%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET265-6 : 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 : n025.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 03:18:18 EDT 2024

% Result   : Unsatisfiable 19.16s 3.17s
% Output   : Refutation 19.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1638
% Syntax   : Number of formulae    : 5293 ( 135 unt;   0 def)
%            Number of atoms       : 19743 (1841 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 25711 (11261   ~;12916   |;   0   &)
%                                         (1534 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   28 (   3 avg)
%            Number of predicates  : 1546 (1544 usr;1535 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;  14 con; 0-3 aty)
%            Number of variables   : 7128 (7128   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f41835,plain,
    $false,
    inference(avatar_sat_refutation,[],[f207,f212,f217,f221,f226,f230,f234,f238,f242,f247,f252,f256,f260,f265,f269,f273,f277,f281,f285,f289,f293,f297,f301,f306,f311,f316,f321,f325,f329,f333,f337,f341,f345,f349,f353,f357,f361,f374,f378,f382,f387,f391,f396,f426,f430,f434,f441,f446,f450,f454,f458,f462,f466,f470,f479,f501,f505,f509,f513,f518,f526,f530,f534,f541,f545,f554,f558,f562,f566,f570,f577,f586,f590,f594,f598,f611,f615,f626,f630,f643,f647,f652,f656,f666,f671,f675,f679,f684,f688,f693,f698,f704,f720,f725,f729,f733,f737,f741,f747,f752,f759,f763,f781,f791,f804,f813,f817,f821,f825,f886,f890,f894,f917,f921,f930,f939,f949,f953,f957,f961,f965,f987,f1006,f1010,f1014,f1018,f1022,f1026,f1085,f1089,f1093,f1097,f1106,f1110,f1157,f1161,f1165,f1169,f1173,f1223,f1232,f1241,f1245,f1249,f1275,f1279,f1288,f1292,f1296,f1300,f1318,f1322,f1353,f1363,f1367,f1371,f1375,f1379,f1446,f1450,f1454,f1458,f1466,f1475,f1479,f1517,f1525,f1532,f1545,f1551,f1558,f1580,f1586,f1599,f1611,f1616,f1622,f1641,f1658,f1662,f1706,f1713,f1747,f1775,f1795,f1805,f1810,f1814,f1870,f1908,f1915,f1925,f1937,f1947,f1996,f2000,f2053,f2058,f2069,f2082,f2095,f2099,f2112,f2122,f2126,f2139,f2141,f2225,f2229,f2259,f2263,f2267,f2279,f2289,f2307,f2313,f2336,f2344,f2349,f2354,f2358,f2362,f2366,f2374,f2379,f2383,f2391,f2396,f2404,f2412,f2416,f2426,f2435,f2446,f2450,f2454,f2458,f2469,f2481,f2492,f2497,f2501,f2505,f2521,f2527,f2531,f2542,f2560,f2687,f2691,f2701,f2707,f2711,f2713,f2725,f2729,f2733,f2737,f2741,f2749,f2812,f2816,f2820,f2824,f2828,f2833,f2854,f2907,f2918,f2925,f2932,f2937,f2942,f2947,f2951,f2955,f3044,f3055,f3063,f3068,f3073,f3094,f3108,f3120,f3139,f3143,f3147,f3151,f3155,f3164,f3168,f3174,f3178,f3183,f3189,f3195,f3203,f3212,f3216,f3220,f3224,f3308,f3312,f3326,f3330,f3334,f3460,f3468,f3474,f3480,f3484,f3493,f3500,f3504,f3508,f3512,f3517,f3523,f3527,f3531,f3535,f3539,f3543,f3547,f3597,f3616,f3747,f3755,f3759,f3763,f3767,f3771,f3775,f3779,f3783,f3787,f3791,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f3836,f4200,f4204,f4209,f4213,f4217,f4221,f4225,f4229,f4233,f4237,f4241,f4245,f4250,f4251,f4259,f4268,f4272,f4367,f4643,f4738,f4765,f4769,f4775,f4780,f4784,f4788,f4792,f4796,f4800,f4805,f4809,f4814,f4818,f4822,f4826,f4830,f4834,f4847,f4851,f4856,f5141,f5145,f5172,f5461,f5470,f5477,f5482,f5487,f5497,f5503,f5508,f5512,f5520,f5525,f5530,f5538,f5542,f5546,f5550,f5554,f5558,f5563,f5570,f5578,f5809,f5818,f5879,f5885,f5890,f5894,f5898,f5903,f5908,f5917,f5921,f5925,f5929,f6018,f6022,f6180,f6185,f6189,f6194,f6206,f6210,f6214,f6222,f6228,f6232,f6236,f6400,f6404,f6408,f6412,f6417,f6422,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6463,f6595,f6599,f6805,f6810,f6814,f6818,f6822,f6826,f6830,f6834,f6844,f6992,f7004,f7008,f7012,f7016,f7020,f7024,f7028,f7033,f7037,f7049,f7358,f7362,f7366,f7370,f7383,f7391,f7396,f7401,f7425,f7434,f7439,f7443,f7447,f7457,f7461,f7465,f7469,f7473,f8139,f8143,f8147,f8152,f8157,f8161,f8187,f8194,f8203,f8210,f8221,f8225,f8229,f8233,f8237,f8300,f8304,f8311,f8316,f8320,f8324,f8338,f8342,f8346,f8350,f8354,f8358,f8670,f8705,f8709,f8713,f8717,f8721,f8725,f8729,f8816,f8820,f8828,f8832,f8836,f8840,f8849,f8856,f8983,f8987,f8991,f8995,f9000,f9004,f9065,f9079,f9093,f9097,f9104,f9111,f9116,f9121,f9126,f9132,f9142,f9185,f9189,f9193,f9197,f9201,f9205,f9209,f9236,f9329,f9333,f9340,f9347,f9352,f9356,f9361,f9368,f9373,f9381,f9393,f9397,f9458,f9516,f9520,f9528,f9584,f9658,f9667,f9674,f9681,f9685,f9692,f9696,f9700,f9717,f9721,f9762,f9766,f9770,f9774,f9778,f9782,f9904,f9910,f9918,f9926,f9932,f9940,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9973,f9977,f9981,f10363,f10370,f10374,f10443,f10447,f10547,f10551,f10555,f10563,f10596,f10600,f10604,f10781,f10786,f10791,f10796,f11022,f11026,f11030,f11034,f11038,f11042,f11445,f11449,f11454,f11473,f11477,f11570,f11574,f11608,f11625,f11630,f11641,f11647,f11653,f11736,f11740,f11754,f11758,f11786,f11790,f11866,f11895,f11899,f11903,f12102,f12106,f12110,f12152,f12157,f12162,f12166,f12171,f12179,f12185,f12189,f12193,f12197,f12591,f12596,f12601,f12605,f12609,f12613,f12993,f12997,f13001,f13005,f13009,f13013,f13017,f13143,f13147,f13443,f13467,f13529,f13533,f13564,f13568,f13572,f13639,f13643,f13775,f13779,f13783,f13859,f13863,f13957,f13961,f13965,f14016,f14020,f14024,f14028,f14251,f14266,f14324,f14328,f14332,f14336,f14508,f14512,f14516,f14520,f14604,f14634,f14687,f14695,f14702,f14710,f14808,f14843,f14847,f14851,f14856,f14995,f14999,f15004,f15188,f15211,f15219,f15224,f15229,f15237,f15252,f15261,f15267,f15271,f15275,f15283,f15288,f15292,f15499,f15503,f15509,f15513,f15542,f15546,f15551,f15556,f15560,f15564,f15568,f15579,f15583,f15665,f15669,f15728,f15735,f15769,f15773,f15777,f15793,f15856,f15864,f15869,f15877,f15882,f15886,f15890,f15894,f15898,f15994,f15998,f16014,f16018,f16039,f16047,f16231,f16235,f16281,f16298,f16302,f16365,f16369,f16377,f16383,f16404,f16409,f16413,f16534,f16539,f16543,f16548,f16552,f16557,f16562,f16566,f16570,f16595,f16599,f16603,f16721,f16725,f16729,f16733,f16737,f16926,f16971,f17012,f17016,f17020,f17024,f17043,f17047,f17100,f17220,f17228,f17232,f17236,f17383,f17388,f17393,f17534,f17577,f17605,f17622,f17632,f17637,f17649,f17653,f17657,f17661,f17671,f17704,f17718,f17722,f17726,f17730,f17734,f17738,f17742,f18105,f18109,f18113,f18168,f18200,f18204,f18402,f18406,f18456,f18577,f18716,f18720,f18782,f18826,f18831,f18835,f18899,f18903,f18907,f18911,f18915,f18919,f19164,f19244,f19248,f19252,f19257,f19262,f19266,f19270,f19480,f19487,f19491,f19541,f19547,f19597,f19601,f19605,f19668,f19713,f19717,f19743,f19747,f19751,f20082,f20086,f20264,f20268,f20299,f20322,f20371,f20375,f20379,f20423,f20427,f20478,f20500,f20504,f20508,f20530,f20534,f20569,f20573,f20625,f20771,f20785,f20789,f20794,f20798,f20848,f20852,f20924,f20929,f20933,f20964,f20968,f20972,f20976,f20980,f20984,f20988,f21007,f21292,f21310,f21319,f21330,f21347,f21377,f21407,f21421,f21486,f21490,f21520,f21553,f21618,f21622,f21897,f21903,f21908,f21912,f21917,f21922,f21927,f21931,f21936,f21941,f21946,f21950,f21954,f21958,f21963,f21967,f21971,f21976,f21984,f21988,f21992,f21996,f22000,f22004,f22008,f22012,f22016,f22020,f22024,f22028,f22032,f22036,f22040,f22044,f22048,f22052,f22057,f22062,f22067,f22072,f22077,f22082,f22086,f22164,f22755,f22954,f22963,f22985,f22986,f23107,f23113,f23122,f23126,f23130,f23135,f23140,f23153,f23157,f23161,f23165,f23169,f23173,f23177,f23181,f23195,f23199,f23203,f23208,f23212,f23217,f23221,f23225,f23229,f23233,f23893,f24259,f24263,f24267,f24272,f24276,f24281,f24285,f24289,f24293,f24297,f24301,f24310,f24315,f24320,f24324,f24328,f24333,f24338,f24342,f24346,f24350,f24355,f24359,f24364,f24368,f24372,f24376,f24380,f24384,f24388,f24392,f24396,f24400,f24404,f24408,f24412,f24416,f24420,f24424,f24429,f24434,f24447,f25770,f25810,f25814,f25818,f25825,f25834,f25841,f25846,f25859,f25868,f25872,f25876,f25880,f25884,f25889,f25893,f25897,f25901,f25905,f25909,f25913,f25917,f25921,f25925,f25929,f25945,f25949,f25953,f25957,f25962,f25967,f25971,f25975,f25980,f25985,f26001,f26006,f26019,f26025,f26031,f26035,f26039,f26043,f26364,f26734,f27191,f27195,f27202,f27207,f27215,f27219,f27223,f27227,f27231,f27235,f27239,f27642,f27646,f27651,f27655,f27660,f27664,f27668,f27672,f27802,f27830,f27858,f27862,f27866,f27870,f27874,f27878,f28013,f28017,f28021,f28025,f28029,f28033,f28037,f28043,f28049,f28055,f28062,f28066,f28071,f28076,f28081,f28086,f28090,f28094,f28098,f28102,f28106,f28111,f28115,f28119,f28123,f28131,f28136,f28143,f28348,f28353,f28357,f28361,f28365,f28369,f28378,f28386,f28488,f29854,f29858,f29862,f29878,f29884,f29888,f29892,f29897,f29905,f29916,f29921,f29926,f29930,f29934,f29938,f29942,f29946,f29950,f29954,f29958,f29963,f29967,f29971,f29975,f29979,f29983,f29987,f29991,f29995,f29999,f30003,f30008,f30012,f30017,f30021,f30026,f30030,f30034,f30038,f30042,f30046,f30051,f30055,f30059,f30063,f30067,f30071,f30075,f30079,f30083,f30087,f30091,f30095,f30100,f30105,f30109,f30113,f30118,f30131,f30136,f30140,f30144,f30148,f30152,f30156,f30294,f32107,f32285,f32289,f32294,f32300,f32308,f32415,f32424,f32431,f32436,f32442,f32447,f32452,f32456,f32460,f32464,f32468,f32472,f32476,f32480,f32484,f32488,f32492,f32501,f32503,f32674,f32678,f32682,f32686,f32690,f32694,f32698,f32702,f32706,f32711,f32715,f32719,f32723,f32727,f32731,f32735,f32794,f33242,f33900,f34217,f34223,f34228,f34232,f34236,f34240,f34244,f34248,f34252,f34256,f34260,f34264,f34268,f34272,f34276,f34280,f34284,f34288,f34292,f34300,f34305,f34310,f34315,f34319,f34323,f34327,f34331,f34335,f34339,f34343,f34347,f34351,f34355,f34359,f34363,f34367,f34372,f34376,f34381,f34385,f34389,f34396,f34443,f34456,f34461,f34465,f34469,f34473,f34485,f34490,f34495,f34500,f34505,f34509,f34513,f34517,f34525,f35160,f35815,f37080,f37085,f37089,f37093,f37097,f37101,f37105,f37109,f37113,f37117,f37121,f37136,f37140,f37144,f37148,f37152,f37156,f37160,f37164,f37168,f37172,f37176,f37180,f37184,f37188,f37192,f37196,f37200,f37204,f37208,f37212,f37216,f37232,f37236,f37240,f37244,f37248,f37252,f37256,f37260,f37264,f37268,f37272,f37276,f37280,f37284,f37288,f37292,f37296,f37300,f37304,f37309,f37314,f37329,f37333,f37351,f37355,f37359,f37363,f37367,f37385,f37390,f37394,f37398,f37403,f37407,f37415,f37420,f37429,f37446,f37463,f37587,f39191,f40123,f41122,f41123,f41333,f41704,f41708,f41726,f41731,f41736,f41740,f41760,f41765,f41773,f41778,f41785,f41805,f41813,f41817,f41821,f41825,f41829,f41833,f41834]) ).

