spl0_433
  <=> ! [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_433])]) ).

fof(f4953,plain,
    ( spl0_418
  <=> ! [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_418])]) ).

fof(f4956,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_248
    | ~ spl0_418 ),
    inference(forward_demodulation,[],[f4954,f2395]) ).

fof(f4954,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_418 ),
    inference(avatar_component_clause,[],[f4953]) ).

fof(f5022,plain,
    ( spl0_432
    | ~ spl0_248
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f4951,f4947,f2393,f5020]) ).

fof(f5020,plain,
    ( spl0_432
  <=> ! [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_432])]) ).

fof(f4947,plain,
    ( spl0_417
  <=> ! [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_417])]) ).

fof(f4951,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_248
    | ~ spl0_417 ),
    inference(forward_demodulation,[],[f4950,f2395]) ).

fof(f4950,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_248
    | ~ spl0_417 ),
    inference(forward_demodulation,[],[f4948,f2395]) ).

fof(f4948,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_417 ),
    inference(avatar_component_clause,[],[f4947]) ).

fof(f5010,plain,
    ( spl0_431
    | ~ spl0_142
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1446,f1405,f1126,f5008]) ).

fof(f5008,plain,
    ( spl0_431
  <=> ! [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_431])]) ).

fof(f1446,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_142
    | ~ spl0_171 ),
    inference(duplicate_literal_removal,[],[f1427]) ).

fof(f1427,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_142
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f1127]) ).

fof(f5006,plain,
    ( spl0_430
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1445,f1405,f1130,f5004]) ).

fof(f5004,plain,
    ( spl0_430
  <=> ! [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_430])]) ).

fof(f1445,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(duplicate_literal_removal,[],[f1428]) ).

fof(f1428,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_143
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f1131]) ).

fof(f5002,plain,
    ( spl0_429
    | ~ spl0_25
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1377,f1351,f311,f5000]) ).

fof(f5000,plain,
    ( spl0_429
  <=> ! [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_429])]) ).

fof(f1377,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_25
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1364]) ).

fof(f1364,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_25
    | ~ spl0_166 ),
    inference(superposition,[],[f312,f1352]) ).

fof(f4998,plain,
    ( spl0_428
    | ~ spl0_25
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1372,f1351,f311,f4996]) ).

fof(f4996,plain,
    ( spl0_428
  <=> ! [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_428])]) ).

fof(f1372,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_25
    | ~ spl0_166 ),
    inference(duplicate_literal_removal,[],[f1369]) ).

fof(f1369,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_25
    | ~ spl0_166 ),
    inference(superposition,[],[f312,f1352]) ).

fof(f4994,plain,
    ( spl0_427
    | ~ spl0_33
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1306,f1290,f347,f4992]) ).

fof(f4992,plain,
    ( spl0_427
  <=> ! [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_427])]) ).

fof(f1306,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_33
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f348]) ).

fof(f4990,plain,
    ( spl0_426
    | ~ spl0_34
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1305,f1290,f351,f4988]) ).

fof(f4988,plain,
    ( spl0_426
  <=> ! [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_426])]) ).

fof(f1305,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_34
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f352]) ).

fof(f4985,plain,
    ( spl0_425
    | ~ spl0_45
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1301,f1286,f405,f4983]) ).

fof(f1301,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_45
    | ~ spl0_159 ),
    inference(superposition,[],[f1287,f407]) ).

fof(f4980,plain,
    ( spl0_424
    | ~ spl0_44
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1300,f1286,f400,f4978]) ).

fof(f1300,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_44
    | ~ spl0_159 ),
    inference(superposition,[],[f1287,f402]) ).

fof(f4976,plain,
    ( spl0_423
    | ~ spl0_43
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1296,f1286,f396,f4974]) ).

fof(f4974,plain,
    ( spl0_423
  <=> ! [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_423])]) ).

fof(f1296,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 )
    | ~ spl0_43
    | ~ spl0_159 ),
    inference(superposition,[],[f1287,f397]) ).

fof(f4972,plain,
    ( spl0_422
    | ~ spl0_33
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1168,f1130,f347,f4970]) ).

fof(f4970,plain,
    ( spl0_422
  <=> ! [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_422])]) ).

fof(f1168,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_33
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f348]) ).

fof(f4968,plain,
    ( spl0_421
    | ~ spl0_34
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1167,f1130,f351,f4966]) ).

fof(f4966,plain,
    ( spl0_421
  <=> ! [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_421])]) ).

fof(f1167,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_34
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f352]) ).

fof(f4964,plain,
    ( spl0_420
    | ~ spl0_33
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1150,f1126,f347,f4962]) ).

fof(f4962,plain,
    ( spl0_420
  <=> ! [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_420])]) ).

fof(f1150,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_33
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f348]) ).

fof(f4960,plain,
    ( spl0_419
    | ~ spl0_34
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1149,f1126,f351,f4958]) ).

fof(f4958,plain,
    ( spl0_419
  <=> ! [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_419])]) ).

fof(f1149,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_34
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f352]) ).

fof(f4955,plain,
    ( spl0_418
    | ~ spl0_29
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1036,f1001,f331,f4953]) ).

fof(f1036,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_29
    | ~ spl0_133 ),
    inference(resolution,[],[f1002,f332]) ).

fof(f4949,plain,
    ( spl0_417
    | ~ spl0_29
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1032,f997,f331,f4947]) ).

fof(f1032,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_29
    | ~ spl0_132 ),
    inference(resolution,[],[f998,f332]) ).

fof(f4945,plain,
    ( spl0_416
    | ~ spl0_51
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1015,f962,f463,f4943]) ).

fof(f4943,plain,
    ( spl0_416
  <=> ! [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_416])]) ).

fof(f1015,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_51
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f464]) ).

fof(f4825,plain,
    ( spl0_415
    | ~ spl0_248
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f4412,f4409,f2393,f4823]) ).

fof(f4823,plain,
    ( spl0_415
  <=> ! [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_415])]) ).

fof(f4409,plain,
    ( spl0_407
  <=> ! [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_407])]) ).

fof(f4412,plain,
    ( ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_248
    | ~ spl0_407 ),
    inference(forward_demodulation,[],[f4410,f2395]) ).

fof(f4410,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_407 ),
    inference(avatar_component_clause,[],[f4409]) ).

fof(f4685,plain,
    ( spl0_413
    | ~ spl0_414
    | ~ spl0_118
    | ~ spl0_378 ),
    inference(avatar_split_clause,[],[f4444,f3872,f918,f4682,f4678]) ).

fof(f4678,plain,
    ( spl0_413
  <=> null_class = complement(w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f4682,plain,
    ( spl0_414
  <=> subclass(complement(w),z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f4444,plain,
    ( ~ subclass(complement(w),z)
    | null_class = complement(w)
    | ~ spl0_118
    | ~ spl0_378 ),
    inference(duplicate_literal_removal,[],[f4430]) ).

fof(f4430,plain,
    ( ~ subclass(complement(w),z)
    | null_class = complement(w)
    | null_class = complement(w)
    | ~ spl0_118
    | ~ spl0_378 ),
    inference(resolution,[],[f3873,f919]) ).

fof(f4448,plain,
    ( spl0_412
    | ~ spl0_137
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1444,f1405,f1050,f4446]) ).

fof(f1444,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_137
    | ~ spl0_171 ),
    inference(duplicate_literal_removal,[],[f1429]) ).

fof(f1429,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_137
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f1051]) ).

fof(f4429,plain,
    ( ~ spl0_410
    | spl0_411
    | ~ spl0_14
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1345,f1329,f266,f4426,f4422]) ).

fof(f4422,plain,
    ( spl0_410
  <=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f4426,plain,
    ( spl0_411
  <=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f1345,plain,
    ( null_class = cross_product(unordered_pair(null_class,null_class),universal_class)
    | ~ inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class))))
    | ~ spl0_14
    | ~ spl0_164 ),
    inference(resolution,[],[f1330,f267]) ).

fof(f4420,plain,
    ( spl0_409
    | ~ spl0_22
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1307,f1290,f299,f4418]) ).

fof(f4418,plain,
    ( spl0_409
  <=> ! [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_409])]) ).

fof(f1307,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_22
    | ~ spl0_160 ),
    inference(resolution,[],[f1291,f300]) ).

fof(f4416,plain,
    ( spl0_408
    | ~ spl0_24
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1295,f1286,f307,f4414]) ).

fof(f4414,plain,
    ( spl0_408
  <=> ! [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_408])]) ).

fof(f1295,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) )
    | ~ spl0_24
    | ~ spl0_159 ),
    inference(resolution,[],[f1287,f308]) ).

fof(f4411,plain,
    ( spl0_407
    | ~ spl0_48
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1234,f1197,f447,f4409]) ).

fof(f1234,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_48
    | ~ spl0_149 ),
    inference(resolution,[],[f1198,f448]) ).

fof(f4407,plain,
    ( spl0_406
    | ~ spl0_119
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1170,f1130,f922,f4405]) ).

fof(f4405,plain,
    ( spl0_406
  <=> ! [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_406])]) ).

fof(f1170,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 )
    | ~ spl0_119
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f923]) ).

fof(f4403,plain,
    ( spl0_405
    | ~ spl0_41
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1164,f1130,f388,f4401]) ).

fof(f4401,plain,
    ( spl0_405
  <=> ! [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_405])]) ).

fof(f1164,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_41
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f389]) ).

fof(f4399,plain,
    ( spl0_404
    | ~ spl0_119
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1152,f1126,f922,f4397]) ).

fof(f4397,plain,
    ( spl0_404
  <=> ! [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_404])]) ).

fof(f1152,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 )
    | ~ spl0_119
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f923]) ).

fof(f4395,plain,
    ( spl0_403
    | ~ spl0_41
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1146,f1126,f388,f4393]) ).

fof(f4393,plain,
    ( spl0_403
  <=> ! [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_403])]) ).

fof(f1146,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_41
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f389]) ).

fof(f4391,plain,
    ( spl0_402
    | ~ spl0_33
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1090,f1046,f347,f4389]) ).

fof(f4389,plain,
    ( spl0_402
  <=> ! [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_402])]) ).

fof(f1090,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_33
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f348]) ).

fof(f4387,plain,
    ( spl0_401
    | ~ spl0_34
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1089,f1046,f351,f4385]) ).

fof(f4385,plain,
    ( spl0_401
  <=> ! [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_401])]) ).

fof(f1089,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_34
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f352]) ).

fof(f4383,plain,
    ( spl0_400
    | ~ spl0_33
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1069,f1042,f347,f4381]) ).

fof(f4381,plain,
    ( spl0_400
  <=> ! [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_400])]) ).

fof(f1069,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_33
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f348]) ).

fof(f4379,plain,
    ( spl0_399
    | ~ spl0_34
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1068,f1042,f351,f4377]) ).

fof(f4377,plain,
    ( spl0_399
  <=> ! [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_399])]) ).

fof(f1068,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_34
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f352]) ).

fof(f4375,plain,
    ( spl0_398
    | ~ spl0_123
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1027,f993,f958,f4373]) ).

fof(f4373,plain,
    ( spl0_398
  <=> ! [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_398])]) ).

fof(f1027,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) )
    | ~ spl0_123
    | ~ spl0_131 ),
    inference(resolution,[],[f994,f959]) ).

fof(f4371,plain,
    ( spl0_397
    | ~ spl0_51
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f878,f834,f463,f4369]) ).

fof(f4369,plain,
    ( spl0_397
  <=> ! [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_397])]) ).

fof(f878,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_51
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f464]) ).

fof(f3978,plain,
    ( spl0_395
    | ~ spl0_396
    | ~ spl0_118
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f3929,f3786,f918,f3975,f3971]) ).

fof(f3971,plain,
    ( spl0_395
  <=> null_class = complement(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f3975,plain,
    ( spl0_396
  <=> subclass(complement(y),x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f3929,plain,
    ( ~ subclass(complement(y),x)
    | null_class = complement(y)
    | ~ spl0_118
    | ~ spl0_373 ),
    inference(duplicate_literal_removal,[],[f3915]) ).

fof(f3915,plain,
    ( ~ subclass(complement(y),x)
    | null_class = complement(y)
    | null_class = complement(y)
    | ~ spl0_118
    | ~ spl0_373 ),
    inference(resolution,[],[f3787,f919]) ).

fof(f3953,plain,
    ( spl0_394
    | ~ spl0_112
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1773,f1747,f834,f3951]) ).

fof(f3951,plain,
    ( spl0_394
  <=> ! [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_394])]) ).

fof(f1773,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_112
    | ~ spl0_204 ),
    inference(superposition,[],[f835,f1748]) ).

fof(f3949,plain,
    ( spl0_393
    | ~ spl0_34
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1394,f1391,f351,f3947]) ).

fof(f3947,plain,
    ( spl0_393
  <=> ! [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_393])]) ).

fof(f1394,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_34
    | ~ spl0_169 ),
    inference(resolution,[],[f1392,f352]) ).

fof(f3945,plain,
    ( spl0_392
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1371,f1351,f3943]) ).