fof(f41834,plain,
    ( spl0_1
    | ~ spl0_27
    | ~ spl0_1523 ),
    inference(avatar_split_clause,[],[f41787,f41738,f319,f204]) ).

fof(f204,plain,
    ( spl0_1
  <=> subclass(domain_of(intersection(x,y)),domain_of(x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f319,plain,
    ( spl0_27
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f41738,plain,
    ( spl0_1523
  <=> ! [X0] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(x,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).

fof(f41787,plain,
    ( subclass(domain_of(intersection(x,y)),domain_of(x))
    | ~ spl0_27
    | ~ spl0_1523 ),
    inference(resolution,[],[f41739,f320]) ).

fof(f320,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f319]) ).

fof(f41739,plain,
    ( ! [X0] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(x,X0)))
    | ~ spl0_1523 ),
    inference(avatar_component_clause,[],[f41738]) ).

fof(f41833,plain,
    ( spl0_1534
    | ~ spl0_124
    | ~ spl0_235
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3298,f3149,f2310,f955,f41831]) ).

fof(f41831,plain,
    ( spl0_1534
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(complement(compose(element_relation,complement(singleton_relation)))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).

fof(f955,plain,
    ( spl0_124
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f2310,plain,
    ( spl0_235
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f3149,plain,
    ( spl0_316
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f3298,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(complement(compose(element_relation,complement(singleton_relation)))))
        | subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_235
    | ~ spl0_316 ),
    inference(forward_demodulation,[],[f3282,f2312]) ).

fof(f2312,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2310]) ).

fof(f3282,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,X1),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f956]) ).

fof(f956,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f955]) ).

fof(f3150,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f3149]) ).

fof(f41829,plain,
    ( spl0_1533
    | ~ spl0_30
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3274,f3149,f331,f41827]) ).

fof(f41827,plain,
    ( spl0_1533
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(unordered_pair(X2,not_subclass_element(X0,X1))))
        | ~ member(not_subclass_element(X0,X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).

fof(f331,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f3274,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(unordered_pair(X2,not_subclass_element(X0,X1))))
        | ~ member(not_subclass_element(X0,X1),universal_class) )
    | ~ spl0_30
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f332]) ).

fof(f332,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f331]) ).

fof(f41825,plain,
    ( spl0_1532
    | ~ spl0_29
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3273,f3149,f327,f41823]) ).

fof(f41823,plain,
    ( spl0_1532
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(unordered_pair(not_subclass_element(X0,X1),X2)))
        | ~ member(not_subclass_element(X0,X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).

fof(f327,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f3273,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(unordered_pair(not_subclass_element(X0,X1),X2)))
        | ~ member(not_subclass_element(X0,X1),universal_class) )
    | ~ spl0_29
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f328]) ).

fof(f328,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f41821,plain,
    ( spl0_1531
    | ~ spl0_44
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2976,f2818,f424,f41819]) ).

fof(f41819,plain,
    ( spl0_1531
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(complement(X1)))
        | member(regular(X0),X1)
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).

fof(f424,plain,
    ( spl0_44
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f2818,plain,
    ( spl0_292
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f2976,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(complement(X1)))
        | member(regular(X0),X1)
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_44
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f425]) ).

fof(f425,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f424]) ).

fof(f2819,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f2818]) ).

fof(f41817,plain,
    ( spl0_1530
    | ~ spl0_69
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2869,f2310,f564,f41815]) ).

fof(f41815,plain,
    ( spl0_1530
  <=> ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).

fof(f564,plain,
    ( spl0_69
  <=> ! [X8] :
        ( function(X8)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f2869,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0) )
    | ~ spl0_69
    | ~ spl0_235 ),
    inference(superposition,[],[f565,f2312]) ).

fof(f565,plain,
    ( ! [X8] :
        ( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | function(X8) )
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f564]) ).

fof(f41813,plain,
    ( spl0_1529
    | ~ spl0_164
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2786,f2735,f1365,f41811]) ).

fof(f41811,plain,
    ( spl0_1529
  <=> ! [X0] :
        ( subclass(subset_relation,intersection(X0,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(subset_relation,intersection(X0,cross_product(universal_class,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).

fof(f1365,plain,
    ( spl0_164
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f2735,plain,
    ( spl0_286
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f2786,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(X0,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(subset_relation,intersection(X0,cross_product(universal_class,universal_class))),X0) )
    | ~ spl0_164
    | ~ spl0_286 ),
    inference(duplicate_literal_removal,[],[f2781]) ).

fof(f2781,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(X0,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(subset_relation,intersection(X0,cross_product(universal_class,universal_class))),X0)
        | subclass(subset_relation,intersection(X0,cross_product(universal_class,universal_class))) )
    | ~ spl0_164
    | ~ spl0_286 ),
    inference(resolution,[],[f2736,f1366]) ).

fof(f1366,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1365]) ).

fof(f2736,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2735]) ).

fof(f41805,plain,
    ( ~ spl0_1527
    | ~ spl0_1528
    | spl0_182
    | ~ spl0_1521 ),
    inference(avatar_split_clause,[],[f41779,f41729,f1538,f41802,f41798]) ).

fof(f41798,plain,
    ( spl0_1527
  <=> member(first(null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).

fof(f41802,plain,
    ( spl0_1528
  <=> member(second(null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).

fof(f1538,plain,
    ( spl0_182
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f41729,plain,
    ( spl0_1521
  <=> ! [X0,X1] :
        ( member(null_class,cross_product(X0,X1))
        | ~ member(second(null_class),X1)
        | ~ member(first(null_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).

fof(f41779,plain,
    ( ~ member(second(null_class),universal_class)
    | ~ member(first(null_class),universal_class)
    | spl0_182
    | ~ spl0_1521 ),
    inference(resolution,[],[f1540,f41730]) ).

fof(f41730,plain,
    ( ! [X0,X1] :
        ( member(null_class,cross_product(X0,X1))
        | ~ member(second(null_class),X1)
        | ~ member(first(null_class),X0) )
    | ~ spl0_1521 ),
    inference(avatar_component_clause,[],[f41729]) ).

fof(f1540,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_182 ),
    inference(avatar_component_clause,[],[f1538]) ).

fof(f41785,plain,
    ( spl0_1526
    | spl0_182
    | ~ spl0_21
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f864,f815,f291,f1538,f41783]) ).

fof(f41783,plain,
    ( spl0_1526
  <=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).

fof(f291,plain,
    ( spl0_21
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f815,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f864,plain,
    ( ! [X0,X1] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f292]) ).

fof(f292,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f291]) ).

fof(f816,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f815]) ).

fof(f41778,plain,
    ( spl0_173
    | ~ spl0_79
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f4252,f1538,f628,f1463]) ).

fof(f1463,plain,
    ( spl0_173
  <=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f628,plain,
    ( spl0_79
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f4252,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | ~ spl0_79
    | ~ spl0_182 ),
    inference(resolution,[],[f1539,f629]) ).

fof(f629,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f1539,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f1538]) ).

fof(f41773,plain,
    ( ~ spl0_926
    | ~ spl0_1525 ),
    inference(avatar_contradiction_clause,[],[f41769]) ).

fof(f41769,plain,
    ( $false
    | ~ spl0_926
    | ~ spl0_1525 ),
    inference(resolution,[],[f41759,f18167]) ).

fof(f18167,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_926 ),
    inference(avatar_component_clause,[],[f18166]) ).

fof(f18166,plain,
    ( spl0_926
  <=> ! [X0] : ~ member(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f41759,plain,
    ( member(unordered_pair(first(null_class),first(null_class)),null_class)
    | ~ spl0_1525 ),
    inference(avatar_component_clause,[],[f41757]) ).

fof(f41757,plain,
    ( spl0_1525
  <=> member(unordered_pair(first(null_class),first(null_class)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).

fof(f41765,plain,
    ( ~ spl0_9
    | spl0_1524 ),
    inference(avatar_contradiction_clause,[],[f41761]) ).

fof(f41761,plain,
    ( $false
    | ~ spl0_9
    | spl0_1524 ),
    inference(resolution,[],[f41755,f241]) ).

fof(f241,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f240,plain,
    ( spl0_9
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f41755,plain,
    ( ~ member(unordered_pair(first(null_class),first(null_class)),universal_class)
    | spl0_1524 ),
    inference(avatar_component_clause,[],[f41753]) ).

fof(f41753,plain,
    ( spl0_1524
  <=> member(unordered_pair(first(null_class),first(null_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).

fof(f41760,plain,
    ( ~ spl0_1524
    | spl0_1525
    | ~ spl0_29
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41228,f1463,f327,f41757,f41753]) ).

fof(f41228,plain,
    ( member(unordered_pair(first(null_class),first(null_class)),null_class)
    | ~ member(unordered_pair(first(null_class),first(null_class)),universal_class)
    | ~ spl0_29
    | ~ spl0_173 ),
    inference(superposition,[],[f328,f1465]) ).

fof(f1465,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f1463]) ).

fof(f41740,plain,
    ( spl0_1523
    | ~ spl0_145
    | ~ spl0_1430 ),
    inference(avatar_split_clause,[],[f41548,f34515,f1171,f41738]) ).

fof(f1171,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f34515,plain,
    ( spl0_1430
  <=> ! [X0] : null_class = intersection(intersection(x,X0),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).

fof(f41548,plain,
    ( ! [X0] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(x,X0)))
    | ~ spl0_145
    | ~ spl0_1430 ),
    inference(trivial_inequality_removal,[],[f41363]) ).

fof(f41363,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(x,X0))) )
    | ~ spl0_145
    | ~ spl0_1430 ),
    inference(superposition,[],[f1172,f34516]) ).

fof(f34516,plain,
    ( ! [X0] : null_class = intersection(intersection(x,X0),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ spl0_1430 ),
    inference(avatar_component_clause,[],[f34515]) ).

fof(f1172,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1171]) ).

fof(f41736,plain,
    ( ~ spl0_1522
    | spl0_108
    | ~ spl0_182
    | ~ spl0_85
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41131,f1463,f664,f1538,f810,f41733]) ).

fof(f41733,plain,
    ( spl0_1522
  <=> member(first(null_class),second(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).

fof(f810,plain,
    ( spl0_108
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f664,plain,
    ( spl0_85
  <=> ! [X0,X1] :
        ( ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f41131,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | member(null_class,element_relation)
    | ~ member(first(null_class),second(null_class))
    | ~ spl0_85
    | ~ spl0_173 ),
    inference(superposition,[],[f665,f1465]) ).

fof(f665,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f664]) ).

fof(f41731,plain,
    ( spl0_1521
    | ~ spl0_77
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41129,f1463,f613,f41729]) ).

fof(f613,plain,
    ( spl0_77
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,X0)
        | ~ member(X3,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f41129,plain,
    ( ! [X0,X1] :
        ( member(null_class,cross_product(X0,X1))
        | ~ member(second(null_class),X1)
        | ~ member(first(null_class),X0) )
    | ~ spl0_77
    | ~ spl0_173 ),
    inference(superposition,[],[f614,f1465]) ).

fof(f614,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | ~ member(X3,X1)
        | ~ member(X2,X0) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f41726,plain,
    ( spl0_1520
    | ~ spl0_72
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41128,f1463,f584,f41724]) ).

fof(f41724,plain,
    ( spl0_1520
  <=> ! [X0] :
        ( ~ member(null_class,compose_class(X0))
        | second(null_class) = compose(X0,first(null_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).

fof(f584,plain,
    ( spl0_72
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f41128,plain,
    ( ! [X0] :
        ( ~ member(null_class,compose_class(X0))
        | second(null_class) = compose(X0,first(null_class)) )
    | ~ spl0_72
    | ~ spl0_173 ),
    inference(superposition,[],[f585,f1465]) ).

fof(f585,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
        | compose(X0,X1) = X4 )
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f584]) ).

fof(f41708,plain,
    ( spl0_1519
    | ~ spl0_68
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41127,f1463,f560,f41706]) ).

fof(f41706,plain,
    ( spl0_1519
  <=> ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(first(null_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).

fof(f560,plain,
    ( spl0_68
  <=> ! [X0,X3,X2,X1] :
        ( member(X2,X0)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f41127,plain,
    ( ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(first(null_class),X0) )
    | ~ spl0_68
    | ~ spl0_173 ),
    inference(superposition,[],[f561,f1465]) ).

fof(f561,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f560]) ).

fof(f41704,plain,
    ( spl0_1518
    | ~ spl0_67
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41126,f1463,f556,f41702]) ).

fof(f41702,plain,
    ( spl0_1518
  <=> ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(second(null_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).

fof(f556,plain,
    ( spl0_67
  <=> ! [X0,X3,X2,X1] :
        ( member(X3,X1)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f41126,plain,
    ( ! [X0,X1] :
        ( ~ member(null_class,cross_product(X0,X1))
        | member(second(null_class),X1) )
    | ~ spl0_67
    | ~ spl0_173 ),
    inference(superposition,[],[f557,f1465]) ).

fof(f557,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X3,X1) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f556]) ).

fof(f41333,plain,
    ( spl0_1516
    | ~ spl0_1517
    | ~ spl0_64
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f41125,f1463,f539,f41330,f41326]) ).

fof(f41326,plain,
    ( spl0_1516
  <=> second(null_class) = domain_of(first(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).

fof(f41330,plain,
    ( spl0_1517
  <=> member(null_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).

fof(f539,plain,
    ( spl0_64
  <=> ! [X0,X1] :
        ( domain_of(X0) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f41125,plain,
    ( ~ member(null_class,domain_relation)
    | second(null_class) = domain_of(first(null_class))
    | ~ spl0_64
    | ~ spl0_173 ),
    inference(superposition,[],[f540,f1465]) ).

fof(f540,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f539]) ).

fof(f41123,plain,
    ( spl0_173
    | ~ spl0_79
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f2718,f2698,f628,f1463]) ).

fof(f2698,plain,
    ( spl0_280
  <=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f2718,plain,
    ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
    | ~ spl0_79
    | ~ spl0_280 ),
    inference(resolution,[],[f2700,f629]) ).

fof(f2700,plain,
    ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_280 ),
    inference(avatar_component_clause,[],[f2698]) ).

fof(f41122,plain,
    ( spl0_1515
    | ~ spl0_49
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2571,f2499,f448,f41120]) ).

fof(f41120,plain,
    ( spl0_1515
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,complement(intersection(X0,X1)))
        | ~ member(unordered_pair(X2,X3),X1)
        | ~ member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).

fof(f448,plain,
    ( spl0_49
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f2499,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f2571,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,complement(intersection(X0,X1)))
        | ~ member(unordered_pair(X2,X3),X1)
        | ~ member(unordered_pair(X2,X3),X0) )
    | ~ spl0_49
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f449]) ).

fof(f449,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f448]) ).

fof(f2500,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f2499]) ).

fof(f40123,plain,
    ( spl0_1
    | spl0_1513
    | ~ spl0_1514
    | ~ spl0_1382
    | ~ spl0_1435 ),
    inference(avatar_split_clause,[],[f37123,f37078,f34258,f40120,f40117,f204]) ).

fof(f40117,plain,
    ( spl0_1513
  <=> ! [X0] : ~ subclass(subset_relation,domain_of(intersection(X0,x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).

fof(f40120,plain,
    ( spl0_1514
  <=> subclass(domain_of(intersection(x,y)),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).

fof(f34258,plain,
    ( spl0_1382
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(subset_relation,X2)
        | member(not_subclass_element(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).

fof(f37078,plain,
    ( spl0_1435
  <=> ! [X0] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(X0,x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).

fof(f37123,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(intersection(x,y)),singleton_relation)
        | ~ subclass(subset_relation,domain_of(intersection(X0,x)))
        | subclass(domain_of(intersection(x,y)),domain_of(x)) )
    | ~ spl0_1382
    | ~ spl0_1435 ),
    inference(resolution,[],[f37079,f34259]) ).

fof(f34259,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),X2)
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(subset_relation,X2)
        | subclass(X0,X1) )
    | ~ spl0_1382 ),
    inference(avatar_component_clause,[],[f34258]) ).

fof(f37079,plain,
    ( ! [X0] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(X0,x)))
    | ~ spl0_1435 ),
    inference(avatar_component_clause,[],[f37078]) ).

fof(f39191,plain,
    ( spl0_1511
    | spl0_1
    | ~ spl0_1512
    | ~ spl0_1355
    | ~ spl0_1435 ),
    inference(avatar_split_clause,[],[f37125,f37078,f32680,f39188,f204,f39185]) ).

fof(f39185,plain,
    ( spl0_1511
  <=> ! [X0] : ~ inductive(domain_of(intersection(X0,x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).

fof(f39188,plain,
    ( spl0_1512
  <=> subclass(domain_of(intersection(x,y)),omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).

fof(f32680,plain,
    ( spl0_1355
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,omega)
        | member(not_subclass_element(X0,X1),X2)
        | ~ inductive(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).

fof(f37125,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(intersection(x,y)),omega)
        | subclass(domain_of(intersection(x,y)),domain_of(x))
        | ~ inductive(domain_of(intersection(X0,x))) )
    | ~ spl0_1355
    | ~ spl0_1435 ),
    inference(resolution,[],[f37079,f32681]) ).

fof(f32681,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),X2)
        | ~ subclass(X0,omega)
        | subclass(X0,X1)
        | ~ inductive(X2) )
    | ~ spl0_1355 ),
    inference(avatar_component_clause,[],[f32680]) ).

fof(f37587,plain,
    ( spl0_1510
    | ~ spl0_50
    | ~ spl0_1477 ),
    inference(avatar_split_clause,[],[f37319,f37270,f452,f37585]) ).

fof(f37585,plain,
    ( spl0_1510
  <=> ! [X0,X1] : ~ subclass(domain_of(intersection(x,y)),domain_of(intersection(x,cross_product(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).

fof(f452,plain,
    ( spl0_50
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f37270,plain,
    ( spl0_1477
  <=> ! [X0] : ~ subclass(domain_of(intersection(x,y)),domain_of(intersection(X0,x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).

fof(f37319,plain,
    ( ! [X0,X1] : ~ subclass(domain_of(intersection(x,y)),domain_of(intersection(x,cross_product(X0,X1))))
    | ~ spl0_50
    | ~ spl0_1477 ),
    inference(superposition,[],[f37271,f453]) ).

fof(f453,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f452]) ).

fof(f37271,plain,
    ( ! [X0] : ~ subclass(domain_of(intersection(x,y)),domain_of(intersection(X0,x)))
    | ~ spl0_1477 ),
    inference(avatar_component_clause,[],[f37270]) ).

fof(f37463,plain,
    ( spl0_1508
    | ~ spl0_1509
    | ~ spl0_360
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f10970,f10793,f3753,f37460,f37456]) ).

fof(f37456,plain,
    ( spl0_1508
  <=> member(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).

fof(f37460,plain,
    ( spl0_1509
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).

fof(f3753,plain,
    ( spl0_360
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f10793,plain,
    ( spl0_686
  <=> not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f10970,plain,
    ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),subset_relation)
    | member(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),universal_class)
    | ~ spl0_360
    | ~ spl0_686 ),
    inference(superposition,[],[f3754,f10795]) ).

fof(f10795,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_686 ),
    inference(avatar_component_clause,[],[f10793]) ).

fof(f3754,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_360 ),
    inference(avatar_component_clause,[],[f3753]) ).

fof(f37446,plain,
    ( spl0_1506
    | ~ spl0_1507
    | ~ spl0_360
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10896,f10783,f3753,f37443,f37439]) ).

fof(f37439,plain,
    ( spl0_1506
  <=> member(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).

fof(f37443,plain,
    ( spl0_1507
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).

fof(f10783,plain,
    ( spl0_684
  <=> not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f10896,plain,
    ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),subset_relation)
    | member(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),universal_class)
    | ~ spl0_360
    | ~ spl0_684 ),
    inference(superposition,[],[f3754,f10785]) ).

fof(f10785,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_684 ),
    inference(avatar_component_clause,[],[f10783]) ).

fof(f37429,plain,
    ( spl0_1504
    | ~ spl0_1505
    | ~ spl0_360
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f10822,f10778,f3753,f37426,f37422]) ).

fof(f37422,plain,
    ( spl0_1504
  <=> member(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).

fof(f37426,plain,
    ( spl0_1505
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).

fof(f10778,plain,
    ( spl0_683
  <=> not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f10822,plain,
    ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),subset_relation)
    | member(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),universal_class)
    | ~ spl0_360
    | ~ spl0_683 ),
    inference(superposition,[],[f3754,f10780]) ).

fof(f10780,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_683 ),
    inference(avatar_component_clause,[],[f10778]) ).

fof(f37420,plain,
    ( spl0_1501
    | ~ spl0_1503
    | ~ spl0_61
    | ~ spl0_681 ),
    inference(avatar_split_clause,[],[f10704,f10598,f524,f37417,f37409]) ).

fof(f37409,plain,
    ( spl0_1501
  <=> ! [X2,X0,X1] : member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).

fof(f37417,plain,
    ( spl0_1503
  <=> subclass(universal_class,flip(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).

fof(f524,plain,
    ( spl0_61
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f10598,plain,
    ( spl0_681
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f10704,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(element_relation))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_61
    | ~ spl0_681 ),
    inference(resolution,[],[f10599,f525]) ).

fof(f525,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f10599,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(X3,X3))),X0)
        | ~ subclass(universal_class,flip(X0)) )
    | ~ spl0_681 ),
    inference(avatar_component_clause,[],[f10598]) ).

fof(f37415,plain,
    ( spl0_1501
    | ~ spl0_1502
    | ~ spl0_61
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10619,f10594,f524,f37412,f37409]) ).

fof(f37412,plain,
    ( spl0_1502
  <=> subclass(universal_class,rotate(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).

fof(f10594,plain,
    ( spl0_680
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f10619,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(element_relation))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_61
    | ~ spl0_680 ),
    inference(resolution,[],[f10595,f525]) ).

fof(f10595,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(X3,X3))),X0)
        | ~ subclass(universal_class,rotate(X0)) )
    | ~ spl0_680 ),
    inference(avatar_component_clause,[],[f10594]) ).

fof(f37407,plain,
    ( spl0_1500
    | ~ spl0_64
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9588,f9579,f539,f37405]) ).

fof(f37405,plain,
    ( spl0_1500
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),domain_relation)
        | second(unordered_pair(X0,X1)) = domain_of(first(unordered_pair(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).

fof(f9579,plain,
    ( spl0_630
  <=> ! [X2,X3] : unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f9588,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),domain_relation)
        | second(unordered_pair(X0,X1)) = domain_of(first(unordered_pair(X0,X1))) )
    | ~ spl0_64
    | ~ spl0_630 ),
    inference(superposition,[],[f540,f9580]) ).

fof(f9580,plain,
    ( ! [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)))))
    | ~ spl0_630 ),
    inference(avatar_component_clause,[],[f9579]) ).

fof(f37403,plain,
    ( spl0_1499
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_626 ),
    inference(avatar_split_clause,[],[f9561,f9514,f2364,f2310,f37400]) ).

fof(f37400,plain,
    ( spl0_1499
  <=> subclass(singleton_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_1499])]) ).

fof(f2364,plain,
    ( spl0_244
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f9514,plain,
    ( spl0_626
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f9561,plain,
    ( subclass(singleton_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_626 ),
    inference(forward_demodulation,[],[f9560,f2312]) ).

fof(f9560,plain,
    ( subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_244
    | ~ spl0_626 ),
    inference(duplicate_literal_removal,[],[f9529]) ).

fof(f9529,plain,
    ( subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | subclass(identity_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_244
    | ~ spl0_626 ),
    inference(resolution,[],[f9515,f2365]) ).

fof(f2365,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2364]) ).

fof(f9515,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_626 ),
    inference(avatar_component_clause,[],[f9514]) ).

fof(f37398,plain,
    ( spl0_1498
    | ~ spl0_27
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f6585,f6406,f319,f37396]) ).

fof(f37396,plain,
    ( spl0_1498
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).

fof(f6406,plain,
    ( spl0_481
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | ~ member(not_subclass_element(X0,X1),X2)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f6585,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0))
        | subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_481 ),
    inference(duplicate_literal_removal,[],[f6514]) ).

fof(f6514,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0))
        | subclass(X0,X1)
        | subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_481 ),
    inference(resolution,[],[f6407,f320]) ).

fof(f6407,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X2)
        | member(not_subclass_element(X0,X1),null_class)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) )
    | ~ spl0_481 ),
    inference(avatar_component_clause,[],[f6406]) ).

fof(f37394,plain,
    ( spl0_1497
    | ~ spl0_130
    | ~ spl0_451 ),
    inference(avatar_split_clause,[],[f5866,f5816,f1012,f37392]) ).

fof(f37392,plain,
    ( spl0_1497
  <=> ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).

fof(f1012,plain,
    ( spl0_130
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f5816,plain,
    ( spl0_451
  <=> ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f5866,plain,
    ( ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_130
    | ~ spl0_451 ),
    inference(duplicate_literal_removal,[],[f5855]) ).

fof(f5855,plain,
    ( ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_130
    | ~ spl0_451 ),
    inference(resolution,[],[f5817,f1013]) ).

fof(f1013,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1012]) ).

fof(f5817,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) )
    | ~ spl0_451 ),
    inference(avatar_component_clause,[],[f5816]) ).

fof(f37390,plain,
    ( ~ spl0_1496
    | ~ spl0_603
    | ~ spl0_915
    | ~ spl0_1477 ),
    inference(avatar_split_clause,[],[f37324,f37270,f17701,f9140,f37387]) ).

fof(f37387,plain,
    ( spl0_1496
  <=> subclass(domain_of(intersection(x,y)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).