fof(f3943,plain,
    ( spl0_392
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1371,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_166 ),
    inference(equality_factoring,[],[f1352]) ).

fof(f3941,plain,
    ( spl0_391
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1370,f1351,f3939]) ).

fof(f3939,plain,
    ( spl0_391
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f1370,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_166 ),
    inference(equality_factoring,[],[f1352]) ).

fof(f3937,plain,
    ( spl0_390
    | ~ spl0_142
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1342,f1324,f1126,f3935]) ).

fof(f3935,plain,
    ( spl0_390
  <=> ! [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_390])]) ).

fof(f1324,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

fof(f1342,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_142
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1337]) ).

fof(f1337,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_142
    | ~ spl0_163 ),
    inference(resolution,[],[f1325,f1127]) ).

fof(f1325,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_163 ),
    inference(avatar_component_clause,[],[f1324]) ).

fof(f3933,plain,
    ( spl0_389
    | ~ spl0_143
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1341,f1324,f1130,f3931]) ).

fof(f3931,plain,
    ( spl0_389
  <=> ! [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_389])]) ).

fof(f1341,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_143
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1338]) ).

fof(f1338,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_143
    | ~ spl0_163 ),
    inference(resolution,[],[f1325,f1131]) ).

fof(f3914,plain,
    ( spl0_388
    | ~ spl0_24
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1219,f1189,f307,f3912]) ).

fof(f3912,plain,
    ( spl0_388
  <=> ! [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_388])]) ).

fof(f1189,plain,
    ( spl0_147
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1219,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_24
    | ~ spl0_147 ),
    inference(resolution,[],[f1190,f308]) ).

fof(f1190,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1189]) ).

fof(f3910,plain,
    ( spl0_387
    | ~ spl0_22
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1169,f1130,f299,f3908]) ).

fof(f3908,plain,
    ( spl0_387
  <=> ! [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_387])]) ).

fof(f1169,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_22
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f300]) ).

fof(f3906,plain,
    ( spl0_386
    | ~ spl0_22
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1151,f1126,f299,f3904]) ).

fof(f3904,plain,
    ( spl0_386
  <=> ! [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_386])]) ).

fof(f1151,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_22
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f300]) ).

fof(f3902,plain,
    ( spl0_385
    | ~ spl0_119
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1110,f1050,f922,f3900]) ).

fof(f3900,plain,
    ( spl0_385
  <=> ! [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_385])]) ).

fof(f1110,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 )
    | ~ spl0_119
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f923]) ).

fof(f3898,plain,
    ( spl0_384
    | ~ spl0_41
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1104,f1050,f388,f3896]) ).

fof(f1104,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_41
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f389]) ).

fof(f3894,plain,
    ( spl0_383
    | ~ spl0_119
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1092,f1046,f922,f3892]) ).

fof(f3892,plain,
    ( spl0_383
  <=> ! [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_383])]) ).

fof(f1092,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 )
    | ~ spl0_119
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f923]) ).

fof(f3890,plain,
    ( spl0_382
    | ~ spl0_41
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1086,f1046,f388,f3888]) ).

fof(f3888,plain,
    ( spl0_382
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f1086,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_41
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f389]) ).

fof(f3886,plain,
    ( spl0_381
    | ~ spl0_119
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1071,f1042,f922,f3884]) ).

fof(f3884,plain,
    ( spl0_381
  <=> ! [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_381])]) ).

fof(f1071,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 )
    | ~ spl0_119
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f923]) ).

fof(f3882,plain,
    ( spl0_380
    | ~ spl0_41
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1065,f1042,f388,f3880]) ).

fof(f3880,plain,
    ( spl0_380
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f1065,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_41
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f389]) ).

fof(f3878,plain,
    ( spl0_379
    | ~ spl0_118
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1028,f993,f918,f3876]) ).

fof(f3876,plain,
    ( spl0_379
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f1028,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) )
    | ~ spl0_118
    | ~ spl0_131 ),
    inference(resolution,[],[f994,f919]) ).

fof(f3874,plain,
    ( spl0_378
    | ~ spl0_2
    | ~ spl0_359 ),
    inference(avatar_split_clause,[],[f3662,f3589,f211,f3872]) ).

fof(f3589,plain,
    ( spl0_359
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f3662,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,z)
        | member(regular(X0),w) )
    | ~ spl0_2
    | ~ spl0_359 ),
    inference(resolution,[],[f3590,f213]) ).

fof(f3590,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X1,X2)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),X2) )
    | ~ spl0_359 ),
    inference(avatar_component_clause,[],[f3589]) ).

fof(f3870,plain,
    ( spl0_377
    | ~ spl0_117
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1008,f958,f855,f3868]) ).

fof(f3868,plain,
    ( spl0_377
  <=> ! [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_377])]) ).

fof(f1008,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_117
    | ~ spl0_123 ),
    inference(resolution,[],[f959,f856]) ).

fof(f3866,plain,
    ( spl0_376
    | ~ spl0_70
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f914,f855,f574,f3864]) ).

fof(f3864,plain,
    ( spl0_376
  <=> ! [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_376])]) ).

fof(f914,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_70
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f575]) ).

fof(f3862,plain,
    ( spl0_375
    | ~ spl0_71
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f913,f855,f578,f3860]) ).

fof(f3860,plain,
    ( spl0_375
  <=> ! [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_375])]) ).

fof(f913,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_71
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f579]) ).

fof(f3858,plain,
    ( spl0_374
    | ~ spl0_59
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f890,f838,f518,f3856]) ).

fof(f3856,plain,
    ( spl0_374
  <=> ! [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_374])]) ).

fof(f890,plain,
    ( ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_59
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f519]) ).

fof(f3788,plain,
    ( spl0_373
    | ~ spl0_1
    | ~ spl0_359 ),
    inference(avatar_split_clause,[],[f3661,f3589,f206,f3786]) ).

fof(f3661,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,x)
        | member(regular(X0),y) )
    | ~ spl0_1
    | ~ spl0_359 ),
    inference(resolution,[],[f3590,f208]) ).

fof(f3724,plain,
    ( spl0_372
    | ~ spl0_248
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3613,f3610,f2393,f3722]) ).

fof(f3722,plain,
    ( spl0_372
  <=> ! [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_372])]) ).

fof(f3610,plain,
    ( spl0_364
  <=> ! [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_364])]) ).

fof(f3613,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_248
    | ~ spl0_364 ),
    inference(forward_demodulation,[],[f3611,f2395]) ).

fof(f3611,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_364 ),
    inference(avatar_component_clause,[],[f3610]) ).

fof(f3720,plain,
    ( spl0_371
    | ~ spl0_248
    | ~ spl0_363 ),
    inference(avatar_split_clause,[],[f3608,f3605,f2393,f3718]) ).

fof(f3718,plain,
    ( spl0_371
  <=> ! [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_371])]) ).

fof(f3605,plain,
    ( spl0_363
  <=> ! [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_363])]) ).

fof(f3608,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_248
    | ~ spl0_363 ),
    inference(forward_demodulation,[],[f3606,f2395]) ).

fof(f3606,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_363 ),
    inference(avatar_component_clause,[],[f3605]) ).

fof(f3637,plain,
    ( spl0_370
    | ~ spl0_74
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1456,f1409,f597,f3635]) ).

fof(f3635,plain,
    ( spl0_370
  <=> ! [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_370])]) ).

fof(f1456,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) )
    | ~ spl0_74
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f598]) ).

fof(f3633,plain,
    ( spl0_369
    | ~ spl0_137
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1340,f1324,f1050,f3631]) ).

fof(f3631,plain,
    ( spl0_369
  <=> ! [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_369])]) ).

fof(f1340,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_137
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1339]) ).

fof(f1339,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_137
    | ~ spl0_163 ),
    inference(resolution,[],[f1325,f1051]) ).

fof(f3629,plain,
    ( spl0_368
    | ~ spl0_33
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1108,f1050,f347,f3627]) ).

fof(f3627,plain,
    ( spl0_368
  <=> ! [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_368])]) ).

fof(f1108,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_33
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f348]) ).

fof(f3625,plain,
    ( spl0_367
    | ~ spl0_34
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1107,f1050,f351,f3623]) ).

fof(f3623,plain,
    ( spl0_367
  <=> ! [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_367])]) ).

fof(f1107,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_34
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f352]) ).

fof(f3621,plain,
    ( spl0_366
    | ~ spl0_22
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1091,f1046,f299,f3619]) ).

fof(f3619,plain,
    ( spl0_366
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f1091,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_22
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f300]) ).

fof(f3617,plain,
    ( spl0_365
    | ~ spl0_22
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1070,f1042,f299,f3615]) ).

fof(f3615,plain,
    ( spl0_365
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f1070,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_22
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f300]) ).

fof(f3612,plain,
    ( spl0_364
    | ~ spl0_41
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1035,f1001,f388,f3610]) ).

fof(f1035,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_41
    | ~ spl0_133 ),
    inference(resolution,[],[f1002,f389]) ).

fof(f3607,plain,
    ( spl0_363
    | ~ spl0_41
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1031,f997,f388,f3605]) ).

fof(f1031,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_41
    | ~ spl0_132 ),
    inference(resolution,[],[f998,f389]) ).

fof(f3603,plain,
    ( spl0_362
    | ~ spl0_29
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1026,f993,f331,f3601]) ).

fof(f3601,plain,
    ( spl0_362
  <=> ! [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_362])]) ).

fof(f1026,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_29
    | ~ spl0_131 ),
    inference(resolution,[],[f994,f332]) ).

fof(f3599,plain,
    ( spl0_361
    | ~ spl0_41
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1025,f993,f388,f3597]) ).

fof(f3597,plain,
    ( spl0_361
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f1025,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_41
    | ~ spl0_131 ),
    inference(resolution,[],[f994,f389]) ).

fof(f3595,plain,
    ( spl0_360
    | ~ spl0_119
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1020,f962,f922,f3593]) ).

fof(f3593,plain,
    ( spl0_360
  <=> ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f1020,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 )
    | ~ spl0_119
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f923]) ).

fof(f3591,plain,
    ( spl0_359
    | ~ spl0_41
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1014,f962,f388,f3589]) ).

fof(f1014,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_41
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f389]) ).

fof(f3587,plain,
    ( ~ spl0_358
    | ~ spl0_6
    | ~ spl0_11
    | ~ spl0_275
    | ~ spl0_279 ),
    inference(avatar_split_clause,[],[f2666,f2574,f2537,f252,f231,f3584]) ).

fof(f3584,plain,
    ( spl0_358
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f231,plain,
    ( spl0_6
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f2537,plain,
    ( spl0_275
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f2574,plain,
    ( spl0_279
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f2666,plain,
    ( ~ subclass(universal_class,null_class)
    | ~ spl0_6
    | ~ spl0_11
    | ~ spl0_275
    | ~ spl0_279 ),
    inference(forward_demodulation,[],[f2645,f2564]) ).

fof(f2564,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_6
    | ~ spl0_275 ),
    inference(resolution,[],[f2538,f232]) ).

fof(f232,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f2538,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2537]) ).

fof(f2645,plain,
    ( ~ subclass(universal_class,complement(universal_class))
    | ~ spl0_11
    | ~ spl0_279 ),
    inference(resolution,[],[f2575,f253]) ).

fof(f2575,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_279 ),
    inference(avatar_component_clause,[],[f2574]) ).

fof(f3579,plain,
    ( ~ spl0_356
    | spl0_357
    | ~ spl0_117
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f929,f918,f855,f3576,f3572]) ).

fof(f3572,plain,
    ( spl0_356
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f929,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | ~ spl0_117
    | ~ spl0_118 ),
    inference(resolution,[],[f919,f856]) ).

fof(f3569,plain,
    ( spl0_354
    | ~ spl0_248
    | ~ spl0_353 ),
    inference(avatar_split_clause,[],[f3568,f3553,f2393,f3559]) ).

fof(f3559,plain,
    ( spl0_354
  <=> member(null_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f3553,plain,
    ( spl0_353
  <=> member(null_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f3568,plain,
    ( member(null_class,singleton_relation)
    | ~ spl0_248
    | ~ spl0_353 ),
    inference(forward_demodulation,[],[f3555,f2395]) ).

fof(f3555,plain,
    ( member(null_class,identity_relation)
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f3553]) ).

fof(f3567,plain,
    ( spl0_355
    | spl0_353
    | ~ spl0_54
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f898,f838,f475,f3553,f3565]) ).

fof(f3565,plain,
    ( spl0_355
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f475,plain,
    ( spl0_54
  <=> ! [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_54])]) ).

fof(f898,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) )
    | ~ spl0_54
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f476]) ).

fof(f476,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f475]) ).

fof(f3562,plain,
    ( ~ spl0_354
    | ~ spl0_248
    | spl0_353 ),
    inference(avatar_split_clause,[],[f3557,f3553,f2393,f3559]) ).

fof(f3557,plain,
    ( ~ member(null_class,singleton_relation)
    | ~ spl0_248
    | spl0_353 ),
    inference(forward_demodulation,[],[f3554,f2395]) ).