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

fof(f17701,plain,
    ( spl0_915
  <=> null_class = domain_of(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f37324,plain,
    ( ~ subclass(domain_of(intersection(x,y)),null_class)
    | ~ spl0_603
    | ~ spl0_915
    | ~ spl0_1477 ),
    inference(forward_demodulation,[],[f37320,f17703]) ).

fof(f17703,plain,
    ( null_class = domain_of(null_class)
    | ~ spl0_915 ),
    inference(avatar_component_clause,[],[f17701]) ).

fof(f37320,plain,
    ( ~ subclass(domain_of(intersection(x,y)),domain_of(null_class))
    | ~ spl0_603
    | ~ spl0_1477 ),
    inference(superposition,[],[f37271,f9141]) ).

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

fof(f37385,plain,
    ( spl0_1495
    | ~ spl0_130
    | ~ spl0_450 ),
    inference(avatar_split_clause,[],[f5838,f5807,f1012,f37383]) ).

fof(f37383,plain,
    ( spl0_1495
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).

fof(f5807,plain,
    ( spl0_450
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f5838,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_130
    | ~ spl0_450 ),
    inference(duplicate_literal_removal,[],[f5827]) ).

fof(f5827,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_130
    | ~ spl0_450 ),
    inference(resolution,[],[f5808,f1013]) ).

fof(f5808,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_450 ),
    inference(avatar_component_clause,[],[f5807]) ).

fof(f37367,plain,
    ( spl0_1494
    | spl0_1318
    | ~ spl0_106
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f5610,f5510,f802,f30129,f37365]) ).

fof(f37365,plain,
    ( spl0_1494
  <=> ! [X2] :
        ( null_class = X2
        | ~ subclass(universal_class,X2)
        | ~ subclass(universal_class,regular(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).

fof(f30129,plain,
    ( spl0_1318
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).

fof(f802,plain,
    ( spl0_106
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f5510,plain,
    ( spl0_434
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | ~ member(unordered_pair(X0,X1),X2)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f5610,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2))
        | ~ subclass(universal_class,X2) )
    | ~ spl0_106
    | ~ spl0_434 ),
    inference(resolution,[],[f5511,f803]) ).

fof(f803,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f802]) ).

fof(f5511,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X0,X1),X2)
        | member(unordered_pair(X0,X1),null_class)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) )
    | ~ spl0_434 ),
    inference(avatar_component_clause,[],[f5510]) ).

fof(f37363,plain,
    ( spl0_1493
    | ~ spl0_316
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5077,f4790,f3149,f37361]) ).

fof(f37361,plain,
    ( spl0_1493
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).

fof(f4790,plain,
    ( spl0_407
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f5077,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5033]) ).

fof(f5033,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | subclass(intersection(X0,intersection(X1,X2)),X3)
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_407 ),
    inference(resolution,[],[f4791,f3150]) ).

fof(f4791,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1)
        | subclass(intersection(X0,intersection(X1,X2)),X3) )
    | ~ spl0_407 ),
    inference(avatar_component_clause,[],[f4790]) ).

fof(f37359,plain,
    ( spl0_1492
    | ~ spl0_316
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5019,f4786,f3149,f37357]) ).

fof(f37357,plain,
    ( spl0_1492
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).

fof(f4786,plain,
    ( spl0_406
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f5019,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_316
    | ~ spl0_406 ),
    inference(duplicate_literal_removal,[],[f4975]) ).

fof(f4975,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | subclass(intersection(X0,intersection(X1,X2)),X3)
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_316
    | ~ spl0_406 ),
    inference(resolution,[],[f4787,f3150]) ).

fof(f4787,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2)
        | subclass(intersection(X0,intersection(X1,X2)),X3) )
    | ~ spl0_406 ),
    inference(avatar_component_clause,[],[f4786]) ).

fof(f37355,plain,
    ( spl0_1491
    | ~ spl0_316
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4960,f4782,f3149,f37353]) ).

fof(f37353,plain,
    ( spl0_1491
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).

fof(f4782,plain,
    ( spl0_405
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f4960,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_316
    | ~ spl0_405 ),
    inference(duplicate_literal_removal,[],[f4916]) ).

fof(f4916,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | subclass(intersection(intersection(X0,X1),X2),X3)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_316
    | ~ spl0_405 ),
    inference(resolution,[],[f4783,f3150]) ).

fof(f4783,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0)
        | subclass(intersection(intersection(X0,X1),X2),X3) )
    | ~ spl0_405 ),
    inference(avatar_component_clause,[],[f4782]) ).

fof(f37351,plain,
    ( spl0_1490
    | ~ spl0_316
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f4902,f4778,f3149,f37349]) ).

fof(f37349,plain,
    ( spl0_1490
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).

fof(f4778,plain,
    ( spl0_404
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f4902,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_404 ),
    inference(duplicate_literal_removal,[],[f4858]) ).

fof(f4858,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | subclass(intersection(intersection(X0,X1),X2),X3)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_404 ),
    inference(resolution,[],[f4779,f3150]) ).

fof(f4779,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1)
        | subclass(intersection(intersection(X0,X1),X2),X3) )
    | ~ spl0_404 ),
    inference(avatar_component_clause,[],[f4778]) ).

fof(f37333,plain,
    ( spl0_1489
    | spl0_1142
    | ~ spl0_13
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4842,f4763,f258,f24444,f37331]) ).

fof(f37331,plain,
    ( spl0_1489
  <=> ! [X0,X1] :
        ( regular(omega) = X0
        | ~ inductive(unordered_pair(X0,X1))
        | regular(omega) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).

fof(f24444,plain,
    ( spl0_1142
  <=> null_class = omega ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f258,plain,
    ( spl0_13
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f4763,plain,
    ( spl0_401
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f4842,plain,
    ( ! [X0,X1] :
        ( null_class = omega
        | regular(omega) = X0
        | regular(omega) = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_401 ),
    inference(resolution,[],[f4764,f259]) ).

fof(f259,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f4764,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_401 ),
    inference(avatar_component_clause,[],[f4763]) ).

fof(f37329,plain,
    ( spl0_1488
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4734,f4270,f2310,f393,f37327]) ).

fof(f37327,plain,
    ( spl0_1488
  <=> ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).

fof(f393,plain,
    ( spl0_43
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f4270,plain,
    ( spl0_397
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f4734,plain,
    ( ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_397 ),
    inference(forward_demodulation,[],[f4733,f2312]) ).

fof(f4733,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation)
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_397 ),
    inference(forward_demodulation,[],[f4706,f2312]) ).

fof(f4706,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation)
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_43
    | ~ spl0_397 ),
    inference(superposition,[],[f4271,f395]) ).

fof(f395,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f393]) ).

fof(f4271,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_397 ),
    inference(avatar_component_clause,[],[f4270]) ).

fof(f37314,plain,
    ( spl0_1487
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4732,f4270,f2310,f384,f37312]) ).

fof(f37312,plain,
    ( spl0_1487
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(X0,singleton_relation)
        | ~ subclass(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).

fof(f384,plain,
    ( spl0_41
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f4732,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(X0,singleton_relation)
        | ~ subclass(X0,element_relation) )
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_397 ),
    inference(forward_demodulation,[],[f4705,f2312]) ).

fof(f4705,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation)
        | ~ subclass(X0,element_relation) )
    | ~ spl0_41
    | ~ spl0_397 ),
    inference(superposition,[],[f4271,f386]) ).

fof(f386,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f384]) ).

fof(f37309,plain,
    ( spl0_1486
    | ~ spl0_389
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4721,f4270,f4231,f37307]) ).

fof(f37307,plain,
    ( spl0_1486
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X2))
        | ~ subclass(intersection(null_class,X0),X2)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).

fof(f4231,plain,
    ( spl0_389
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f4721,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X2))
        | ~ subclass(intersection(null_class,X0),X2)
        | null_class = X1 )
    | ~ spl0_389
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4677]) ).

fof(f4677,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X2))
        | ~ subclass(intersection(null_class,X0),X2)
        | subclass(intersection(null_class,X0),intersection(X1,X2))
        | null_class = X1 )
    | ~ spl0_389
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f4232]) ).

fof(f4232,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | subclass(intersection(null_class,X0),X1)
        | null_class = X2 )
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f4231]) ).

fof(f37304,plain,
    ( spl0_1485
    | ~ spl0_391
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4720,f4270,f4239,f37302]) ).

fof(f37302,plain,
    ( spl0_1485
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X2))
        | ~ subclass(intersection(X0,null_class),X2)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).

fof(f4239,plain,
    ( spl0_391
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f4720,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X2))
        | ~ subclass(intersection(X0,null_class),X2)
        | null_class = X1 )
    | ~ spl0_391
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4678]) ).

fof(f4678,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X2))
        | ~ subclass(intersection(X0,null_class),X2)
        | subclass(intersection(X0,null_class),intersection(X1,X2))
        | null_class = X1 )
    | ~ spl0_391
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f4240]) ).

fof(f4240,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | subclass(intersection(X0,null_class),X1)
        | null_class = X2 )
    | ~ spl0_391 ),
    inference(avatar_component_clause,[],[f4239]) ).

fof(f37300,plain,
    ( spl0_1484
    | ~ spl0_390
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4719,f4270,f4235,f37298]) ).

fof(f37298,plain,
    ( spl0_1484
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X3))
        | ~ subclass(intersection(X0,X1),X3)
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).

fof(f4235,plain,
    ( spl0_390
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f4719,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X3))
        | ~ subclass(intersection(X0,X1),X3)
        | ~ subclass(X1,X2) )
    | ~ spl0_390
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4679]) ).

fof(f4679,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X3))
        | ~ subclass(intersection(X0,X1),X3)
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X3)) )
    | ~ spl0_390
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f4236]) ).

fof(f4236,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X3)
        | ~ subclass(X1,X3)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f4235]) ).

fof(f37296,plain,
    ( spl0_1483
    | ~ spl0_388
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4718,f4270,f4227,f37294]) ).

fof(f37294,plain,
    ( spl0_1483
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X3))
        | ~ subclass(intersection(X0,X1),X3)
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).

fof(f4227,plain,
    ( spl0_388
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f4718,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X3))
        | ~ subclass(intersection(X0,X1),X3)
        | ~ subclass(X0,X2) )
    | ~ spl0_388
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4680]) ).

fof(f4680,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X3))
        | ~ subclass(intersection(X0,X1),X3)
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X3)) )
    | ~ spl0_388
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f4228]) ).

fof(f4228,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X3)
        | ~ subclass(X0,X3)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f4227]) ).

fof(f37292,plain,
    ( spl0_1482
    | ~ spl0_40
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4701,f4270,f380,f37290]) ).

fof(f37290,plain,
    ( spl0_1482
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | ~ subclass(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).

fof(f380,plain,
    ( spl0_40
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f4701,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | ~ subclass(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_397 ),
    inference(superposition,[],[f4271,f381]) ).

fof(f381,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f380]) ).

fof(f37288,plain,
    ( spl0_1481
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4596,f4235,f2310,f761,f37286]) ).

fof(f37286,plain,
    ( spl0_1481
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X1,X0),X2)
        | member(not_subclass_element(intersection(X1,X0),X2),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).

fof(f761,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f4596,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X1,X0),X2)
        | member(not_subclass_element(intersection(X1,X0),X2),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_390 ),
    inference(forward_demodulation,[],[f4574,f2312]) ).

fof(f4574,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(intersection(X1,X0),X2)
        | member(not_subclass_element(intersection(X1,X0),X2),subset_relation) )
    | ~ spl0_103
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f762]) ).

fof(f762,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f761]) ).

fof(f37284,plain,
    ( spl0_1480
    | ~ spl0_97
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4576,f4235,f731,f37282]) ).

fof(f37282,plain,
    ( spl0_1480
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X1,X0),X2)
        | member(not_subclass_element(intersection(X1,X0),X2),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).

fof(f731,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f4576,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X1,X0),X2)
        | member(not_subclass_element(intersection(X1,X0),X2),element_relation) )
    | ~ spl0_97
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f732]) ).

fof(f732,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f731]) ).

fof(f37280,plain,
    ( spl0_1479
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4500,f4227,f2310,f761,f37278]) ).

fof(f37278,plain,
    ( spl0_1479
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),X2)
        | member(not_subclass_element(intersection(X0,X1),X2),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).

fof(f4500,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),X2)
        | member(not_subclass_element(intersection(X0,X1),X2),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_388 ),
    inference(forward_demodulation,[],[f4478,f2312]) ).

fof(f4478,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(intersection(X0,X1),X2)
        | member(not_subclass_element(intersection(X0,X1),X2),subset_relation) )
    | ~ spl0_103
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f762]) ).

fof(f37276,plain,
    ( spl0_1478
    | ~ spl0_97
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4480,f4227,f731,f37274]) ).

fof(f37274,plain,
    ( spl0_1478
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),X2)
        | member(not_subclass_element(intersection(X0,X1),X2),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).

fof(f4480,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),X2)
        | member(not_subclass_element(intersection(X0,X1),X2),element_relation) )
    | ~ spl0_97
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f732]) ).

fof(f37272,plain,
    ( spl0_1
    | spl0_1477
    | ~ spl0_130
    | ~ spl0_1435 ),
    inference(avatar_split_clause,[],[f37126,f37078,f1012,f37270,f204]) ).

fof(f37126,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(intersection(x,y)),domain_of(intersection(X0,x)))
        | subclass(domain_of(intersection(x,y)),domain_of(x)) )
    | ~ spl0_130
    | ~ spl0_1435 ),
    inference(resolution,[],[f37079,f1013]) ).

fof(f37268,plain,
    ( spl0_1476
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4450,f4223,f2310,f393,f37266]) ).

fof(f37266,plain,
    ( spl0_1476
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).

fof(f4223,plain,
    ( spl0_387
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f4450,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(forward_demodulation,[],[f4449,f2312]) ).

fof(f4449,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = intersection(X0,identity_relation) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(forward_demodulation,[],[f4435,f2312]) ).

fof(f4435,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = intersection(X0,identity_relation) )
    | ~ spl0_43
    | ~ spl0_387 ),
    inference(superposition,[],[f4224,f395]) ).

fof(f4224,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X1)
        | null_class = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f4223]) ).

fof(f37264,plain,
    ( spl0_1475
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4448,f4223,f2310,f384,f37262]) ).

fof(f37262,plain,
    ( spl0_1475
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).

fof(f4448,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(forward_demodulation,[],[f4434,f2312]) ).

fof(f4434,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_41
    | ~ spl0_387 ),
    inference(superposition,[],[f4224,f386]) ).

fof(f37260,plain,
    ( spl0_1474
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4447,f4223,f2310,f761,f37258]) ).

fof(f37258,plain,
    ( spl0_1474
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(singleton_relation,X1))),subset_relation)
        | null_class = intersection(X0,intersection(singleton_relation,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).

fof(f4447,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(singleton_relation,X1))),subset_relation)
        | null_class = intersection(X0,intersection(singleton_relation,X1)) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(forward_demodulation,[],[f4446,f2312]) ).

fof(f4446,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,intersection(singleton_relation,X1))
        | member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_387 ),
    inference(forward_demodulation,[],[f4427,f2312]) ).

fof(f4427,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,intersection(identity_relation,X1))
        | member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_387 ),
    inference(resolution,[],[f4224,f762]) ).

fof(f37256,plain,
    ( spl0_1473
    | ~ spl0_292
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4438,f4223,f2818,f37254]) ).

fof(f37254,plain,
    ( spl0_1473
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).

fof(f4438,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_387 ),
    inference(duplicate_literal_removal,[],[f4410]) ).

fof(f4410,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | null_class = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_387 ),
    inference(resolution,[],[f4224,f2819]) ).

fof(f37252,plain,
    ( spl0_1472
    | ~ spl0_97
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4429,f4223,f731,f37250]) ).

fof(f37250,plain,
    ( spl0_1472
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,intersection(singleton_relation,X1))
        | member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).

fof(f4429,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,intersection(singleton_relation,X1))
        | member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) )
    | ~ spl0_97
    | ~ spl0_387 ),
    inference(resolution,[],[f4224,f732]) ).

fof(f37248,plain,
    ( spl0_1471
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_386 ),
    inference(avatar_split_clause,[],[f4406,f4219,f2310,f761,f37246]) ).

fof(f37246,plain,
    ( spl0_1471
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,singleton_relation))),subset_relation)
        | null_class = intersection(X0,intersection(X1,singleton_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).

fof(f4219,plain,
    ( spl0_386
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f4406,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,singleton_relation))),subset_relation)
        | null_class = intersection(X0,intersection(X1,singleton_relation)) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_386 ),
    inference(forward_demodulation,[],[f4405,f2312]) ).

fof(f4405,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,intersection(X1,singleton_relation))
        | member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_386 ),
    inference(forward_demodulation,[],[f4386,f2312]) ).

fof(f4386,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,intersection(X1,identity_relation))
        | member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_386 ),
    inference(resolution,[],[f4220,f762]) ).

fof(f4220,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X2)
        | null_class = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_386 ),
    inference(avatar_component_clause,[],[f4219]) ).

fof(f37244,plain,
    ( spl0_1470
    | ~ spl0_292
    | ~ spl0_386 ),
    inference(avatar_split_clause,[],[f4397,f4219,f2818,f37242]) ).

fof(f37242,plain,
    ( spl0_1470
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).

fof(f4397,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_292
    | ~ spl0_386 ),
    inference(duplicate_literal_removal,[],[f4369]) ).

fof(f4369,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | null_class = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_292
    | ~ spl0_386 ),
    inference(resolution,[],[f4220,f2819]) ).

fof(f37240,plain,
    ( spl0_1469
    | ~ spl0_97
    | ~ spl0_386 ),
    inference(avatar_split_clause,[],[f4388,f4219,f731,f37238]) ).

fof(f37238,plain,
    ( spl0_1469
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,intersection(X1,singleton_relation))
        | member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).

fof(f4388,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,intersection(X1,singleton_relation))
        | member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) )
    | ~ spl0_97
    | ~ spl0_386 ),
    inference(resolution,[],[f4220,f732]) ).

fof(f37236,plain,
    ( spl0_1468
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4362,f4215,f2310,f393,f37234]) ).

fof(f37234,plain,
    ( spl0_1468
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).

fof(f4215,plain,
    ( spl0_385
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f4362,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(forward_demodulation,[],[f4361,f2312]) ).

fof(f4361,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(forward_demodulation,[],[f4347,f2312]) ).

fof(f4347,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_43
    | ~ spl0_385 ),
    inference(superposition,[],[f4216,f395]) ).

fof(f4216,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X0)
        | null_class = intersection(intersection(X0,X1),X2) )
    | ~ spl0_385 ),
    inference(avatar_component_clause,[],[f4215]) ).

fof(f37232,plain,
    ( spl0_1467
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4360,f4215,f2310,f384,f37230]) ).

fof(f37230,plain,
    ( spl0_1467
  <=> ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).

fof(f4360,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(forward_demodulation,[],[f4346,f2312]) ).

fof(f4346,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_41
    | ~ spl0_385 ),
    inference(superposition,[],[f4216,f386]) ).

fof(f37216,plain,
    ( spl0_1466
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4359,f4215,f2310,f761,f37214]) ).

fof(f37214,plain,
    ( spl0_1466
  <=> ! [X0,X1] :
        ( member(regular(intersection(intersection(singleton_relation,X0),X1)),subset_relation)
        | null_class = intersection(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).

fof(f4359,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(intersection(singleton_relation,X0),X1)),subset_relation)
        | null_class = intersection(intersection(singleton_relation,X0),X1) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(forward_demodulation,[],[f4358,f2312]) ).

fof(f4358,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(singleton_relation,X0),X1)
        | member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_385 ),
    inference(forward_demodulation,[],[f4339,f2312]) ).

fof(f4339,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(identity_relation,X0),X1)
        | member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_385 ),
    inference(resolution,[],[f4216,f762]) ).

fof(f37212,plain,
    ( spl0_1465
    | ~ spl0_292
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4350,f4215,f2818,f37210]) ).

fof(f37210,plain,
    ( spl0_1465
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).

fof(f4350,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_292
    | ~ spl0_385 ),
    inference(duplicate_literal_removal,[],[f4322]) ).

fof(f4322,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | null_class = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_292
    | ~ spl0_385 ),
    inference(resolution,[],[f4216,f2819]) ).

fof(f37208,plain,
    ( spl0_1464
    | ~ spl0_97
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4341,f4215,f731,f37206]) ).

fof(f37206,plain,
    ( spl0_1464
  <=> ! [X0,X1] :
        ( null_class = intersection(intersection(singleton_relation,X0),X1)
        | member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).

fof(f4341,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(singleton_relation,X0),X1)
        | member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) )
    | ~ spl0_97
    | ~ spl0_385 ),
    inference(resolution,[],[f4216,f732]) ).

fof(f37204,plain,
    ( spl0_1463
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f4320,f4211,f2310,f761,f37202]) ).

fof(f37202,plain,
    ( spl0_1463
  <=> ! [X0,X1] :
        ( member(regular(intersection(intersection(X0,singleton_relation),X1)),subset_relation)
        | null_class = intersection(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).

fof(f4211,plain,
    ( spl0_384
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f4320,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(intersection(X0,singleton_relation),X1)),subset_relation)
        | null_class = intersection(intersection(X0,singleton_relation),X1) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_384 ),
    inference(forward_demodulation,[],[f4319,f2312]) ).

fof(f4319,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,singleton_relation),X1)
        | member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_384 ),
    inference(forward_demodulation,[],[f4300,f2312]) ).

fof(f4300,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,identity_relation),X1)
        | member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_384 ),
    inference(resolution,[],[f4212,f762]) ).

fof(f4212,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X1)
        | null_class = intersection(intersection(X0,X1),X2) )
    | ~ spl0_384 ),
    inference(avatar_component_clause,[],[f4211]) ).

fof(f37200,plain,
    ( spl0_1462
    | ~ spl0_292
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f4311,f4211,f2818,f37198]) ).

fof(f37198,plain,
    ( spl0_1462
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).

fof(f4311,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_384 ),
    inference(duplicate_literal_removal,[],[f4283]) ).

fof(f4283,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | null_class = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_384 ),
    inference(resolution,[],[f4212,f2819]) ).

fof(f37196,plain,
    ( spl0_1461
    | ~ spl0_97
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f4302,f4211,f731,f37194]) ).

fof(f37194,plain,
    ( spl0_1461
  <=> ! [X0,X1] :
        ( null_class = intersection(intersection(X0,singleton_relation),X1)
        | member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).

fof(f4302,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,singleton_relation),X1)
        | member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) )
    | ~ spl0_97
    | ~ spl0_384 ),
    inference(resolution,[],[f4212,f732]) ).

fof(f37192,plain,
    ( spl0_1460
    | ~ spl0_25
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4015,f3785,f308,f37190]) ).

fof(f37190,plain,
    ( spl0_1460
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,application_function)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).

fof(f308,plain,
    ( spl0_25
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f3785,plain,
    ( spl0_368
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f4015,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,application_function)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_25
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f310]) ).

fof(f310,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f308]) ).

fof(f3786,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X1,X3)
        | subclass(X0,X2)
        | ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_368 ),
    inference(avatar_component_clause,[],[f3785]) ).

fof(f37188,plain,
    ( spl0_1459
    | ~ spl0_24
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4011,f3785,f303,f37186]) ).

fof(f37186,plain,
    ( spl0_1459
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,composition_function)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).

fof(f303,plain,
    ( spl0_24
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f4011,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,composition_function)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_24
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f305]) ).

fof(f305,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f303]) ).

fof(f37184,plain,
    ( spl0_1458
    | ~ spl0_21
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4006,f3785,f291,f37182]) ).

fof(f37182,plain,
    ( spl0_1458
  <=> ! [X0,X3,X2,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,compose(X2,X3))
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).

fof(f4006,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,compose(X2,X3))
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_21
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f292]) ).

fof(f37180,plain,
    ( spl0_1457
    | ~ spl0_22
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f3993,f3785,f295,f37178]) ).

fof(f37178,plain,
    ( spl0_1457
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,X2)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ function(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).

fof(f295,plain,
    ( spl0_22
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f3993,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,X2)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ function(X2) )
    | ~ spl0_22
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f296]) ).

fof(f296,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f295]) ).

fof(f37176,plain,
    ( spl0_1456
    | ~ spl0_50
    | ~ spl0_1435 ),
    inference(avatar_split_clause,[],[f37130,f37078,f452,f37174]) ).

fof(f37174,plain,
    ( spl0_1456
  <=> ! [X0,X1] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(x,cross_product(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).

fof(f37130,plain,
    ( ! [X0,X1] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(x,cross_product(X0,X1))))
    | ~ spl0_50
    | ~ spl0_1435 ),
    inference(superposition,[],[f37079,f453]) ).

fof(f37172,plain,
    ( spl0_1455
    | ~ spl0_20
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f3937,f3777,f287,f37170]) ).

fof(f37170,plain,
    ( spl0_1455
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = intersection(X2,X0)
        | ~ member(regular(intersection(X2,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).

fof(f287,plain,
    ( spl0_20
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f3777,plain,
    ( spl0_366
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f3937,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = intersection(X2,X0)
        | ~ member(regular(intersection(X2,X0)),X1) )
    | ~ spl0_20
    | ~ spl0_366 ),
    inference(resolution,[],[f3778,f288]) ).

fof(f288,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f287]) ).

fof(f3778,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X1,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f3777]) ).

fof(f37168,plain,
    ( spl0_1454
    | ~ spl0_20
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3870,f3769,f287,f37166]) ).

fof(f37166,plain,
    ( spl0_1454
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = intersection(X0,X2)
        | ~ member(regular(intersection(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).