fof(f3554,plain,
    ( ~ member(null_class,identity_relation)
    | spl0_353 ),
    inference(avatar_component_clause,[],[f3553]) ).

fof(f3556,plain,
    ( spl0_352
    | spl0_353
    | ~ spl0_55
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f897,f838,f479,f3553,f3550]) ).

fof(f3550,plain,
    ( spl0_352
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f479,plain,
    ( spl0_55
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f897,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_55
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f480]) ).

fof(f480,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f479]) ).

fof(f3543,plain,
    ( spl0_350
    | ~ spl0_351
    | ~ spl0_81
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f863,f834,f641,f3540,f3537]) ).

fof(f3537,plain,
    ( spl0_350
  <=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f3540,plain,
    ( spl0_351
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f863,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_81
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f642]) ).

fof(f3429,plain,
    ( spl0_349
    | ~ spl0_6
    | ~ spl0_275
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f2568,f2541,f2537,f231,f3427]) ).

fof(f3427,plain,
    ( spl0_349
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f2541,plain,
    ( spl0_276
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f2568,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_6
    | ~ spl0_275
    | ~ spl0_276 ),
    inference(forward_demodulation,[],[f2566,f2564]) ).

fof(f2566,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_6
    | ~ spl0_276 ),
    inference(resolution,[],[f2542,f232]) ).

fof(f2542,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f2541]) ).

fof(f3415,plain,
    ( spl0_348
    | ~ spl0_248
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f3280,f3276,f2393,f3413]) ).

fof(f3413,plain,
    ( spl0_348
  <=> ! [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_348])]) ).

fof(f3276,plain,
    ( spl0_337
  <=> ! [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_337])]) ).

fof(f3280,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_248
    | ~ spl0_337 ),
    inference(forward_demodulation,[],[f3279,f2395]) ).

fof(f3279,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_248
    | ~ spl0_337 ),
    inference(forward_demodulation,[],[f3277,f2395]) ).

fof(f3277,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_337 ),
    inference(avatar_component_clause,[],[f3276]) ).

fof(f3411,plain,
    ( spl0_347
    | ~ spl0_248
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3269,f3265,f2393,f3409]) ).

fof(f3409,plain,
    ( spl0_347
  <=> ! [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_347])]) ).

fof(f3265,plain,
    ( spl0_335
  <=> ! [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_335])]) ).

fof(f3269,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_248
    | ~ spl0_335 ),
    inference(forward_demodulation,[],[f3268,f2395]) ).

fof(f3268,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_248
    | ~ spl0_335 ),
    inference(forward_demodulation,[],[f3266,f2395]) ).

fof(f3266,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f3265]) ).

fof(f3407,plain,
    ( spl0_346
    | ~ spl0_248
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3263,f3260,f2393,f3405]) ).

fof(f3405,plain,
    ( spl0_346
  <=> ! [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_346])]) ).

fof(f3260,plain,
    ( spl0_334
  <=> ! [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_334])]) ).

fof(f3263,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_248
    | ~ spl0_334 ),
    inference(forward_demodulation,[],[f3261,f2395]) ).

fof(f3261,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f3260]) ).

fof(f3393,plain,
    ( spl0_345
    | ~ spl0_248
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3254,f3250,f2393,f3391]) ).

fof(f3391,plain,
    ( spl0_345
  <=> ! [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_345])]) ).

fof(f3250,plain,
    ( spl0_332
  <=> ! [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_332])]) ).

fof(f3254,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_248
    | ~ spl0_332 ),
    inference(forward_demodulation,[],[f3253,f2395]) ).

fof(f3253,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_248
    | ~ spl0_332 ),
    inference(forward_demodulation,[],[f3251,f2395]) ).

fof(f3251,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f3250]) ).

fof(f3312,plain,
    ( spl0_344
    | ~ spl0_8
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1482,f1417,f240,f3310]) ).

fof(f3310,plain,
    ( spl0_344
  <=> ! [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_344])]) ).

fof(f1417,plain,
    ( spl0_174
  <=> ! [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_174])]) ).

fof(f1482,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_8
    | ~ spl0_174 ),
    inference(resolution,[],[f1418,f241]) ).

fof(f1418,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_174 ),
    inference(avatar_component_clause,[],[f1417]) ).

fof(f3308,plain,
    ( spl0_343
    | ~ spl0_59
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1481,f1417,f518,f3306]) ).

fof(f3306,plain,
    ( spl0_343
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f1481,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_59
    | ~ spl0_174 ),
    inference(resolution,[],[f1418,f519]) ).

fof(f3304,plain,
    ( spl0_342
    | ~ spl0_71
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1449,f1409,f578,f3302]) ).

fof(f3302,plain,
    ( spl0_342
  <=> ! [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_342])]) ).

fof(f1449,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_71
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f579]) ).

fof(f3300,plain,
    ( spl0_341
    | ~ spl0_28
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1447,f1405,f327,f3298]) ).

fof(f1447,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_28
    | ~ spl0_171 ),
    inference(duplicate_literal_removal,[],[f1426]) ).

fof(f1426,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0))
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_28
    | ~ spl0_171 ),
    inference(resolution,[],[f1406,f328]) ).

fof(f3292,plain,
    ( spl0_339
    | spl0_340
    | ~ spl0_14
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f1223,f1193,f266,f3289,f3286]) ).

fof(f3286,plain,
    ( spl0_339
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f3289,plain,
    ( spl0_340
  <=> member(null_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f1223,plain,
    ( ! [X0] :
        ( member(null_class,null_class)
        | ~ member(null_class,X0)
        | null_class = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_14
    | ~ spl0_148 ),
    inference(resolution,[],[f1194,f267]) ).

fof(f3284,plain,
    ( spl0_338
    | ~ spl0_108
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1173,f1130,f789,f3282]) ).

fof(f3282,plain,
    ( spl0_338
  <=> ! [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_338])]) ).

fof(f1173,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
    | ~ spl0_108
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f790]) ).

fof(f3278,plain,
    ( spl0_337
    | ~ spl0_109
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1172,f1130,f793,f3276]) ).

fof(f1172,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_109
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f794]) ).

fof(f3274,plain,
    ( ~ spl0_336
    | ~ spl0_5
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3014,f2578,f226,f3271]) ).

fof(f3271,plain,
    ( spl0_336
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f226,plain,
    ( spl0_5
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f2578,plain,
    ( spl0_280
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f3014,plain,
    ( ~ inductive(choice)
    | ~ spl0_5
    | ~ spl0_280 ),
    inference(resolution,[],[f2579,f228]) ).

fof(f228,plain,
    ( function(choice)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f226]) ).

fof(f2579,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_280 ),
    inference(avatar_component_clause,[],[f2578]) ).

fof(f3267,plain,
    ( spl0_335
    | ~ spl0_45
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1161,f1126,f405,f3265]) ).

fof(f1161,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_45
    | ~ spl0_142 ),
    inference(superposition,[],[f1127,f407]) ).

fof(f3262,plain,
    ( spl0_334
    | ~ spl0_44
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1160,f1126,f400,f3260]) ).

fof(f1160,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_44
    | ~ spl0_142 ),
    inference(superposition,[],[f1127,f402]) ).

fof(f3258,plain,
    ( spl0_333
    | ~ spl0_108
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1155,f1126,f789,f3256]) ).

fof(f3256,plain,
    ( spl0_333
  <=> ! [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_333])]) ).

fof(f1155,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
    | ~ spl0_108
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f790]) ).

fof(f3252,plain,
    ( spl0_332
    | ~ spl0_109
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1154,f1126,f793,f3250]) ).

fof(f1154,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_109
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f794]) ).

fof(f3248,plain,
    ( spl0_331
    | ~ spl0_24
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1121,f1058,f307,f3246]) ).

fof(f3246,plain,
    ( spl0_331
  <=> ! [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_331])]) ).

fof(f1121,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_24
    | ~ spl0_139 ),
    inference(resolution,[],[f1059,f308]) ).

fof(f3244,plain,
    ( spl0_330
    | ~ spl0_24
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1118,f1054,f307,f3242]) ).

fof(f3242,plain,
    ( spl0_330
  <=> ! [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_330])]) ).

fof(f1118,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_24
    | ~ spl0_138 ),
    inference(resolution,[],[f1055,f308]) ).

fof(f3240,plain,
    ( spl0_329
    | ~ spl0_22
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1109,f1050,f299,f3238]) ).

fof(f1109,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_22
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f300]) ).

fof(f3236,plain,
    ( spl0_328
    | ~ spl0_33
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1018,f962,f347,f3234]) ).

fof(f3234,plain,
    ( spl0_328
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f1018,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_33
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f348]) ).

fof(f3232,plain,
    ( spl0_327
    | ~ spl0_34
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1017,f962,f351,f3230]) ).

fof(f3230,plain,
    ( spl0_327
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f1017,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_34
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f352]) ).

fof(f3228,plain,
    ( spl0_326
    | ~ spl0_29
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f911,f855,f331,f3226]) ).

fof(f3226,plain,
    ( spl0_326
  <=> ! [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_326])]) ).

fof(f911,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_29
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f332]) ).

fof(f3209,plain,
    ( spl0_325
    | ~ spl0_248
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3145,f3017,f2393,f3207]) ).

fof(f3207,plain,
    ( spl0_325
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f3017,plain,
    ( spl0_313
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f3145,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_248
    | ~ spl0_313 ),
    inference(forward_demodulation,[],[f3020,f2395]) ).

fof(f3020,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_248
    | ~ spl0_313 ),
    inference(forward_demodulation,[],[f3018,f2395]) ).

fof(f3018,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f3017]) ).

fof(f3188,plain,
    ( spl0_324
    | ~ spl0_248
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3032,f3029,f2393,f3186]) ).

fof(f3186,plain,
    ( spl0_324
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f3029,plain,
    ( spl0_315
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f3032,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_248
    | ~ spl0_315 ),
    inference(forward_demodulation,[],[f3030,f2395]) ).

fof(f3030,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3029]) ).

fof(f3167,plain,
    ( spl0_323
    | ~ spl0_248
    | ~ spl0_309 ),
    inference(avatar_split_clause,[],[f3151,f2939,f2393,f3164]) ).

fof(f3164,plain,
    ( spl0_323
  <=> member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f2939,plain,
    ( spl0_309
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f3151,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_248
    | ~ spl0_309 ),
    inference(forward_demodulation,[],[f2941,f2395]) ).

fof(f2941,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_309 ),
    inference(avatar_component_clause,[],[f2939]) ).

fof(f3162,plain,
    ( spl0_322
    | ~ spl0_248
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f3146,f2916,f2393,f3159]) ).

fof(f3159,plain,
    ( spl0_322
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f2916,plain,
    ( spl0_308
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f3146,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_248
    | ~ spl0_308 ),
    inference(forward_demodulation,[],[f2918,f2395]) ).

fof(f2918,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_308 ),
    inference(avatar_component_clause,[],[f2916]) ).

fof(f3157,plain,
    ( ~ spl0_321
    | ~ spl0_117
    | spl0_311 ),
    inference(avatar_split_clause,[],[f3008,f3004,f855,f3154]) ).

fof(f3154,plain,
    ( spl0_321
  <=> member(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f3004,plain,
    ( spl0_311
  <=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f3008,plain,
    ( ~ member(singleton_relation,subset_relation)
    | ~ spl0_117
    | spl0_311 ),
    inference(resolution,[],[f3006,f856]) ).

fof(f3006,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | spl0_311 ),
    inference(avatar_component_clause,[],[f3004]) ).

fof(f3149,plain,
    ( spl0_244
    | ~ spl0_246
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2953,f2393,f2383,f2363]) ).

fof(f2953,plain,
    ( null_class = singleton_relation
    | ~ spl0_246
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f2385,f2395]) ).

fof(f2385,plain,
    ( null_class = identity_relation
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f2383]) ).

fof(f3138,plain,
    ( spl0_320
    | ~ spl0_244
    | ~ spl0_248
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3022,f3017,f2393,f2363,f3136]) ).

fof(f3136,plain,
    ( spl0_320
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f3022,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) )
    | ~ spl0_244
    | ~ spl0_248
    | ~ spl0_313 ),
    inference(forward_demodulation,[],[f3021,f2395]) ).

fof(f3021,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_244
    | ~ spl0_248
    | ~ spl0_313 ),
    inference(forward_demodulation,[],[f3020,f2365]) ).

fof(f2365,plain,
    ( null_class = singleton_relation
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2363]) ).

fof(f3112,plain,
    ( ~ spl0_319
    | spl0_153
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2376,f2363,f1213,f3109]) ).

fof(f3109,plain,
    ( spl0_319
  <=> member(singleton_relation,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f2376,plain,
    ( ~ member(singleton_relation,w)
    | spl0_153
    | ~ spl0_244 ),
    inference(superposition,[],[f1214,f2365]) ).

fof(f1214,plain,
    ( ~ member(null_class,w)
    | spl0_153 ),
    inference(avatar_component_clause,[],[f1213]) ).

fof(f3044,plain,
    ( spl0_318
    | ~ spl0_11
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1769,f1747,f252,f3042]) ).

fof(f3042,plain,
    ( spl0_318
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f1769,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_11
    | ~ spl0_204 ),
    inference(superposition,[],[f253,f1748]) ).

fof(f3040,plain,
    ( spl0_317
    | ~ spl0_70
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1450,f1409,f574,f3038]) ).

fof(f3038,plain,
    ( spl0_317
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f1450,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) )
    | ~ spl0_70
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f575]) ).

fof(f3036,plain,
    ( spl0_316
    | ~ spl0_108
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1113,f1050,f789,f3034]) ).

fof(f3034,plain,
    ( spl0_316
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f1113,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_108
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f790]) ).

fof(f3031,plain,
    ( spl0_315
    | ~ spl0_109
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1112,f1050,f793,f3029]) ).

fof(f1112,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_109
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f794]) ).

fof(f3026,plain,
    ( spl0_314
    | ~ spl0_108
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1095,f1046,f789,f3024]) ).

fof(f3024,plain,
    ( spl0_314
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f1095,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) )
    | ~ spl0_108
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f790]) ).

fof(f3019,plain,
    ( spl0_313
    | ~ spl0_109
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1094,f1046,f793,f3017]) ).

fof(f1094,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_109
    | ~ spl0_136 ),
    inference(resolution,[],[f1047,f794]) ).

fof(f3013,plain,
    ( ~ spl0_312
    | spl0_122
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2375,f2363,f939,f3010]) ).

fof(f3010,plain,
    ( spl0_312
  <=> member(singleton_relation,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f2375,plain,
    ( ~ member(singleton_relation,y)
    | spl0_122
    | ~ spl0_244 ),
    inference(superposition,[],[f940,f2365]) ).

fof(f940,plain,
    ( ~ member(null_class,y)
    | spl0_122 ),
    inference(avatar_component_clause,[],[f939]) ).

fof(f3007,plain,
    ( ~ spl0_311
    | ~ spl0_248
    | spl0_270 ),
    inference(avatar_split_clause,[],[f3000,f2508,f2393,f3004]) ).

fof(f2508,plain,
    ( spl0_270
  <=> member(identity_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f3000,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_248
    | spl0_270 ),
    inference(forward_demodulation,[],[f2509,f2395]) ).

fof(f2509,plain,
    ( ~ member(identity_relation,cross_product(universal_class,universal_class))
    | spl0_270 ),
    inference(avatar_component_clause,[],[f2508]) ).

fof(f2996,plain,
    ( spl0_310
    | ~ spl0_41
    | ~ spl0_248
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2962,f2508,f2393,f388,f2994]) ).

fof(f2994,plain,
    ( spl0_310
  <=> ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f2962,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) )
    | ~ spl0_41
    | ~ spl0_248
    | ~ spl0_270 ),
    inference(forward_demodulation,[],[f2957,f2395]) ).

fof(f2957,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(identity_relation,X0) )
    | ~ spl0_41
    | ~ spl0_270 ),
    inference(resolution,[],[f2510,f389]) ).

fof(f2510,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f2508]) ).

fof(f2942,plain,
    ( spl0_246
    | spl0_309
    | ~ spl0_45
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1080,f1042,f405,f2939,f2383]) ).

fof(f1080,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ spl0_45
    | ~ spl0_135 ),
    inference(superposition,[],[f1043,f407]) ).

fof(f2919,plain,
    ( spl0_244
    | spl0_308
    | ~ spl0_44
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1079,f1042,f400,f2916,f2363]) ).

fof(f1079,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | null_class = singleton_relation
    | ~ spl0_44
    | ~ spl0_135 ),
    inference(superposition,[],[f1043,f402]) ).

fof(f2914,plain,
    ( ~ spl0_307
    | ~ spl0_117
    | spl0_243 ),
    inference(avatar_split_clause,[],[f2361,f2357,f855,f2911]) ).

fof(f2911,plain,
    ( spl0_307
  <=> member(omega,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f2357,plain,
    ( spl0_243
  <=> member(omega,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f2361,plain,
    ( ~ member(omega,subset_relation)
    | ~ spl0_117
    | spl0_243 ),
    inference(resolution,[],[f2358,f856]) ).

fof(f2358,plain,
    ( ~ member(omega,cross_product(universal_class,universal_class))
    | spl0_243 ),
    inference(avatar_component_clause,[],[f2357]) ).

fof(f2909,plain,
    ( spl0_306
    | ~ spl0_108
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1074,f1042,f789,f2907]) ).

fof(f2907,plain,
    ( spl0_306
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f1074,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) )
    | ~ spl0_108
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f790]) ).

fof(f2905,plain,
    ( spl0_305
    | ~ spl0_109
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1073,f1042,f793,f2903]) ).

fof(f2903,plain,
    ( spl0_305
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f1073,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) )
    | ~ spl0_109
    | ~ spl0_135 ),
    inference(resolution,[],[f1043,f794]) ).

fof(f2901,plain,
    ( spl0_304
    | ~ spl0_22
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1019,f962,f299,f2899]) ).

fof(f1019,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_22
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f300]) ).

fof(f2897,plain,
    ( spl0_303
    | ~ spl0_41
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f910,f855,f388,f2895]) ).

fof(f2895,plain,
    ( spl0_303
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f910,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_41
    | ~ spl0_117 ),
    inference(resolution,[],[f856,f389]) ).

fof(f2893,plain,
    ( spl0_302
    | ~ spl0_41
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f877,f834,f388,f2891]) ).

fof(f2891,plain,
    ( spl0_302
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f877,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_41
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f389]) ).

fof(f2828,plain,
    ( spl0_300
    | ~ spl0_301
    | ~ spl0_62
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1452,f1409,f535,f2825,f2822]) ).

fof(f2822,plain,
    ( spl0_300
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f2825,plain,
    ( spl0_301
  <=> subclass(domain_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f1452,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,element_relation)
        | ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) )
    | ~ spl0_62
    | ~ spl0_172 ),
    inference(resolution,[],[f1410,f536]) ).

fof(f2820,plain,
    ( spl0_299
    | ~ spl0_28
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1343,f1324,f327,f2818]) ).

fof(f2818,plain,
    ( spl0_299
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f1343,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_28
    | ~ spl0_163 ),
    inference(duplicate_literal_removal,[],[f1336]) ).

fof(f1336,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_28
    | ~ spl0_163 ),
    inference(resolution,[],[f1325,f328]) ).

fof(f2816,plain,
    ( spl0_298
    | ~ spl0_78
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1159,f1126,f621,f2814]) ).

fof(f2814,plain,
    ( spl0_298
  <=> ! [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_298])]) ).

fof(f1159,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_78
    | ~ spl0_142 ),
    inference(superposition,[],[f1127,f623]) ).

fof(f2812,plain,
    ( spl0_297
    | ~ spl0_108
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1023,f962,f789,f2810]) ).

fof(f2810,plain,
    ( spl0_297
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f1023,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) )
    | ~ spl0_108
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f790]) ).

fof(f2808,plain,
    ( spl0_296
    | ~ spl0_109
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1022,f962,f793,f2806]) ).

fof(f2806,plain,
    ( spl0_296
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f1022,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) )
    | ~ spl0_109
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f794]) ).

fof(f2796,plain,
    ( spl0_294
    | ~ spl0_286
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f2795,f2781,f2613,f2787]) ).

fof(f2787,plain,
    ( spl0_294
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f2781,plain,
    ( spl0_293
  <=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f2795,plain,
    ( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_286
    | ~ spl0_293 ),
    inference(forward_demodulation,[],[f2783,f2615]) ).

fof(f2615,plain,
    ( null_class = subset_relation
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2613]) ).

fof(f2783,plain,
    ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f2781]) ).

fof(f2794,plain,
    ( spl0_295
    | spl0_293
    | ~ spl0_36
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f893,f838,f359,f2781,f2792]) ).

fof(f2792,plain,
    ( spl0_295
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f359,plain,
    ( spl0_36
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f893,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_36
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f360]) ).

fof(f360,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f359]) ).

fof(f2790,plain,
    ( ~ spl0_294
    | ~ spl0_286
    | spl0_293 ),
    inference(avatar_split_clause,[],[f2785,f2781,f2613,f2787]) ).

fof(f2785,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_286
    | spl0_293 ),
    inference(forward_demodulation,[],[f2782,f2615]) ).

fof(f2782,plain,
    ( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_293 ),
    inference(avatar_component_clause,[],[f2781]) ).

fof(f2784,plain,
    ( spl0_292
    | spl0_293
    | ~ spl0_35
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f892,f838,f355,f2781,f2778]) ).

fof(f2778,plain,
    ( spl0_292
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f355,plain,
    ( spl0_35
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f892,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_35
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f356]) ).

fof(f356,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f355]) ).

fof(f2776,plain,
    ( spl0_291
    | ~ spl0_33
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f881,f834,f347,f2774]) ).

fof(f881,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_33
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f348]) ).

fof(f2772,plain,
    ( spl0_290
    | ~ spl0_34
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f880,f834,f351,f2770]) ).

fof(f2770,plain,
    ( spl0_290
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f880,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_34
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f352]) ).

fof(f2680,plain,
    ( ~ spl0_289
    | spl0_122
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2625,f2613,f939,f2677]) ).

fof(f2677,plain,
    ( spl0_289
  <=> member(subset_relation,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f2625,plain,
    ( ~ member(subset_relation,y)
    | spl0_122
    | ~ spl0_286 ),
    inference(superposition,[],[f940,f2615]) ).

fof(f2640,plain,
    ( spl0_288
    | ~ spl0_6
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1293,f1286,f231,f2638]) ).

fof(f2638,plain,
    ( spl0_288
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f1293,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_6
    | ~ spl0_159 ),
    inference(resolution,[],[f1287,f232]) ).

fof(f2620,plain,
    ( spl0_286
    | spl0_287
    | ~ spl0_78
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1078,f1042,f621,f2617,f2613]) ).

fof(f2617,plain,
    ( spl0_287
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f1078,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_78
    | ~ spl0_135 ),
    inference(superposition,[],[f1043,f623]) ).

fof(f2611,plain,
    ( spl0_285
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1030,f997,f299,f2609]) ).

fof(f2609,plain,
    ( spl0_285
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f1030,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(resolution,[],[f998,f300]) ).

fof(f2607,plain,
    ( ~ spl0_284
    | spl0_282
    | ~ spl0_27
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f902,f838,f320,f2593,f2604]) ).

fof(f2604,plain,
    ( spl0_284
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f2593,plain,
    ( spl0_282
  <=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f320,plain,
    ( spl0_27
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f902,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_27
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f322]) ).

fof(f322,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f320]) ).

fof(f2601,plain,
    ( spl0_283
    | ~ spl0_45
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2235,f2211,f405,f2598]) ).

fof(f2598,plain,
    ( spl0_283
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f2235,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_45
    | ~ spl0_236 ),
    inference(superposition,[],[f2212,f407]) ).

fof(f2596,plain,
    ( ~ spl0_281
    | spl0_282
    | ~ spl0_26
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f900,f838,f315,f2593,f2589]) ).

fof(f2589,plain,
    ( spl0_281
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f315,plain,
    ( spl0_26
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f900,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_26
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f317]) ).

fof(f317,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f315]) ).

fof(f2580,plain,
    ( spl0_280
    | spl0_187
    | ~ spl0_24
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f888,f838,f307,f1570,f2578]) ).

fof(f1570,plain,
    ( spl0_187
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f888,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_24
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f308]) ).

fof(f2576,plain,
    ( spl0_279
    | ~ spl0_22
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f882,f834,f299,f2574]) ).

fof(f882,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_22
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f300]) ).

fof(f2572,plain,
    ( spl0_278
    | ~ spl0_74
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f865,f834,f597,f2570]) ).

fof(f2570,plain,
    ( spl0_278
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f865,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_74
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f598]) ).

fof(f2561,plain,
    ( spl0_277
    | ~ spl0_41
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f2514,f1570,f388,f2559]) ).

fof(f2559,plain,
    ( spl0_277
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f2514,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_41
    | ~ spl0_187 ),
    inference(resolution,[],[f1571,f389]) ).

fof(f1571,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1570]) ).

fof(f2543,plain,
    ( spl0_276
    | ~ spl0_123
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1114,f1050,f958,f2541]) ).

fof(f1114,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_123
    | ~ spl0_137 ),
    inference(duplicate_literal_removal,[],[f1103]) ).

fof(f1103,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_123
    | ~ spl0_137 ),
    inference(resolution,[],[f1051,f959]) ).

fof(f2539,plain,
    ( spl0_275
    | ~ spl0_118
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1024,f962,f918,f2537]) ).

fof(f1024,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_118
    | ~ spl0_124 ),
    inference(duplicate_literal_removal,[],[f1013]) ).

fof(f1013,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_118
    | ~ spl0_124 ),
    inference(resolution,[],[f963,f919]) ).

fof(f2535,plain,
    ( spl0_274
    | ~ spl0_23
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f954,f926,f303,f2533]) ).

fof(f2533,plain,
    ( spl0_274
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f303,plain,
    ( spl0_23
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f954,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_23
    | ~ spl0_120 ),
    inference(resolution,[],[f927,f304]) ).