fof(f3769,plain,
    ( spl0_364
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f3870,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = intersection(X0,X2)
        | ~ member(regular(intersection(X0,X2)),X1) )
    | ~ spl0_20
    | ~ spl0_364 ),
    inference(resolution,[],[f3770,f288]) ).

fof(f3770,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X0,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_364 ),
    inference(avatar_component_clause,[],[f3769]) ).

fof(f37164,plain,
    ( spl0_1453
    | ~ spl0_20
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3717,f3541,f287,f37162]) ).

fof(f37162,plain,
    ( spl0_1453
  <=> ! [X0,X1] :
        ( subclass(X0,complement(complement(X1)))
        | ~ subclass(X0,universal_class)
        | ~ member(not_subclass_element(X0,complement(complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).

fof(f3541,plain,
    ( spl0_355
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f3717,plain,
    ( ! [X0,X1] :
        ( subclass(X0,complement(complement(X1)))
        | ~ subclass(X0,universal_class)
        | ~ member(not_subclass_element(X0,complement(complement(X1))),X1) )
    | ~ spl0_20
    | ~ spl0_355 ),
    inference(resolution,[],[f3542,f288]) ).

fof(f3542,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_355 ),
    inference(avatar_component_clause,[],[f3541]) ).

fof(f37160,plain,
    ( spl0_1452
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3705,f3537,f2310,f393,f37158]) ).

fof(f37158,plain,
    ( spl0_1452
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).

fof(f3537,plain,
    ( spl0_354
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f3705,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_354 ),
    inference(forward_demodulation,[],[f3703,f2312]) ).

fof(f3703,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_354 ),
    inference(superposition,[],[f3538,f395]) ).

fof(f3538,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_354 ),
    inference(avatar_component_clause,[],[f3537]) ).

fof(f37156,plain,
    ( spl0_1451
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3704,f3537,f2310,f384,f37154]) ).

fof(f37154,plain,
    ( spl0_1451
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).

fof(f3704,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,X1) )
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_354 ),
    inference(forward_demodulation,[],[f3702,f2312]) ).

fof(f3702,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_41
    | ~ spl0_354 ),
    inference(superposition,[],[f3538,f386]) ).

fof(f37152,plain,
    ( spl0_1450
    | ~ spl0_34
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3560,f3498,f347,f37150]) ).

fof(f37150,plain,
    ( spl0_1450
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,flip(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).

fof(f347,plain,
    ( spl0_34
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f3498,plain,
    ( spl0_345
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f3560,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,flip(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_34
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f348]) ).

fof(f348,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f3499,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X1,X2)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),X2) )
    | ~ spl0_345 ),
    inference(avatar_component_clause,[],[f3498]) ).

fof(f37148,plain,
    ( spl0_1449
    | ~ spl0_33
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3559,f3498,f343,f37146]) ).

fof(f37146,plain,
    ( spl0_1449
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,rotate(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).

fof(f343,plain,
    ( spl0_33
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f3559,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,rotate(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_33
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f344]) ).

fof(f344,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f37144,plain,
    ( spl0_1448
    | ~ spl0_38
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3446,f3332,f372,f37142]) ).

fof(f37142,plain,
    ( spl0_1448
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(subset_relation,X2)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).

fof(f372,plain,
    ( spl0_38
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f3332,plain,
    ( spl0_335
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f3446,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(subset_relation,X2)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),X2) )
    | ~ spl0_38
    | ~ spl0_335 ),
    inference(resolution,[],[f3333,f373]) ).

fof(f373,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f372]) ).

fof(f3333,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f3332]) ).

fof(f37140,plain,
    ( spl0_1447
    | ~ spl0_38
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3433,f3328,f372,f37138]) ).

fof(f37138,plain,
    ( spl0_1447
  <=> ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(not_subclass_element(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).

fof(f3328,plain,
    ( spl0_334
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f3433,plain,
    ( ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(not_subclass_element(singleton_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_334 ),
    inference(resolution,[],[f3329,f373]) ).

fof(f3329,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f3328]) ).

fof(f37136,plain,
    ( spl0_1446
    | ~ spl0_38
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f3421,f3324,f372,f37134]) ).

fof(f37134,plain,
    ( spl0_1446
  <=> ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | member(not_subclass_element(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).

fof(f3324,plain,
    ( spl0_333
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f3421,plain,
    ( ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | member(not_subclass_element(singleton_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_333 ),
    inference(resolution,[],[f3325,f373]) ).

fof(f3325,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_333 ),
    inference(avatar_component_clause,[],[f3324]) ).

fof(f37121,plain,
    ( spl0_1445
    | ~ spl0_38
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3407,f3310,f372,f37119]) ).

fof(f37119,plain,
    ( spl0_1445
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(subset_relation,X2)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).

fof(f3310,plain,
    ( spl0_332
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f3407,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(subset_relation,X2)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),X2) )
    | ~ spl0_38
    | ~ spl0_332 ),
    inference(resolution,[],[f3311,f373]) ).

fof(f3311,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f3310]) ).

fof(f37117,plain,
    ( spl0_1444
    | ~ spl0_38
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f3340,f3193,f372,f37115]) ).

fof(f37115,plain,
    ( spl0_1444
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(element_relation,X2)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).

fof(f3193,plain,
    ( spl0_324
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f3340,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(element_relation,X2)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),X2) )
    | ~ spl0_38
    | ~ spl0_324 ),
    inference(resolution,[],[f3194,f373]) ).

fof(f3194,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f3193]) ).

fof(f37113,plain,
    ( spl0_1443
    | ~ spl0_38
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f3318,f3172,f372,f37111]) ).

fof(f37111,plain,
    ( spl0_1443
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(element_relation,X2)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).

fof(f3172,plain,
    ( spl0_320
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f3318,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(element_relation,X2)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),X2) )
    | ~ spl0_38
    | ~ spl0_320 ),
    inference(resolution,[],[f3173,f373]) ).

fof(f3173,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_320 ),
    inference(avatar_component_clause,[],[f3172]) ).

fof(f37109,plain,
    ( spl0_1442
    | ~ spl0_164
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3127,f3092,f1365,f37107]) ).

fof(f37107,plain,
    ( spl0_1442
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X1,subset_relation))
        | ~ subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,subset_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).

fof(f3092,plain,
    ( spl0_310
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f3127,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,subset_relation))
        | ~ subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,subset_relation)),X1) )
    | ~ spl0_164
    | ~ spl0_310 ),
    inference(duplicate_literal_removal,[],[f3123]) ).

fof(f3123,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,subset_relation))
        | ~ subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,subset_relation)),X1)
        | subclass(X0,intersection(X1,subset_relation)) )
    | ~ spl0_164
    | ~ spl0_310 ),
    inference(resolution,[],[f3093,f1366]) ).

fof(f3093,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f3092]) ).

fof(f37105,plain,
    ( spl0_1441
    | ~ spl0_164
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f3101,f2940,f1365,f37103]) ).

fof(f37103,plain,
    ( spl0_1441
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X1,element_relation))
        | ~ subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,element_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).

fof(f2940,plain,
    ( spl0_302
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f3101,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,element_relation))
        | ~ subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,element_relation)),X1) )
    | ~ spl0_164
    | ~ spl0_302 ),
    inference(duplicate_literal_removal,[],[f3097]) ).

fof(f3097,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,element_relation))
        | ~ subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,element_relation)),X1)
        | subclass(X0,intersection(X1,element_relation)) )
    | ~ spl0_164
    | ~ spl0_302 ),
    inference(resolution,[],[f2941,f1366]) ).

fof(f2941,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),element_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302 ),
    inference(avatar_component_clause,[],[f2940]) ).

fof(f37101,plain,
    ( spl0_1440
    | ~ spl0_124
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3050,f2818,f2310,f955,f37099]) ).

fof(f37099,plain,
    ( spl0_1440
  <=> ! [X0] :
        ( ~ subclass(X0,complement(complement(compose(element_relation,complement(singleton_relation)))))
        | null_class = X0
        | ~ member(regular(X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).

fof(f3050,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(complement(compose(element_relation,complement(singleton_relation)))))
        | null_class = X0
        | ~ member(regular(X0),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f2977,f2312]) ).

fof(f2977,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(regular(X0),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f956]) ).

fof(f37097,plain,
    ( spl0_1439
    | ~ spl0_125
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3049,f2818,f2310,f959,f37095]) ).

fof(f37095,plain,
    ( spl0_1439
  <=> ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).

fof(f959,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f3049,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) )
    | ~ spl0_125
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f2979,f2312]) ).

fof(f2979,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(regular(X0),identity_relation) )
    | ~ spl0_125
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f960]) ).

fof(f960,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f959]) ).

fof(f37093,plain,
    ( spl0_1438
    | ~ spl0_198
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2585,f2499,f1711,f37091]) ).

fof(f37091,plain,
    ( spl0_1438
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,complement(X2))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).

fof(f1711,plain,
    ( spl0_198
  <=> ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f2585,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,complement(X2))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_268 ),
    inference(superposition,[],[f2500,f1712]) ).

fof(f1712,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198 ),
    inference(avatar_component_clause,[],[f1711]) ).

fof(f37089,plain,
    ( spl0_1437
    | ~ spl0_44
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2573,f2499,f424,f37087]) ).

fof(f37087,plain,
    ( spl0_1437
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(complement(X0)))
        | member(unordered_pair(X1,X2),X0)
        | ~ member(unordered_pair(X1,X2),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).

fof(f2573,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(complement(X0)))
        | member(unordered_pair(X1,X2),X0)
        | ~ member(unordered_pair(X1,X2),universal_class) )
    | ~ spl0_44
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f425]) ).

fof(f37085,plain,
    ( spl0_1436
    | ~ spl0_76
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2249,f2227,f608,f37082]) ).

fof(f37082,plain,
    ( spl0_1436
  <=> subclass(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_1436])]) ).

fof(f608,plain,
    ( spl0_76
  <=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f2227,plain,
    ( spl0_224
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f2249,plain,
    ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_76
    | ~ spl0_224 ),
    inference(superposition,[],[f2228,f610]) ).

fof(f610,plain,
    ( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f608]) ).

fof(f2228,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f2227]) ).

fof(f37080,plain,
    ( spl0_1435
    | ~ spl0_145
    | ~ spl0_1423 ),
    inference(avatar_split_clause,[],[f36356,f34483,f1171,f37078]) ).

fof(f34483,plain,
    ( spl0_1423
  <=> ! [X0] : null_class = intersection(intersection(X0,x),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).

fof(f36356,plain,
    ( ! [X0] : ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(X0,x)))
    | ~ spl0_145
    | ~ spl0_1423 ),
    inference(trivial_inequality_removal,[],[f36191]) ).

fof(f36191,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(intersection(X0,x))) )
    | ~ spl0_145
    | ~ spl0_1423 ),
    inference(superposition,[],[f1172,f34484]) ).

fof(f34484,plain,
    ( ! [X0] : null_class = intersection(intersection(X0,x),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ spl0_1423 ),
    inference(avatar_component_clause,[],[f34483]) ).

fof(f35815,plain,
    ( spl0_1434
    | ~ spl0_836
    | ~ spl0_1325 ),
    inference(avatar_split_clause,[],[f34419,f30292,f15771,f35813]) ).

fof(f35813,plain,
    ( spl0_1434
  <=> ! [X0] : null_class = intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(x,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).

fof(f15771,plain,
    ( spl0_836
  <=> ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f30292,plain,
    ( spl0_1325
  <=> ! [X0] : subclass(intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(x,X0)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).

fof(f34419,plain,
    ( ! [X0] : null_class = intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(x,X0))
    | ~ spl0_836
    | ~ spl0_1325 ),
    inference(resolution,[],[f30293,f15772]) ).

fof(f15772,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 )
    | ~ spl0_836 ),
    inference(avatar_component_clause,[],[f15771]) ).

fof(f30293,plain,
    ( ! [X0] : subclass(intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(x,X0)),null_class)
    | ~ spl0_1325 ),
    inference(avatar_component_clause,[],[f30292]) ).

fof(f35160,plain,
    ( spl0_1433
    | ~ spl0_836
    | ~ spl0_1320 ),
    inference(avatar_split_clause,[],[f31579,f30138,f15771,f35158]) ).

fof(f35158,plain,
    ( spl0_1433
  <=> ! [X0] : null_class = intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(X0,x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).

fof(f30138,plain,
    ( spl0_1320
  <=> ! [X0] : subclass(intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(X0,x)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).

fof(f31579,plain,
    ( ! [X0] : null_class = intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(X0,x))
    | ~ spl0_836
    | ~ spl0_1320 ),
    inference(resolution,[],[f30139,f15772]) ).

fof(f30139,plain,
    ( ! [X0] : subclass(intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(X0,x)),null_class)
    | ~ spl0_1320 ),
    inference(avatar_component_clause,[],[f30138]) ).

fof(f34525,plain,
    ( ~ spl0_1431
    | spl0_1432
    | ~ spl0_268
    | ~ spl0_900 ),
    inference(avatar_split_clause,[],[f17242,f17234,f2499,f34523,f34519]) ).

fof(f34519,plain,
    ( spl0_1431
  <=> subclass(universal_class,complement(application_function)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).

fof(f34523,plain,
    ( spl0_1432
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ member(X0,domain_of(X1))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).