fof(f304,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f303]) ).

fof(f2531,plain,
    ( ~ spl0_272
    | spl0_273
    | ~ spl0_8
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f949,f926,f240,f2528,f2524]) ).

fof(f2524,plain,
    ( spl0_272
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f2528,plain,
    ( spl0_273
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f949,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_8
    | ~ spl0_120 ),
    inference(resolution,[],[f927,f241]) ).

fof(f2520,plain,
    ( ~ spl0_271
    | ~ spl0_117
    | spl0_270 ),
    inference(avatar_split_clause,[],[f2515,f2508,f855,f2517]) ).

fof(f2517,plain,
    ( spl0_271
  <=> member(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f2515,plain,
    ( ~ member(identity_relation,subset_relation)
    | ~ spl0_117
    | spl0_270 ),
    inference(resolution,[],[f2509,f856]) ).

fof(f2511,plain,
    ( spl0_270
    | ~ spl0_187
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2506,f2383,f1570,f2508]) ).

fof(f2506,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_187
    | ~ spl0_246 ),
    inference(forward_demodulation,[],[f1571,f2385]) ).

fof(f2501,plain,
    ( spl0_269
    | spl0_187
    | ~ spl0_20
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f899,f838,f291,f1570,f2499]) ).

fof(f2499,plain,
    ( spl0_269
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f291,plain,
    ( spl0_20
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f899,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_20
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f292]) ).

fof(f292,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f291]) ).

fof(f2497,plain,
    ( spl0_267
    | ~ spl0_268
    | ~ spl0_108
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f885,f834,f789,f2494,f2491]) ).

fof(f2491,plain,
    ( spl0_267
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2494,plain,
    ( spl0_268
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f885,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_108
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f790]) ).

fof(f2489,plain,
    ( spl0_265
    | ~ spl0_266
    | ~ spl0_109
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f884,f834,f793,f2486,f2483]) ).

fof(f2483,plain,
    ( spl0_265
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f2486,plain,
    ( spl0_266
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f884,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_109
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f794]) ).

fof(f2481,plain,
    ( spl0_263
    | ~ spl0_264
    | ~ spl0_88
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f869,f834,f683,f2478,f2475]) ).

fof(f2475,plain,
    ( spl0_263
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f2478,plain,
    ( spl0_264
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f869,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_88
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f684]) ).

fof(f2473,plain,
    ( spl0_262
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f859,f834,f574,f2471]) ).

fof(f2471,plain,
    ( spl0_262
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f859,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f575]) ).

fof(f2469,plain,
    ( ~ spl0_261
    | spl0_122
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2404,f2383,f939,f2466]) ).

fof(f2466,plain,
    ( spl0_261
  <=> member(identity_relation,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f2404,plain,
    ( ~ member(identity_relation,y)
    | spl0_122
    | ~ spl0_246 ),
    inference(superposition,[],[f940,f2385]) ).

fof(f2464,plain,
    ( spl0_260
    | ~ spl0_71
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f858,f834,f578,f2462]) ).

fof(f2462,plain,
    ( spl0_260
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f858,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_71
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f579]) ).

fof(f2459,plain,
    ( spl0_258
    | ~ spl0_259
    | ~ spl0_40
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f814,f396,f384,f2456,f2453]) ).

fof(f2453,plain,
    ( spl0_258
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f2456,plain,
    ( spl0_259
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f384,plain,
    ( spl0_40
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f814,plain,
    ( ! [X0] :
        ( ~ inductive(null_class)
        | member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_43 ),
    inference(superposition,[],[f385,f397]) ).

fof(f385,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(null_class,X0) )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f384]) ).

fof(f2451,plain,
    ( spl0_257
    | ~ spl0_28
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f806,f793,f327,f2449]) ).

fof(f2449,plain,
    ( spl0_257
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f806,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_28
    | ~ spl0_109 ),
    inference(resolution,[],[f794,f328]) ).

fof(f2447,plain,
    ( spl0_256
    | ~ spl0_28
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f802,f789,f327,f2445]) ).

fof(f2445,plain,
    ( spl0_256
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f802,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_28
    | ~ spl0_108 ),
    inference(resolution,[],[f790,f328]) ).

fof(f2443,plain,
    ( spl0_255
    | ~ spl0_39
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f672,f637,f371,f2441]) ).

fof(f2441,plain,
    ( spl0_255
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f371,plain,
    ( spl0_39
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f637,plain,
    ( spl0_80
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f672,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_39
    | ~ spl0_80 ),
    inference(resolution,[],[f638,f372]) ).

fof(f372,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f638,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f637]) ).

fof(f2439,plain,
    ( ~ spl0_254
    | spl0_187
    | ~ spl0_16
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f901,f838,f274,f1570,f2436]) ).

fof(f2436,plain,
    ( spl0_254
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f901,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_16
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f276]) ).

fof(f276,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f2434,plain,
    ( ~ spl0_253
    | spl0_187
    | ~ spl0_13
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f894,f838,f261,f1570,f2431]) ).

fof(f2431,plain,
    ( spl0_253
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f261,plain,
    ( spl0_13
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f894,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_13
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f263]) ).

fof(f263,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f2429,plain,
    ( spl0_251
    | ~ spl0_252
    | ~ spl0_87
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f868,f834,f679,f2426,f2423]) ).

fof(f2423,plain,
    ( spl0_251
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f2426,plain,
    ( spl0_252
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f868,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_87
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f680]) ).

fof(f2421,plain,
    ( spl0_249
    | ~ spl0_250
    | ~ spl0_67
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f866,f834,f557,f2418,f2415]) ).

fof(f2415,plain,
    ( spl0_249
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f2418,plain,
    ( spl0_250
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f866,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_67
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f558]) ).

fof(f2396,plain,
    ( spl0_248
    | ~ spl0_244
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2391,f2383,f2363,f2393]) ).

fof(f2391,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_244
    | ~ spl0_246 ),
    inference(forward_demodulation,[],[f2385,f2365]) ).

fof(f2390,plain,
    ( spl0_246
    | spl0_247
    | ~ spl0_25
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f809,f793,f311,f2387,f2383]) ).

fof(f2387,plain,
    ( spl0_247
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f809,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_25
    | ~ spl0_109 ),
    inference(resolution,[],[f794,f312]) ).

fof(f2370,plain,
    ( spl0_244
    | spl0_245
    | ~ spl0_25
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f805,f789,f311,f2367,f2363]) ).

fof(f2367,plain,
    ( spl0_245
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f805,plain,
    ( member(regular(singleton_relation),element_relation)
    | null_class = singleton_relation
    | ~ spl0_25
    | ~ spl0_108 ),
    inference(resolution,[],[f790,f312]) ).

fof(f2360,plain,
    ( ~ spl0_242
    | spl0_243
    | ~ spl0_24
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f798,f781,f307,f2357,f2353]) ).

fof(f2353,plain,
    ( spl0_242
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f781,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f798,plain,
    ( member(omega,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_24
    | ~ spl0_106 ),
    inference(resolution,[],[f782,f308]) ).

fof(f782,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f781]) ).

fof(f2260,plain,
    ( ~ spl0_4
    | ~ spl0_234 ),
    inference(avatar_contradiction_clause,[],[f2257]) ).

fof(f2257,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_234 ),
    inference(resolution,[],[f2202,f223]) ).

fof(f223,plain,
    ( inductive(omega)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f221]) ).

fof(f2202,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2201]) ).

fof(f2201,plain,
    ( spl0_234
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f2259,plain,
    ( ~ spl0_103
    | ~ spl0_234 ),
    inference(avatar_contradiction_clause,[],[f2258]) ).

fof(f2258,plain,
    ( $false
    | ~ spl0_103
    | ~ spl0_234 ),
    inference(resolution,[],[f2202,f766]) ).

fof(f766,plain,
    ( inductive(universal_class)
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f764]) ).

fof(f764,plain,
    ( spl0_103
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f2256,plain,
    ( spl0_241
    | ~ spl0_41
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f2205,f760,f388,f2254]) ).

fof(f2254,plain,
    ( spl0_241
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f2205,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_41
    | ~ spl0_102 ),
    inference(resolution,[],[f761,f389]) ).

fof(f2252,plain,
    ( spl0_240
    | ~ spl0_20
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f955,f926,f291,f2250]) ).

fof(f2250,plain,
    ( spl0_240
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f955,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_20
    | ~ spl0_120 ),
    inference(resolution,[],[f927,f292]) ).

fof(f2248,plain,
    ( spl0_238
    | ~ spl0_239
    | ~ spl0_62
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f861,f834,f535,f2245,f2242]) ).

fof(f2242,plain,
    ( spl0_238
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2245,plain,
    ( spl0_239
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f861,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_62
    | ~ spl0_112 ),
    inference(resolution,[],[f835,f536]) ).

fof(f2240,plain,
    ( spl0_237
    | ~ spl0_44
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2234,f2211,f400,f2237]) ).

fof(f2237,plain,
    ( spl0_237
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f2234,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_44
    | ~ spl0_236 ),
    inference(superposition,[],[f2212,f402]) ).

fof(f2213,plain,
    ( spl0_236
    | ~ spl0_29
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1180,f1130,f331,f2211]) ).

fof(f1180,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_29
    | ~ spl0_143 ),
    inference(duplicate_literal_removal,[],[f1163]) ).

fof(f1163,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_29
    | ~ spl0_143 ),
    inference(resolution,[],[f1131,f332]) ).

fof(f2209,plain,
    ( spl0_235
    | ~ spl0_29
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1162,f1126,f331,f2207]) ).

fof(f1162,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_29
    | ~ spl0_142 ),
    inference(duplicate_literal_removal,[],[f1145]) ).

fof(f1145,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_29
    | ~ spl0_142 ),
    inference(resolution,[],[f1127,f332]) ).

fof(f2203,plain,
    ( spl0_234
    | spl0_102
    | ~ spl0_6
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f886,f838,f231,f760,f2201]) ).

fof(f886,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_6
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f232]) ).

fof(f2199,plain,
    ( ~ spl0_233
    | spl0_203
    | ~ spl0_14
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f807,f793,f266,f1742,f2196]) ).

fof(f2196,plain,
    ( spl0_233
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f1742,plain,
    ( spl0_203
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f807,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_14
    | ~ spl0_109 ),
    inference(resolution,[],[f794,f267]) ).

fof(f2194,plain,
    ( ~ spl0_231
    | spl0_232
    | ~ spl0_16
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f956,f926,f274,f2191,f2187]) ).

fof(f2187,plain,
    ( spl0_231
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2191,plain,
    ( spl0_232
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f956,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_16
    | ~ spl0_120 ),
    inference(resolution,[],[f927,f276]) ).

fof(f2185,plain,
    ( ~ spl0_229
    | spl0_230
    | ~ spl0_13
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f952,f926,f261,f2182,f2178]) ).

fof(f2178,plain,
    ( spl0_229
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f2182,plain,
    ( spl0_230
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f952,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_13
    | ~ spl0_120 ),
    inference(resolution,[],[f927,f263]) ).

fof(f2167,plain,
    ( spl0_228
    | ~ spl0_92
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f720,f716,f701,f2165]) ).

fof(f2165,plain,
    ( spl0_228
  <=> ! [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_228])]) ).

fof(f720,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_92
    | ~ spl0_95 ),
    inference(resolution,[],[f717,f702]) ).

fof(f2163,plain,
    ( spl0_227
    | ~ spl0_53
    | ~ spl0_92
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f774,f769,f701,f471,f2161]) ).

fof(f2161,plain,
    ( spl0_227
  <=> ! [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_227])]) ).

fof(f769,plain,
    ( spl0_104
  <=> ! [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_104])]) ).

fof(f774,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_53
    | ~ spl0_92
    | ~ spl0_104 ),
    inference(forward_demodulation,[],[f772,f472]) ).

fof(f772,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_92
    | ~ spl0_104 ),
    inference(resolution,[],[f770,f702]) ).

fof(f770,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_104 ),
    inference(avatar_component_clause,[],[f769]) ).

fof(f2159,plain,
    ( ~ spl0_225
    | spl0_226
    | ~ spl0_12
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f950,f926,f256,f2156,f2152]) ).

fof(f2152,plain,
    ( spl0_225
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2156,plain,
    ( spl0_226
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f256,plain,
    ( spl0_12
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f950,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_12
    | ~ spl0_120 ),
    inference(resolution,[],[f927,f258]) ).

fof(f258,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f2144,plain,
    ( spl0_224
    | ~ spl0_73
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f773,f769,f586,f2142]) ).

fof(f2142,plain,
    ( spl0_224
  <=> ! [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_224])]) ).

fof(f773,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_73
    | ~ spl0_104 ),
    inference(resolution,[],[f770,f587]) ).

fof(f2131,plain,
    ( spl0_223
    | ~ spl0_85
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f723,f716,f662,f2129]) ).

fof(f2129,plain,
    ( spl0_223
  <=> ! [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_223])]) ).

fof(f723,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_85
    | ~ spl0_95 ),
    inference(resolution,[],[f717,f663]) ).

fof(f2127,plain,
    ( spl0_222
    | ~ spl0_82
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f667,f662,f645,f2125]) ).

fof(f2125,plain,
    ( spl0_222
  <=> ! [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_222])]) ).

fof(f667,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_82
    | ~ spl0_85 ),
    inference(resolution,[],[f663,f646]) ).

fof(f2114,plain,
    ( spl0_221
    | ~ spl0_28
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f721,f716,f327,f2112]) ).

fof(f721,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_28
    | ~ spl0_95 ),
    inference(resolution,[],[f717,f328]) ).

fof(f2101,plain,
    ( spl0_220
    | ~ spl0_25
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f724,f716,f311,f2099]) ).

fof(f724,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_25
    | ~ spl0_95 ),
    inference(resolution,[],[f717,f312]) ).

fof(f2090,plain,
    ( spl0_219
    | ~ spl0_79
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f758,f755,f626,f2088]) ).

fof(f758,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_79
    | ~ spl0_101 ),
    inference(resolution,[],[f756,f627]) ).

fof(f2037,plain,
    ( spl0_218
    | ~ spl0_79
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f753,f749,f626,f2035]) ).

fof(f753,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_79
    | ~ spl0_100 ),
    inference(resolution,[],[f750,f627]) ).

fof(f2033,plain,
    ( spl0_217
    | ~ spl0_79
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f752,f745,f626,f2031]) ).

fof(f745,plain,
    ( spl0_99
  <=> ! [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_99])]) ).

fof(f752,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_79
    | ~ spl0_99 ),
    inference(resolution,[],[f746,f627]) ).

fof(f746,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_99 ),
    inference(avatar_component_clause,[],[f745]) ).

fof(f1984,plain,
    ( spl0_216
    | ~ spl0_79
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f648,f645,f626,f1982]) ).

fof(f1982,plain,
    ( spl0_216
  <=> ! [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_216])]) ).

fof(f648,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_79
    | ~ spl0_82 ),
    inference(resolution,[],[f646,f627]) ).

fof(f1974,plain,
    ( spl0_215
    | ~ spl0_43
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f729,f716,f396,f1972]) ).

fof(f729,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_43
    | ~ spl0_95 ),
    inference(superposition,[],[f717,f397]) ).

fof(f1970,plain,
    ( ~ spl0_214
    | ~ spl0_14
    | spl0_203 ),
    inference(avatar_split_clause,[],[f1846,f1742,f266,f1967]) ).

fof(f1967,plain,
    ( spl0_214
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f1846,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_14
    | spl0_203 ),
    inference(resolution,[],[f1744,f267]) ).

fof(f1744,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_203 ),
    inference(avatar_component_clause,[],[f1742]) ).

fof(f1957,plain,
    ( spl0_213
    | ~ spl0_73
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f719,f716,f586,f1955]) ).

fof(f719,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_73
    | ~ spl0_95 ),
    inference(resolution,[],[f717,f587]) ).

fof(f1947,plain,
    ( spl0_212
    | ~ spl0_51
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f666,f662,f463,f1945]) ).

fof(f666,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_51
    | ~ spl0_85 ),
    inference(resolution,[],[f663,f464]) ).

fof(f1940,plain,
    ( spl0_211
    | ~ spl0_43
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f726,f716,f396,f1938]) ).

fof(f726,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_43
    | ~ spl0_95 ),
    inference(superposition,[],[f717,f397]) ).

fof(f1902,plain,
    ( spl0_210
    | ~ spl0_41
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f714,f710,f388,f1900]) ).

fof(f710,plain,
    ( spl0_94
  <=> ! [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_94])]) ).

fof(f714,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_41
    | ~ spl0_94 ),
    inference(resolution,[],[f711,f389]) ).

fof(f711,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_94 ),
    inference(avatar_component_clause,[],[f710]) ).

fof(f1845,plain,
    ( spl0_209
    | ~ spl0_53
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f728,f716,f471,f1843]) ).

fof(f728,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_53
    | ~ spl0_95 ),
    inference(superposition,[],[f717,f472]) ).

fof(f1841,plain,
    ( spl0_208
    | ~ spl0_53
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f725,f716,f471,f1839]) ).

fof(f725,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_53
    | ~ spl0_95 ),
    inference(superposition,[],[f717,f472]) ).

fof(f1831,plain,
    ( spl0_207
    | ~ spl0_14
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f722,f716,f266,f1829]) ).

fof(f722,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_14
    | ~ spl0_95 ),
    inference(resolution,[],[f717,f267]) ).

fof(f1811,plain,
    ( spl0_206
    | ~ spl0_28
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f651,f645,f327,f1809]) ).

fof(f651,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_28
    | ~ spl0_82 ),
    inference(resolution,[],[f646,f328]) ).

fof(f1783,plain,
    ( spl0_205
    | ~ spl0_41
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f704,f701,f388,f1781]) ).

fof(f704,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_41
    | ~ spl0_92 ),
    inference(resolution,[],[f702,f389]) ).

fof(f1749,plain,
    ( spl0_204
    | ~ spl0_25
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f650,f645,f311,f1747]) ).

fof(f650,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_25
    | ~ spl0_82 ),
    inference(resolution,[],[f646,f312]) ).

fof(f1745,plain,
    ( ~ spl0_203
    | ~ spl0_117
    | spl0_187 ),
    inference(avatar_split_clause,[],[f1578,f1570,f855,f1742]) ).

fof(f1578,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_117
    | spl0_187 ),
    inference(resolution,[],[f1572,f856]) ).

fof(f1572,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_187 ),
    inference(avatar_component_clause,[],[f1570]) ).

fof(f1738,plain,
    ( spl0_202
    | ~ spl0_79
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f735,f732,f626,f1736]) ).

fof(f735,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_79
    | ~ spl0_96 ),
    inference(resolution,[],[f733,f627]) ).

fof(f1694,plain,
    ( spl0_201
    | ~ spl0_33
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f669,f662,f347,f1692]) ).

fof(f669,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_33
    | ~ spl0_85 ),
    inference(resolution,[],[f663,f348]) ).

fof(f1690,plain,
    ( spl0_200
    | ~ spl0_34
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f668,f662,f351,f1688]) ).

fof(f668,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_34
    | ~ spl0_85 ),
    inference(resolution,[],[f663,f352]) ).

fof(f1673,plain,
    ( spl0_199
    | ~ spl0_22
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f670,f662,f299,f1671]) ).

fof(f670,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_22
    | ~ spl0_85 ),
    inference(resolution,[],[f663,f300]) ).

fof(f1654,plain,
    ( spl0_198
    | ~ spl0_41
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f665,f662,f388,f1652]) ).

fof(f665,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_41
    | ~ spl0_85 ),
    inference(resolution,[],[f663,f389]) ).

fof(f1648,plain,
    ( spl0_197
    | ~ spl0_42
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f555,f552,f392,f1646]) ).

fof(f555,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_42
    | ~ spl0_66 ),
    inference(resolution,[],[f553,f393]) ).

fof(f1636,plain,
    ( ~ spl0_194
    | ~ spl0_195
    | spl0_196
    | ~ spl0_75
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f629,f621,f601,f1633,f1629,f1625]) ).

fof(f1625,plain,
    ( spl0_194
  <=> 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_194])]) ).

fof(f1629,plain,
    ( spl0_195
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f1633,plain,
    ( spl0_196
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f601,plain,
    ( spl0_75
  <=> ! [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_75])]) ).

fof(f629,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_75
    | ~ spl0_78 ),
    inference(superposition,[],[f602,f623]) ).

fof(f602,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_75 ),
    inference(avatar_component_clause,[],[f601]) ).

fof(f1623,plain,
    ( spl0_193
    | ~ spl0_29
    | ~ spl0_53
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f595,f586,f471,f331,f1621]) ).

fof(f595,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_29
    | ~ spl0_53
    | ~ spl0_73 ),
    inference(forward_demodulation,[],[f594,f472]) ).

fof(f594,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_29
    | ~ spl0_73 ),
    inference(resolution,[],[f587,f332]) ).

fof(f1617,plain,
    ( spl0_192
    | ~ spl0_79
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f690,f687,f626,f1615]) ).

fof(f690,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_79
    | ~ spl0_89 ),
    inference(resolution,[],[f688,f627]) ).

fof(f1613,plain,
    ( ~ spl0_191
    | ~ spl0_14
    | spl0_115 ),
    inference(avatar_split_clause,[],[f1557,f846,f266,f1610]) ).

fof(f1610,plain,
    ( spl0_191
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f846,plain,
    ( spl0_115
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1557,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_14
    | spl0_115 ),
    inference(resolution,[],[f847,f267]) ).

fof(f847,plain,
    ( ~ member(null_class,element_relation)
    | spl0_115 ),
    inference(avatar_component_clause,[],[f846]) ).

fof(f1590,plain,
    ( spl0_190
    | ~ spl0_52
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f630,f621,f467,f1588]) ).

fof(f630,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_52
    | ~ spl0_78 ),
    inference(superposition,[],[f468,f623]) ).

fof(f1583,plain,
    ( spl0_189
    | ~ spl0_41
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f635,f626,f388,f1581]) ).

fof(f635,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_41
    | ~ spl0_79 ),
    inference(resolution,[],[f627,f389]) ).

fof(f1577,plain,
    ( ~ spl0_186
    | ~ spl0_187
    | spl0_188
    | ~ spl0_24
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f619,f609,f307,f1574,f1570,f1566]) ).

fof(f1566,plain,
    ( spl0_186
  <=> 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_186])]) ).

fof(f1574,plain,
    ( spl0_188
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f609,plain,
    ( spl0_77
  <=> ! [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_77])]) ).

fof(f619,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_24
    | ~ spl0_77 ),
    inference(resolution,[],[f610,f308]) ).

fof(f610,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_77 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f1564,plain,
    ( spl0_185
    | ~ spl0_42
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f525,f518,f392,f1562]) ).

fof(f1562,plain,
    ( spl0_185
  <=> ! [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_185])]) ).

fof(f525,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_42
    | ~ spl0_59 ),
    inference(resolution,[],[f519,f393]) ).

fof(f1556,plain,
    ( spl0_183
    | spl0_184
    | ~ spl0_43
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f614,f601,f396,f1553,f1550]) ).

fof(f1550,plain,
    ( spl0_183
  <=> ! [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_183])]) ).

fof(f1553,plain,
    ( spl0_184
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f614,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_43
    | ~ spl0_75 ),
    inference(superposition,[],[f602,f397]) ).

fof(f1548,plain,
    ( spl0_182
    | ~ spl0_66
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f565,f561,f552,f1546]) ).

fof(f1546,plain,
    ( spl0_182
  <=> ! [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_182])]) ).

fof(f561,plain,
    ( spl0_68
  <=> ! [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_68])]) ).

fof(f565,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_66
    | ~ spl0_68 ),
    inference(resolution,[],[f562,f553]) ).

fof(f562,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f561]) ).

fof(f1510,plain,
    ( spl0_181
    | ~ spl0_79
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f677,f674,f626,f1508]) ).

fof(f677,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_79
    | ~ spl0_86 ),
    inference(resolution,[],[f675,f627]) ).

fof(f1506,plain,
    ( spl0_179
    | spl0_180
    | ~ spl0_14
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f649,f645,f266,f1503,f1500]) ).

fof(f1500,plain,
    ( spl0_179
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1503,plain,
    ( spl0_180
  <=> 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_180])]) ).

fof(f649,plain,
    ( ! [X0,X1] :
        ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_14
    | ~ spl0_82 ),
    inference(resolution,[],[f646,f267]) ).

fof(f1498,plain,
    ( spl0_178
    | ~ spl0_41
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f616,f605,f388,f1496]) ).

fof(f605,plain,
    ( spl0_76
  <=> ! [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_76])]) ).

fof(f616,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_41
    | ~ spl0_76 ),
    inference(resolution,[],[f606,f389]) ).

fof(f606,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_76 ),
    inference(avatar_component_clause,[],[f605]) ).

fof(f1494,plain,
    ( spl0_177
    | ~ spl0_41
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f612,f601,f388,f1492]) ).

fof(f612,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_41
    | ~ spl0_75 ),
    inference(resolution,[],[f602,f389]) ).

fof(f1490,plain,
    ( spl0_176
    | ~ spl0_42
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f509,f479,f392,f1488]) ).

fof(f1488,plain,
    ( spl0_176
  <=> ! [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_176])]) ).

fof(f509,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_42
    | ~ spl0_55 ),
    inference(resolution,[],[f480,f393]) ).

fof(f1486,plain,
    ( spl0_175
    | ~ spl0_42
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f508,f475,f392,f1484]) ).

fof(f1484,plain,
    ( spl0_175
  <=> ! [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_175])]) ).

fof(f508,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_42
    | ~ spl0_54 ),
    inference(resolution,[],[f476,f393]) ).

fof(f1419,plain,
    ( spl0_174
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f656,f653,f1417]) ).

fof(f653,plain,
    ( spl0_83
  <=> ! [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_83])]) ).

fof(f656,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_83 ),
    inference(equality_resolution,[],[f654]) ).