fof(f17234,plain,
    ( spl0_900
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f17242,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ member(X1,universal_class)
        | ~ member(X0,domain_of(X1))
        | ~ subclass(universal_class,complement(application_function)) )
    | ~ spl0_268
    | ~ spl0_900 ),
    inference(resolution,[],[f17235,f2500]) ).

fof(f17235,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(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)) )
    | ~ spl0_900 ),
    inference(avatar_component_clause,[],[f17234]) ).

fof(f34517,plain,
    ( spl0_1430
    | ~ spl0_836
    | ~ spl0_1309 ),
    inference(avatar_split_clause,[],[f31140,f30089,f15771,f34515]) ).

fof(f30089,plain,
    ( spl0_1309
  <=> ! [X0] : subclass(intersection(intersection(x,X0),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).

fof(f31140,plain,
    ( ! [X0] : null_class = intersection(intersection(x,X0),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ spl0_836
    | ~ spl0_1309 ),
    inference(resolution,[],[f30090,f15772]) ).

fof(f30090,plain,
    ( ! [X0] : subclass(intersection(intersection(x,X0),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)),null_class)
    | ~ spl0_1309 ),
    inference(avatar_component_clause,[],[f30089]) ).

fof(f34513,plain,
    ( spl0_1429
    | ~ spl0_9
    | ~ spl0_733 ),
    inference(avatar_split_clause,[],[f12647,f12589,f240,f34511]) ).

fof(f34511,plain,
    ( spl0_1429
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)),universal_class)
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).

fof(f12589,plain,
    ( spl0_733
  <=> ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f12647,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)),universal_class)
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_9
    | ~ spl0_733 ),
    inference(superposition,[],[f241,f12590]) ).

fof(f12590,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_733 ),
    inference(avatar_component_clause,[],[f12589]) ).

fof(f34509,plain,
    ( spl0_1428
    | ~ spl0_61
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9587,f9579,f524,f34507]) ).

fof(f34507,plain,
    ( spl0_1428
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(first(unordered_pair(X0,X1)),second(unordered_pair(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).

fof(f9587,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(first(unordered_pair(X0,X1)),second(unordered_pair(X0,X1))) )
    | ~ spl0_61
    | ~ spl0_630 ),
    inference(superposition,[],[f525,f9580]) ).

fof(f34505,plain,
    ( spl0_527
    | ~ spl0_1427
    | ~ spl0_235
    | ~ spl0_283
    | spl0_529 ),
    inference(avatar_split_clause,[],[f7429,f7422,f2723,f2310,f34502,f7414]) ).

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

fof(f34502,plain,
    ( spl0_1427
  <=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).

fof(f2723,plain,
    ( spl0_283
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f7422,plain,
    ( spl0_529
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f7429,plain,
    ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_235
    | ~ spl0_283
    | spl0_529 ),
    inference(forward_demodulation,[],[f7427,f2312]) ).

fof(f7427,plain,
    ( null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation)
    | ~ spl0_283
    | spl0_529 ),
    inference(resolution,[],[f7424,f2724]) ).

fof(f2724,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | null_class = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_283 ),
    inference(avatar_component_clause,[],[f2723]) ).

fof(f7424,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
    | spl0_529 ),
    inference(avatar_component_clause,[],[f7422]) ).

fof(f34500,plain,
    ( spl0_527
    | ~ spl0_1426
    | ~ spl0_116
    | spl0_529 ),
    inference(avatar_split_clause,[],[f7428,f7422,f919,f34497,f7414]) ).

fof(f34497,plain,
    ( spl0_1426
  <=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).

fof(f919,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f7428,plain,
    ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_116
    | spl0_529 ),
    inference(resolution,[],[f7424,f920]) ).

fof(f920,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f919]) ).

fof(f34495,plain,
    ( spl0_524
    | ~ spl0_1425
    | ~ spl0_116
    | spl0_525 ),
    inference(avatar_split_clause,[],[f7411,f7393,f919,f34492,f7388]) ).

fof(f7388,plain,
    ( spl0_524
  <=> null_class = complement(compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f34492,plain,
    ( spl0_1425
  <=> subclass(complement(compose(element_relation,complement(singleton_relation))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).

fof(f7393,plain,
    ( spl0_525
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f7411,plain,
    ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),element_relation)
    | null_class = complement(compose(element_relation,complement(singleton_relation)))
    | ~ spl0_116
    | spl0_525 ),
    inference(resolution,[],[f7395,f920]) ).

fof(f7395,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
    | spl0_525 ),
    inference(avatar_component_clause,[],[f7393]) ).

fof(f34490,plain,
    ( ~ spl0_1424
    | spl0_524
    | ~ spl0_285
    | spl0_525 ),
    inference(avatar_split_clause,[],[f7410,f7393,f2731,f7388,f34487]) ).

fof(f34487,plain,
    ( spl0_1424
  <=> subclass(complement(compose(element_relation,complement(singleton_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).

fof(f2731,plain,
    ( spl0_285
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f7410,plain,
    ( null_class = complement(compose(element_relation,complement(singleton_relation)))
    | ~ subclass(complement(compose(element_relation,complement(singleton_relation))),singleton_relation)
    | ~ spl0_285
    | spl0_525 ),
    inference(resolution,[],[f7395,f2732]) ).

fof(f2732,plain,
    ( ! [X0] :
        ( member(regular(X0),element_relation)
        | null_class = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_285 ),
    inference(avatar_component_clause,[],[f2731]) ).

fof(f34485,plain,
    ( spl0_1423
    | ~ spl0_836
    | ~ spl0_1186 ),
    inference(avatar_split_clause,[],[f30718,f26041,f15771,f34483]) ).

fof(f26041,plain,
    ( spl0_1186
  <=> ! [X0] : subclass(intersection(intersection(X0,x),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f30718,plain,
    ( ! [X0] : null_class = intersection(intersection(X0,x),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ spl0_836
    | ~ spl0_1186 ),
    inference(resolution,[],[f26042,f15772]) ).

fof(f26042,plain,
    ( ! [X0] : subclass(intersection(intersection(X0,x),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)),null_class)
    | ~ spl0_1186 ),
    inference(avatar_component_clause,[],[f26041]) ).

fof(f34473,plain,
    ( spl0_652
    | spl0_1422
    | ~ spl0_77
    | ~ spl0_504 ),
    inference(avatar_split_clause,[],[f6919,f6832,f613,f34471,f9912]) ).

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

fof(f34471,plain,
    ( spl0_1422
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).

fof(f6832,plain,
    ( spl0_504
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f6919,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | member(X2,X0)
        | ~ member(X3,universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_77
    | ~ spl0_504 ),
    inference(resolution,[],[f6833,f614]) ).

fof(f6833,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_504 ),
    inference(avatar_component_clause,[],[f6832]) ).

fof(f34469,plain,
    ( spl0_1421
    | ~ spl0_4
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f6339,f6212,f219,f34467]) ).

fof(f34467,plain,
    ( spl0_1421
  <=> ! [X0,X1] :
        ( member(X0,universal_class)
        | null_class = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).

fof(f219,plain,
    ( spl0_4
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f6212,plain,
    ( spl0_473
  <=> ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f6339,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | null_class = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 )
    | ~ spl0_4
    | ~ spl0_473 ),
    inference(resolution,[],[f6213,f220]) ).

fof(f220,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f6213,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_473 ),
    inference(avatar_component_clause,[],[f6212]) ).

fof(f34465,plain,
    ( spl0_1420
    | ~ spl0_4
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f6334,f6208,f219,f34463]) ).

fof(f34463,plain,
    ( spl0_1420
  <=> ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).

fof(f6208,plain,
    ( spl0_472
  <=> ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f6334,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_4
    | ~ spl0_472 ),
    inference(resolution,[],[f6209,f220]) ).

fof(f6209,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_472 ),
    inference(avatar_component_clause,[],[f6208]) ).

fof(f34461,plain,
    ( spl0_274
    | spl0_1418
    | ~ spl0_1419
    | spl0_231
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f6014,f5892,f2310,f2304,f2282,f34458,f34453,f2535]) ).

fof(f2535,plain,
    ( spl0_274
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f34453,plain,
    ( spl0_1418
  <=> member(regular(singleton_relation),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).

fof(f34458,plain,
    ( spl0_1419
  <=> subclass(singleton_relation,regular(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).

fof(f2282,plain,
    ( spl0_231
  <=> null_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2304,plain,
    ( spl0_234
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f5892,plain,
    ( spl0_455
  <=> ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f6014,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,regular(subset_relation))
    | member(regular(singleton_relation),null_class)
    | null_class = subset_relation
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_455 ),
    inference(forward_demodulation,[],[f6013,f2312]) ).

fof(f6013,plain,
    ( ~ subclass(singleton_relation,regular(subset_relation))
    | member(regular(singleton_relation),null_class)
    | null_class = subset_relation
    | null_class = identity_relation
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_455 ),
    inference(forward_demodulation,[],[f6012,f2312]) ).

fof(f6012,plain,
    ( member(regular(singleton_relation),null_class)
    | null_class = subset_relation
    | ~ subclass(identity_relation,regular(subset_relation))
    | null_class = identity_relation
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_455 ),
    inference(forward_demodulation,[],[f5977,f2312]) ).

fof(f5977,plain,
    ( member(regular(identity_relation),null_class)
    | null_class = subset_relation
    | ~ subclass(identity_relation,regular(subset_relation))
    | null_class = identity_relation
    | ~ spl0_234
    | ~ spl0_455 ),
    inference(resolution,[],[f5893,f2306]) ).

fof(f2306,plain,
    ( member(regular(identity_relation),subset_relation)
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2304]) ).

fof(f5893,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | member(regular(X0),null_class)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_455 ),
    inference(avatar_component_clause,[],[f5892]) ).

fof(f34456,plain,
    ( spl0_231
    | ~ spl0_1416
    | spl0_1417
    | spl0_1418
    | ~ spl0_232
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f5959,f5892,f2286,f34453,f34449,f34445,f2282]) ).

fof(f34445,plain,
    ( spl0_1416
  <=> subclass(singleton_relation,regular(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).

fof(f34449,plain,
    ( spl0_1417
  <=> element_relation = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).

fof(f2286,plain,
    ( spl0_232
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f5959,plain,
    ( member(regular(singleton_relation),null_class)
    | element_relation = null_class
    | ~ subclass(singleton_relation,regular(element_relation))
    | null_class = singleton_relation
    | ~ spl0_232
    | ~ spl0_455 ),
    inference(resolution,[],[f5893,f2288]) ).

fof(f2288,plain,
    ( member(regular(singleton_relation),element_relation)
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2286]) ).

fof(f34443,plain,
    ( spl0_1415
    | ~ spl0_5
    | ~ spl0_441 ),
    inference(avatar_split_clause,[],[f5649,f5540,f223,f34441]) ).

fof(f34441,plain,
    ( spl0_1415
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,omega))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).

fof(f223,plain,
    ( spl0_5
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f5540,plain,
    ( spl0_441
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f5649,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,omega))),X1) )
    | ~ spl0_5
    | ~ spl0_441 ),
    inference(resolution,[],[f5541,f225]) ).

fof(f225,plain,
    ( member(omega,universal_class)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f5541,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,universal_class)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
    | ~ spl0_441 ),
    inference(avatar_component_clause,[],[f5540]) ).

fof(f34396,plain,
    ( spl0_1414
    | ~ spl0_879
    | ~ spl0_915
    | ~ spl0_1326
    | ~ spl0_1413 ),
    inference(avatar_split_clause,[],[f34392,f34387,f32105,f17701,f16601,f34394]) ).

fof(f34394,plain,
    ( spl0_1414
  <=> ! [X0,X1] :
        ( member(null_class,X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).

fof(f16601,plain,
    ( spl0_879
  <=> ! [X0] : null_class = intersection(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f32105,plain,
    ( spl0_1326
  <=> ! [X0] : null_class = cross_product(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).

fof(f34387,plain,
    ( spl0_1413
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,null_class))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).

fof(f34392,plain,
    ( ! [X0,X1] :
        ( member(null_class,X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_879
    | ~ spl0_915
    | ~ spl0_1326
    | ~ spl0_1413 ),
    inference(forward_demodulation,[],[f34391,f17703]) ).

fof(f34391,plain,
    ( ! [X0,X1] :
        ( member(domain_of(null_class),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_879
    | ~ spl0_1326
    | ~ spl0_1413 ),
    inference(forward_demodulation,[],[f34390,f16602]) ).

fof(f16602,plain,
    ( ! [X0] : null_class = intersection(X0,null_class)
    | ~ spl0_879 ),
    inference(avatar_component_clause,[],[f16601]) ).

fof(f34390,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,null_class)),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_1326
    | ~ spl0_1413 ),
    inference(forward_demodulation,[],[f34388,f32106]) ).

fof(f32106,plain,
    ( ! [X0] : null_class = cross_product(X0,null_class)
    | ~ spl0_1326 ),
    inference(avatar_component_clause,[],[f32105]) ).

fof(f34388,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,null_class))),X1) )
    | ~ spl0_1413 ),
    inference(avatar_component_clause,[],[f34387]) ).