fof(f654,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_83 ),
    inference(avatar_component_clause,[],[f653]) ).

fof(f1415,plain,
    ( spl0_173
    | ~ spl0_41
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f593,f586,f388,f1413]) ).

fof(f593,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_41
    | ~ spl0_73 ),
    inference(resolution,[],[f587,f389]) ).

fof(f1411,plain,
    ( spl0_172
    | ~ spl0_41
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f590,f570,f388,f1409]) ).

fof(f590,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_41
    | ~ spl0_69 ),
    inference(resolution,[],[f571,f389]) ).

fof(f1407,plain,
    ( spl0_171
    | ~ spl0_29
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f498,f467,f331,f1405]) ).

fof(f498,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_29
    | ~ spl0_52 ),
    inference(resolution,[],[f468,f332]) ).

fof(f1403,plain,
    ( spl0_170
    | ~ spl0_28
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f494,f463,f327,f1401]) ).

fof(f494,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_28
    | ~ spl0_51 ),
    inference(resolution,[],[f464,f328]) ).

fof(f1393,plain,
    ( spl0_169
    | ~ spl0_34
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f631,f621,f351,f1391]) ).

fof(f631,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_34
    | ~ spl0_78 ),
    inference(superposition,[],[f352,f623]) ).

fof(f1386,plain,
    ( ~ spl0_168
    | ~ spl0_14
    | spl0_153 ),
    inference(avatar_split_clause,[],[f1327,f1213,f266,f1383]) ).

fof(f1383,plain,
    ( spl0_168
  <=> inductive(w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1327,plain,
    ( ~ inductive(w)
    | ~ spl0_14
    | spl0_153 ),
    inference(resolution,[],[f1214,f267]) ).

fof(f1357,plain,
    ( spl0_167
    | ~ spl0_53
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f613,f601,f471,f1355]) ).

fof(f613,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_53
    | ~ spl0_75 ),
    inference(superposition,[],[f602,f472]) ).

fof(f1353,plain,
    ( spl0_166
    | ~ spl0_25
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f493,f463,f311,f1351]) ).

fof(f493,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_25
    | ~ spl0_51 ),
    inference(resolution,[],[f464,f312]) ).

fof(f1335,plain,
    ( spl0_165
    | ~ spl0_24
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f568,f561,f307,f1333]) ).

fof(f1333,plain,
    ( spl0_165
  <=> ! [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_165])]) ).

fof(f568,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_24
    | ~ spl0_68 ),
    inference(resolution,[],[f562,f308]) ).

fof(f1331,plain,
    ( spl0_164
    | ~ spl0_43
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f533,f527,f396,f1329]) ).

fof(f527,plain,
    ( spl0_61
  <=> ! [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_61])]) ).

fof(f533,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_43
    | ~ spl0_61 ),
    inference(trivial_inequality_removal,[],[f531]) ).

fof(f531,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_43
    | ~ spl0_61 ),
    inference(superposition,[],[f528,f397]) ).

fof(f528,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f527]) ).

fof(f1326,plain,
    ( spl0_163
    | ~ spl0_29
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f460,f447,f331,f1324]) ).

fof(f460,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_29
    | ~ spl0_48 ),
    inference(resolution,[],[f448,f332]) ).

fof(f1322,plain,
    ( spl0_162
    | ~ spl0_36
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f421,f392,f359,f1320]) ).

fof(f421,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_36
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f360]) ).

fof(f1318,plain,
    ( spl0_161
    | ~ spl0_35
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f420,f392,f355,f1316]) ).

fof(f420,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_35
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f356]) ).

fof(f1292,plain,
    ( spl0_160
    | ~ spl0_41
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f512,f487,f388,f1290]) ).

fof(f487,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f512,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_41
    | ~ spl0_57 ),
    inference(resolution,[],[f488,f389]) ).

fof(f488,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f487]) ).

fof(f1288,plain,
    ( spl0_159
    | ~ spl0_41
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f497,f467,f388,f1286]) ).

fof(f497,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_41
    | ~ spl0_52 ),
    inference(resolution,[],[f468,f389]) ).

fof(f1284,plain,
    ( spl0_157
    | ~ spl0_158
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f428,f392,f320,f1281,f1277]) ).

fof(f1277,plain,
    ( spl0_157
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f428,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_27
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f322]) ).

fof(f1275,plain,
    ( spl0_155
    | ~ spl0_156
    | ~ spl0_26
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f426,f392,f315,f1272,f1268]) ).

fof(f1268,plain,
    ( spl0_155
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f426,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_26
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f317]) ).

fof(f1266,plain,
    ( spl0_154
    | ~ spl0_23
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f424,f392,f303,f1264]) ).

fof(f424,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_23
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f304]) ).

fof(f1216,plain,
    ( ~ spl0_152
    | spl0_153
    | ~ spl0_2
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f904,f838,f211,f1213,f1209]) ).

fof(f1209,plain,
    ( spl0_152
  <=> inductive(z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f904,plain,
    ( member(null_class,w)
    | ~ inductive(z)
    | ~ spl0_2
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f213]) ).

fof(f1207,plain,
    ( spl0_151
    | ~ spl0_53
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f530,f527,f471,f1205]) ).

fof(f1205,plain,
    ( spl0_151
  <=> ! [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_151])]) ).

fof(f530,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_53
    | ~ spl0_61 ),
    inference(superposition,[],[f528,f472]) ).

fof(f1203,plain,
    ( spl0_150
    | ~ spl0_45
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f501,f467,f405,f1201]) ).

fof(f501,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_45
    | ~ spl0_52 ),
    inference(superposition,[],[f468,f407]) ).

fof(f1199,plain,
    ( spl0_149
    | ~ spl0_44
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f500,f467,f400,f1197]) ).

fof(f500,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_44
    | ~ spl0_52 ),
    inference(superposition,[],[f468,f402]) ).

fof(f1195,plain,
    ( spl0_148
    | ~ spl0_43
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f499,f467,f396,f1193]) ).

fof(f499,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_43
    | ~ spl0_52 ),
    inference(superposition,[],[f468,f397]) ).

fof(f1191,plain,
    ( spl0_147
    | ~ spl0_41
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f459,f447,f388,f1189]) ).

fof(f459,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_41
    | ~ spl0_48 ),
    inference(resolution,[],[f448,f389]) ).

fof(f1144,plain,
    ( spl0_146
    | ~ spl0_8
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f567,f561,f240,f1142]) ).

fof(f1142,plain,
    ( spl0_146
  <=> ! [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_146])]) ).

fof(f567,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_8
    | ~ spl0_68 ),
    inference(resolution,[],[f562,f241]) ).

fof(f1140,plain,
    ( spl0_145
    | ~ spl0_20
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f425,f392,f291,f1138]) ).

fof(f425,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_20
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f292]) ).

fof(f1136,plain,
    ( spl0_144
    | ~ spl0_24
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f418,f392,f307,f1134]) ).

fof(f418,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_24
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f308]) ).

fof(f1132,plain,
    ( spl0_143
    | ~ spl0_28
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f382,f351,f327,f1130]) ).

fof(f382,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_28
    | ~ spl0_34 ),
    inference(resolution,[],[f352,f328]) ).

fof(f1128,plain,
    ( spl0_142
    | ~ spl0_28
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f379,f347,f327,f1126]) ).

fof(f379,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_28
    | ~ spl0_33 ),
    inference(resolution,[],[f348,f328]) ).

fof(f1085,plain,
    ( ~ spl0_141
    | ~ spl0_14
    | spl0_122 ),
    inference(avatar_split_clause,[],[f1029,f939,f266,f1082]) ).

fof(f1082,plain,
    ( spl0_141
  <=> inductive(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1029,plain,
    ( ~ inductive(y)
    | ~ spl0_14
    | spl0_122 ),
    inference(resolution,[],[f940,f267]) ).

fof(f1064,plain,
    ( spl0_140
    | ~ spl0_59
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f564,f561,f518,f1062]) ).

fof(f1062,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f564,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_59
    | ~ spl0_68 ),
    inference(resolution,[],[f562,f519]) ).

fof(f1060,plain,
    ( spl0_139
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f415,f388,f343,f1058]) ).

fof(f415,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f344]) ).

fof(f1056,plain,
    ( spl0_138
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f414,f388,f339,f1054]) ).

fof(f414,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f340]) ).

fof(f1052,plain,
    ( spl0_137
    | ~ spl0_28
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f413,f388,f327,f1050]) ).

fof(f413,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_28
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f328]) ).

fof(f1048,plain,
    ( spl0_136
    | ~ spl0_25
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f381,f351,f311,f1046]) ).

fof(f381,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_25
    | ~ spl0_34 ),
    inference(resolution,[],[f352,f312]) ).

fof(f1044,plain,
    ( spl0_135
    | ~ spl0_25
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f378,f347,f311,f1042]) ).

fof(f378,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_25
    | ~ spl0_33 ),
    inference(resolution,[],[f348,f312]) ).

fof(f1007,plain,
    ( spl0_134
    | ~ spl0_14
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f492,f463,f266,f1005]) ).

fof(f492,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_14
    | ~ spl0_51 ),
    inference(resolution,[],[f464,f267]) ).

fof(f1003,plain,
    ( spl0_133
    | ~ spl0_33
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f436,f405,f347,f1001]) ).

fof(f436,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_33
    | ~ spl0_45 ),
    inference(superposition,[],[f348,f407]) ).

fof(f999,plain,
    ( spl0_132
    | ~ spl0_33
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f434,f400,f347,f997]) ).

fof(f434,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_33
    | ~ spl0_44 ),
    inference(superposition,[],[f348,f402]) ).

fof(f995,plain,
    ( spl0_131
    | ~ spl0_34
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f431,f396,f351,f993]) ).

fof(f431,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_34
    | ~ spl0_43 ),
    inference(superposition,[],[f352,f397]) ).

fof(f991,plain,
    ( spl0_129
    | ~ spl0_130
    | ~ spl0_16
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f427,f392,f274,f988,f984]) ).

fof(f984,plain,
    ( spl0_129
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f427,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_16
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f276]) ).

fof(f982,plain,
    ( spl0_127
    | ~ spl0_128
    | ~ spl0_13
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f422,f392,f261,f979,f975]) ).

fof(f975,plain,
    ( spl0_127
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f422,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_13
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f263]) ).

fof(f973,plain,
    ( spl0_125
    | ~ spl0_126
    | ~ spl0_12
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f419,f392,f256,f970,f966]) ).

fof(f966,plain,
    ( spl0_125
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f419,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_12
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f258]) ).

fof(f964,plain,
    ( spl0_124
    | ~ spl0_25
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f412,f388,f311,f962]) ).

fof(f412,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_25
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f312]) ).

fof(f960,plain,
    ( spl0_123
    | ~ spl0_22
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f374,f327,f299,f958]) ).

fof(f374,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_22
    | ~ spl0_28 ),
    inference(resolution,[],[f328,f300]) ).

fof(f942,plain,
    ( ~ spl0_121
    | spl0_122
    | ~ spl0_1
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f903,f838,f206,f939,f935]) ).

fof(f935,plain,
    ( spl0_121
  <=> inductive(x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f903,plain,
    ( member(null_class,y)
    | ~ inductive(x)
    | ~ spl0_1
    | ~ spl0_113 ),
    inference(resolution,[],[f839,f208]) ).

fof(f928,plain,
    ( spl0_120
    | ~ spl0_54
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f592,f582,f475,f926]) ).

fof(f582,plain,
    ( spl0_72
  <=> ! [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_72])]) ).

fof(f592,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_54
    | ~ spl0_72 ),
    inference(resolution,[],[f583,f476]) ).

fof(f583,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_72 ),
    inference(avatar_component_clause,[],[f582]) ).

fof(f924,plain,
    ( spl0_119
    | ~ spl0_33
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f432,f396,f347,f922]) ).

fof(f432,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_33
    | ~ spl0_43 ),
    inference(superposition,[],[f348,f397]) ).

fof(f920,plain,
    ( spl0_118
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f325,f311,f299,f918]) ).

fof(f325,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(resolution,[],[f312,f300]) ).

fof(f857,plain,
    ( spl0_117
    | ~ spl0_33
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f632,f621,f347,f855]) ).

fof(f632,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_33
    | ~ spl0_78 ),
    inference(superposition,[],[f348,f623]) ).

fof(f853,plain,
    ( spl0_116
    | ~ spl0_15
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f423,f392,f270,f851]) ).

fof(f423,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_15
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f271]) ).

fof(f849,plain,
    ( ~ spl0_114
    | spl0_115
    | ~ spl0_14
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f803,f789,f266,f846,f842]) ).

fof(f842,plain,
    ( spl0_114
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f803,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_14
    | ~ spl0_108 ),
    inference(resolution,[],[f790,f267]) ).

fof(f840,plain,
    ( spl0_113
    | ~ spl0_14
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f411,f388,f266,f838]) ).

fof(f411,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_14
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f267]) ).

fof(f836,plain,
    ( spl0_112
    | ~ spl0_11
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f410,f388,f252,f834]) ).

fof(f410,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_11
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f253]) ).

fof(f823,plain,
    ( spl0_111
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f566,f561,f231,f821]) ).

fof(f821,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f566,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(resolution,[],[f562,f232]) ).

fof(f813,plain,
    ( spl0_110
    | ~ spl0_14
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f380,f351,f266,f811]) ).

fof(f811,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f380,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_14
    | ~ spl0_34 ),
    inference(resolution,[],[f352,f267]) ).

fof(f795,plain,
    ( spl0_109
    | ~ spl0_34
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f435,f405,f351,f793]) ).

fof(f435,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_34
    | ~ spl0_45 ),
    inference(superposition,[],[f352,f407]) ).

fof(f791,plain,
    ( spl0_108
    | ~ spl0_34
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f433,f400,f351,f789]) ).

fof(f433,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_34
    | ~ spl0_44 ),
    inference(superposition,[],[f352,f402]) ).

fof(f787,plain,
    ( spl0_107
    | ~ spl0_6
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f416,f392,f231,f785]) ).

fof(f785,plain,
    ( spl0_107
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f416,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_6
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f232]) ).

fof(f783,plain,
    ( spl0_106
    | ~ spl0_7
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f409,f388,f235,f781]) ).

fof(f409,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_7
    | ~ spl0_41 ),
    inference(resolution,[],[f389,f237]) ).

fof(f778,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f204,f776]) ).

fof(f776,plain,
    ( spl0_105
  <=> ! [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_105])]) ).

fof(f204,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,[],[f203,f130]) ).

fof(f130,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(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(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,[],[f202,f130]) ).

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(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,[],[f201,f130]) ).

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(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,[],[f200,f130]) ).

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(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,[],[f199,f130]) ).

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(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,[],[f198,f130]) ).

fof(f198,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,[],[f197,f130]) ).

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(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,[],[f196,f130]) ).

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(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,[],[f195,f130]) ).

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(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,[],[f177,f130]) ).

fof(f177,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,f119,f120,f119,f119,f119,f119,f120]) ).

fof(f120,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(f119,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,f116,f118,f12]) ).

fof(f118,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,f117,f29]) ).

fof(f117,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(f116,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(f771,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f194,f769]) ).

fof(f194,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,[],[f193,f130]) ).

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(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,[],[f192,f130]) ).

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(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,[],[f191,f130]) ).

fof(f191,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,[],[f190,f130]) ).

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(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,[],[f169,f130]) ).

fof(f169,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,f120,f119,f120,f119,f119,f119,f119,f120]) ).

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(f767,plain,
    ( ~ spl0_102
    | spl0_103
    | ~ spl0_6
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f618,f609,f231,f764,f760]) ).

fof(f618,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_6
    | ~ spl0_77 ),
    inference(resolution,[],[f610,f232]) ).

fof(f757,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f189,f755]) ).

fof(f189,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,[],[f168,f130]) ).

fof(f168,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,f120,f120,f119,f120,f120]) ).

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(f751,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f173,f749]) ).

fof(f173,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,f120,f120,f120,f120,f120,f120]) ).

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(f747,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f172,f745]) ).

fof(f172,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,f120,f120,f120,f120,f120,f120]) ).

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(f743,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f157,f741]) ).

fof(f157,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,f120,f120,f120,f120]) ).

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(f739,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f156,f737]) ).

fof(f156,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,f120,f120,f120,f120]) ).

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(f734,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f180,f732]) ).

fof(f180,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,[],[f167]) ).

fof(f167,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,f126,f120,f120]) ).

fof(f126,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(f718,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f171,f716]) ).

fof(f171,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,f120,f120,f118,f118,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(f712,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f154,f710]) ).

fof(f154,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,f120,f120,f120]) ).

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(f708,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f185,f706]) ).

fof(f185,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,[],[f151,f130]) ).

fof(f151,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,f119,f120,f120]) ).

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(f703,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f176,f701]) ).

fof(f176,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,f120]) ).

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(f699,plain,
    ( spl0_91
    | ~ spl0_5
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f671,f637,f226,f696]) ).

fof(f696,plain,
    ( spl0_91
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f671,plain,
    ( single_valued_class(choice)
    | ~ spl0_5
    | ~ spl0_80 ),
    inference(resolution,[],[f638,f228]) ).

fof(f694,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f155,f692]) ).

fof(f155,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,f120,f118,f118,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(f689,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f181,f687]) ).

fof(f181,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,[],[f170]) ).

fof(f170,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,f120,f120]) ).

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(f685,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f153,f683]) ).

fof(f153,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,f120,f120]) ).

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(f681,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f149,f679]) ).

fof(f149,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,f120,f120]) ).

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(f676,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f166,f674]) ).

fof(f166,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,f120,f120]) ).

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(f664,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f188,f662]) ).

fof(f188,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,[],[f187,f130]) ).

fof(f187,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,[],[f163,f130]) ).

fof(f163,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,f119]) ).

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(f660,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f174,f658]) ).

fof(f658,plain,
    ( spl0_84
  <=> ! [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_84])]) ).

fof(f174,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,f117]) ).

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(f655,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f175,f653]) ).

fof(f175,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,f117]) ).

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(f647,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f150,f645]) ).

fof(f150,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,f120]) ).

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(f643,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f147,f641]) ).

fof(f147,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,f126,f120]) ).

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(f639,plain,
    ( spl0_80
    | ~ spl0_55
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f510,f483,f479,f637]) ).

fof(f483,plain,
    ( spl0_56
  <=> ! [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_56])]) ).

fof(f510,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_55
    | ~ spl0_56 ),
    inference(resolution,[],[f484,f480]) ).

fof(f484,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f483]) ).

fof(f628,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f165,f626]) ).

fof(f165,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,f120]) ).

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(f624,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f131,f621]) ).

fof(f131,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(f611,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f186,f609]) ).

fof(f186,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,[],[f161,f130]) ).

fof(f161,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,f118]) ).

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(f607,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f183,f605]) ).

fof(f183,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,[],[f138,f130]) ).

fof(f138,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,f127]) ).

fof(f127,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,f118]) ).

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(f603,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f159,f601]) ).

fof(f159,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,f118]) ).

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(f599,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f152,f597]) ).

fof(f152,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,f120]) ).

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(f588,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f164,f586]) ).

fof(f164,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(f584,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f162,f582]) ).

fof(f162,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(f580,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f143,f578]) ).

fof(f143,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,f120]) ).

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(f576,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f142,f574]) ).

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,f120]) ).

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(f572,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f140,f570]) ).

fof(f140,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,f120]) ).

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(f563,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f160,f561]) ).

fof(f160,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,f117]) ).

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(f559,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f148,f557]) ).

fof(f148,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,f120]) ).

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(f554,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f182,f552]) ).

fof(f182,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,[],[f134,f130]) ).

fof(f134,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,f118]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).

fof(f550,plain,
    ( spl0_64
    | ~ spl0_65
    | ~ spl0_2
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f430,f392,f211,f547,f543]) ).

fof(f543,plain,
    ( spl0_64
  <=> z = w ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f547,plain,
    ( spl0_65
  <=> subclass(w,z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f430,plain,
    ( ~ subclass(w,z)
    | z = w
    | ~ spl0_2
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f213]) ).

fof(f541,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f146,f539]) ).

fof(f539,plain,
    ( spl0_63
  <=> ! [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_63])]) ).

fof(f146,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,f117]) ).

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(f537,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f141,f535]) ).

fof(f141,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,f120]) ).

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(f529,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f144,f527]) ).

fof(f144,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(f524,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f145,f522]) ).

fof(f522,plain,
    ( spl0_60
  <=> ! [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_60])]) ).

fof(f145,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f117]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).

fof(f520,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f135,f518]) ).

fof(f135,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f117]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).

fof(f516,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f79,f514]) ).

fof(f514,plain,
    ( spl0_58
  <=> ! [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_58])]) ).

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(f489,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f184,f487]) ).

fof(f184,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f139,f130]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f116]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).

fof(f485,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f137,f483]) ).

fof(f137,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(f481,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f136,f479]) ).

fof(f136,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(f477,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f132,f475]) ).

fof(f132,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(f473,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f130,f471]) ).

fof(f469,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f23,f467]) ).

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(f465,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f8,f463]) ).

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(f457,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f158,f455]) ).

fof(f455,plain,
    ( spl0_50
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f158,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(f453,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f83,f451]) ).

fof(f451,plain,
    ( spl0_49
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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(f449,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f25,f447]) ).

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(f445,plain,
    ( spl0_46
    | ~ spl0_47
    | ~ spl0_1
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f429,f392,f206,f442,f438]) ).

fof(f438,plain,
    ( spl0_46
  <=> x = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f442,plain,
    ( spl0_47
  <=> subclass(y,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f429,plain,
    ( ~ subclass(y,x)
    | x = y
    | ~ spl0_1
    | ~ spl0_42 ),
    inference(resolution,[],[f393,f208]) ).

fof(f408,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f129,f405]) ).

fof(f129,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(f403,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f104,f400]) ).

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(f398,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f67,f396]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f394,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f7,f392]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f390,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f1,f388]) ).

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(f386,plain,
    ( spl0_40
    | ~ spl0_14
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f377,f347,f266,f384]) ).

fof(f377,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_14
    | ~ spl0_33 ),
    inference(resolution,[],[f348,f267]) ).

fof(f373,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f133,f371]) ).

fof(f133,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(f369,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f110,f367]) ).

fof(f367,plain,
    ( spl0_38
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).

fof(f365,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f88,f363]) ).

fof(f363,plain,
    ( spl0_37
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f361,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f35,f359]) ).

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(f357,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f32,f355]) ).

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(f353,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f22,f351]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f349,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f21,f347]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f345,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f10,f343]) ).

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(f341,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f9,f339]) ).

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(f337,plain,
    ( spl0_30
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f324,f299,f266,f335]) ).

fof(f335,plain,
    ( spl0_30
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f324,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(resolution,[],[f300,f267]) ).

fof(f333,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f3,f331]) ).

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(f329,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f2,f327]) ).

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(f323,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f105,f320]) ).

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(f318,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f95,f315]) ).

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(f313,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f66,f311]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f309,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f62,f307]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f305,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f57,f303]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f301,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f24,f299]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f297,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f109,f295]) ).

fof(f295,plain,
    ( spl0_21
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).

fof(f293,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f92,f291]) ).

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(f289,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f87,f287]) ).

fof(f287,plain,
    ( spl0_19
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f285,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f86,f283]) ).

fof(f283,plain,
    ( spl0_18
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f281,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f82,f279]) ).

fof(f279,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f277,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f98,f274]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f272,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f51,f270]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f268,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f47,f266]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

fof(f264,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f44,f261]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f259,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f18,f256]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f254,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f11,f252]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f250,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f78,f248]) ).

fof(f248,plain,
    ( spl0_10
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f246,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f71,f244]) ).

fof(f244,plain,
    ( spl0_9
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f242,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f178,f240]) ).

fof(f178,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(f238,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f52,f235]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f233,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f4,f231]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f229,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f69,f226]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f224,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f50,f221]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f219,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f115,f216]) ).

fof(f115,axiom,
    ~ subclass(intersection(x,z),intersection(y,w)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_is_monotonic_3) ).

fof(f214,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f114,f211]) ).

fof(f114,axiom,
    subclass(z,w),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_is_monotonic_2) ).

fof(f209,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f113,f206]) ).

fof(f113,axiom,
    subclass(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_is_monotonic_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET201-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 11:30:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (1588)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (1589)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (1591)WARNING: value z3 for option sas not known
% 0.14/0.38  % (1590)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (1592)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (1591)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)
% 0.14/0.38  % (1594)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)
% 0.14/0.38  % (1595)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)
% 0.14/0.38  % (1593)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)
% 0.20/0.41  TRYING [1]
% 0.20/0.41  TRYING [2]
% 0.20/0.47  TRYING [3]
% 0.20/0.56  TRYING [1]
% 0.20/0.56  TRYING [2]
% 0.20/0.57  TRYING [4]
% 1.95/0.64  TRYING [3]
% 3.65/0.88  TRYING [5]
% 6.24/1.25  TRYING [4]
% 7.88/1.48  TRYING [1]
% 7.88/1.49  TRYING [2]
% 7.88/1.50  TRYING [3]
% 8.33/1.54  TRYING [4]
% 8.98/1.67  TRYING [5]
% 11.38/2.04  % (1593)First to succeed.
% 12.02/2.08  % (1593)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1588"
% 12.21/2.09  % (1593)Refutation found. Thanks to Tanya!
% 12.21/2.09  % SZS status Unsatisfiable for theBenchmark
% 12.21/2.09  % SZS output start Proof for theBenchmark
% See solution above
% 12.21/2.10  % (1593)------------------------------
% 12.21/2.10  % (1593)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 12.21/2.10  % (1593)Termination reason: Refutation
% 12.21/2.10  
% 12.21/2.10  % (1593)Memory used [KB]: 17353
% 12.21/2.10  % (1593)Time elapsed: 1.703 s
% 12.21/2.10  % (1593)Instructions burned: 4983 (million)
% 12.21/2.10  % (1588)Success in time 1.73 s
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