fof(f34389,plain,
    ( spl0_1413
    | ~ spl0_80
    | ~ spl0_441 ),
    inference(avatar_split_clause,[],[f5645,f5540,f636,f34387]) ).

fof(f636,plain,
    ( spl0_80
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f5645,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,null_class))),X1) )
    | ~ spl0_80
    | ~ spl0_441 ),
    inference(resolution,[],[f5541,f637]) ).

fof(f637,plain,
    ( member(null_class,universal_class)
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f636]) ).

fof(f34385,plain,
    ( spl0_1412
    | ~ spl0_76
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5064,f4790,f608,f34383]) ).

fof(f34383,plain,
    ( spl0_1412
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,subset_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).

fof(f5064,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,subset_relation),X1) )
    | ~ spl0_76
    | ~ spl0_407 ),
    inference(superposition,[],[f4791,f610]) ).

fof(f34381,plain,
    ( spl0_1411
    | ~ spl0_76
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4947,f4782,f608,f34379]) ).

fof(f34379,plain,
    ( spl0_1411
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(subset_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).

fof(f4947,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(subset_relation,X0),X1) )
    | ~ spl0_76
    | ~ spl0_405 ),
    inference(superposition,[],[f4783,f610]) ).

fof(f34376,plain,
    ( spl0_1410
    | ~ spl0_316
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4634,f4239,f3149,f34374]) ).

fof(f34374,plain,
    ( spl0_1410
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X2
        | ~ subclass(intersection(X0,null_class),complement(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).

fof(f4634,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X2
        | ~ subclass(intersection(X0,null_class),complement(X2)) )
    | ~ spl0_316
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4598]) ).

fof(f4598,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X2
        | subclass(intersection(X0,null_class),X1)
        | ~ subclass(intersection(X0,null_class),complement(X2)) )
    | ~ spl0_316
    | ~ spl0_391 ),
    inference(resolution,[],[f4240,f3150]) ).

fof(f34372,plain,
    ( spl0_1409
    | ~ spl0_316
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4591,f4235,f3149,f34370]) ).

fof(f34370,plain,
    ( spl0_1409
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X3)
        | ~ subclass(intersection(X2,X0),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).

fof(f4591,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X3)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4548]) ).

fof(f4548,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X3)
        | subclass(intersection(X2,X0),X3)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f3150]) ).

fof(f34367,plain,
    ( spl0_1408
    | ~ spl0_316
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f4541,f4231,f3149,f34365]) ).

fof(f34365,plain,
    ( spl0_1408
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X2
        | ~ subclass(intersection(null_class,X0),complement(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).

fof(f4541,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X2
        | ~ subclass(intersection(null_class,X0),complement(X2)) )
    | ~ spl0_316
    | ~ spl0_389 ),
    inference(duplicate_literal_removal,[],[f4505]) ).

fof(f4505,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X2
        | subclass(intersection(null_class,X0),X1)
        | ~ subclass(intersection(null_class,X0),complement(X2)) )
    | ~ spl0_316
    | ~ spl0_389 ),
    inference(resolution,[],[f4232,f3150]) ).

fof(f34363,plain,
    ( spl0_1407
    | ~ spl0_316
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4495,f4227,f3149,f34361]) ).

fof(f34361,plain,
    ( spl0_1407
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X3)
        | ~ subclass(intersection(X0,X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).

fof(f4495,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X3)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4452]) ).

fof(f4452,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X3)
        | subclass(intersection(X0,X2),X3)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_316
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f3150]) ).

fof(f34359,plain,
    ( spl0_1406
    | ~ spl0_292
    | ~ spl0_380 ),
    inference(avatar_split_clause,[],[f4193,f3834,f2818,f34357]) ).

fof(f34357,plain,
    ( spl0_1406
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | null_class = cross_product(X1,X2)
        | ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).

fof(f3834,plain,
    ( spl0_380
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f4193,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | null_class = cross_product(X1,X2)
        | ~ subclass(cross_product(X1,X2),complement(X0)) )
    | ~ spl0_292
    | ~ spl0_380 ),
    inference(duplicate_literal_removal,[],[f4172]) ).

fof(f4172,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | null_class = cross_product(X1,X2)
        | null_class = cross_product(X1,X2)
        | ~ subclass(cross_product(X1,X2),complement(X0)) )
    | ~ spl0_292
    | ~ spl0_380 ),
    inference(resolution,[],[f3835,f2819]) ).

fof(f3835,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_380 ),
    inference(avatar_component_clause,[],[f3834]) ).

fof(f34355,plain,
    ( spl0_1405
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f4150,f3818,f2310,f761,f34353]) ).

fof(f34353,plain,
    ( spl0_1405
  <=> ! [X0] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(singleton_relation)),subset_relation)
        | subclass(intersection(universal_class,X0),complement(singleton_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).

fof(f3818,plain,
    ( spl0_376
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f4150,plain,
    ( ! [X0] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(singleton_relation)),subset_relation)
        | subclass(intersection(universal_class,X0),complement(singleton_relation)) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_376 ),
    inference(forward_demodulation,[],[f4149,f2312]) ).

fof(f4149,plain,
    ( ! [X0] :
        ( subclass(intersection(universal_class,X0),complement(singleton_relation))
        | member(not_subclass_element(intersection(universal_class,X0),complement(identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_376 ),
    inference(forward_demodulation,[],[f4137,f2312]) ).

fof(f4137,plain,
    ( ! [X0] :
        ( subclass(intersection(universal_class,X0),complement(identity_relation))
        | member(not_subclass_element(intersection(universal_class,X0),complement(identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_376 ),
    inference(resolution,[],[f3819,f762]) ).

fof(f3819,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_376 ),
    inference(avatar_component_clause,[],[f3818]) ).

fof(f34351,plain,
    ( spl0_1404
    | ~ spl0_97
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f4139,f3818,f731,f34349]) ).

fof(f34349,plain,
    ( spl0_1404
  <=> ! [X0] :
        ( subclass(intersection(universal_class,X0),complement(singleton_relation))
        | member(not_subclass_element(intersection(universal_class,X0),complement(singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).

fof(f4139,plain,
    ( ! [X0] :
        ( subclass(intersection(universal_class,X0),complement(singleton_relation))
        | member(not_subclass_element(intersection(universal_class,X0),complement(singleton_relation)),element_relation) )
    | ~ spl0_97
    | ~ spl0_376 ),
    inference(resolution,[],[f3819,f732]) ).

fof(f34347,plain,
    ( spl0_1403
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_375 ),
    inference(avatar_split_clause,[],[f4117,f3814,f2310,f761,f34345]) ).

fof(f34345,plain,
    ( spl0_1403
  <=> ! [X0] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(singleton_relation)),subset_relation)
        | subclass(intersection(X0,universal_class),complement(singleton_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).

fof(f3814,plain,
    ( spl0_375
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f4117,plain,
    ( ! [X0] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(singleton_relation)),subset_relation)
        | subclass(intersection(X0,universal_class),complement(singleton_relation)) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_375 ),
    inference(forward_demodulation,[],[f4116,f2312]) ).

fof(f4116,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,universal_class),complement(singleton_relation))
        | member(not_subclass_element(intersection(X0,universal_class),complement(identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_375 ),
    inference(forward_demodulation,[],[f4104,f2312]) ).

fof(f4104,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,universal_class),complement(identity_relation))
        | member(not_subclass_element(intersection(X0,universal_class),complement(identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_375 ),
    inference(resolution,[],[f3815,f762]) ).

fof(f3815,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f3814]) ).

fof(f34343,plain,
    ( spl0_1402
    | ~ spl0_97
    | ~ spl0_375 ),
    inference(avatar_split_clause,[],[f4106,f3814,f731,f34341]) ).

fof(f34341,plain,
    ( spl0_1402
  <=> ! [X0] :
        ( subclass(intersection(X0,universal_class),complement(singleton_relation))
        | member(not_subclass_element(intersection(X0,universal_class),complement(singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).

fof(f4106,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,universal_class),complement(singleton_relation))
        | member(not_subclass_element(intersection(X0,universal_class),complement(singleton_relation)),element_relation) )
    | ~ spl0_97
    | ~ spl0_375 ),
    inference(resolution,[],[f3815,f732]) ).

fof(f34339,plain,
    ( spl0_1401
    | ~ spl0_18
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4010,f3785,f279,f34337]) ).

fof(f34337,plain,
    ( spl0_1401
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,compose_class(X2))
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).

fof(f279,plain,
    ( spl0_18
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f4010,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,compose_class(X2))
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_18
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f280]) ).

fof(f280,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f279]) ).

fof(f34335,plain,
    ( spl0_1400
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f3961,f3777,f2310,f761,f34333]) ).

fof(f34333,plain,
    ( spl0_1400
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).

fof(f3961,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_366 ),
    inference(forward_demodulation,[],[f3946,f2312]) ).

fof(f3946,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | null_class = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_366 ),
    inference(resolution,[],[f3778,f762]) ).

fof(f34331,plain,
    ( spl0_1399
    | ~ spl0_292
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f3955,f3777,f2818,f34329]) ).

fof(f34329,plain,
    ( spl0_1399
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X2,X0)
        | ~ subclass(intersection(X2,X0),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).

fof(f3955,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X2,X0)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_366 ),
    inference(duplicate_literal_removal,[],[f3928]) ).

fof(f3928,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X2,X0)
        | null_class = intersection(X2,X0)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_366 ),
    inference(resolution,[],[f3778,f2819]) ).

fof(f34327,plain,
    ( spl0_1398
    | ~ spl0_97
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f3948,f3777,f731,f34325]) ).

fof(f34325,plain,
    ( spl0_1398
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).

fof(f3948,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),element_relation) )
    | ~ spl0_97
    | ~ spl0_366 ),
    inference(resolution,[],[f3778,f732]) ).

fof(f34323,plain,
    ( spl0_1397
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3894,f3769,f2310,f761,f34321]) ).

fof(f34321,plain,
    ( spl0_1397
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = null_class
        | member(regular(intersection(X0,X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).

fof(f3894,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = null_class
        | member(regular(intersection(X0,X1)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_364 ),
    inference(forward_demodulation,[],[f3879,f2312]) ).

fof(f3879,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | intersection(X0,X1) = null_class
        | member(regular(intersection(X0,X1)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_364 ),
    inference(resolution,[],[f3770,f762]) ).

fof(f34319,plain,
    ( spl0_1396
    | ~ spl0_292
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3888,f3769,f2818,f34317]) ).

fof(f34317,plain,
    ( spl0_1396
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,X2)
        | ~ subclass(intersection(X0,X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).

fof(f3888,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,X2)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_364 ),
    inference(duplicate_literal_removal,[],[f3861]) ).

fof(f3861,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,X2)
        | null_class = intersection(X0,X2)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_292
    | ~ spl0_364 ),
    inference(resolution,[],[f3770,f2819]) ).

fof(f34315,plain,
    ( ~ spl0_1395
    | ~ spl0_37
    | spl0_1393 ),
    inference(avatar_split_clause,[],[f34306,f34302,f359,f34312]) ).

fof(f34312,plain,
    ( spl0_1395
  <=> one_to_one(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).

fof(f359,plain,
    ( spl0_37
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f34302,plain,
    ( spl0_1393
  <=> function(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).

fof(f34306,plain,
    ( ~ one_to_one(subset_relation)
    | ~ spl0_37
    | spl0_1393 ),
    inference(resolution,[],[f34304,f360]) ).

fof(f360,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f359]) ).

fof(f34304,plain,
    ( ~ function(domain_of(flip(cross_product(subset_relation,universal_class))))
    | spl0_1393 ),
    inference(avatar_component_clause,[],[f34302]) ).

fof(f34310,plain,
    ( spl0_1394
    | ~ spl0_97
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3881,f3769,f731,f34308]) ).

fof(f34308,plain,
    ( spl0_1394
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = null_class
        | member(regular(intersection(X0,X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).

fof(f3881,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = null_class
        | member(regular(intersection(X0,X1)),element_relation) )
    | ~ spl0_97
    | ~ spl0_364 ),
    inference(resolution,[],[f3770,f732]) ).

fof(f34305,plain,
    ( ~ spl0_1393
    | spl0_1392
    | ~ spl0_22
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f3743,f3614,f295,f34298,f34302]) ).

fof(f34298,plain,
    ( spl0_1392
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).

fof(f3614,plain,
    ( spl0_358
  <=> ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f3743,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_22
    | ~ spl0_358 ),
    inference(resolution,[],[f3615,f296]) ).

fof(f3615,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_358 ),
    inference(avatar_component_clause,[],[f3614]) ).

fof(f34300,plain,
    ( ~ spl0_1391
    | spl0_1392
    | ~ spl0_22
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f3740,f3595,f295,f34298,f34294]) ).

fof(f34294,plain,
    ( spl0_1391
  <=> function(complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).

fof(f3595,plain,
    ( spl0_357
  <=> ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f3740,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_22
    | ~ spl0_357 ),
    inference(resolution,[],[f3596,f296]) ).

fof(f3596,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f3595]) ).

fof(f34292,plain,
    ( spl0_1390
    | ~ spl0_25
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3572,f3498,f308,f34290]) ).

fof(f34290,plain,
    ( spl0_1390
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).

fof(f3572,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_25
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f310]) ).

fof(f34288,plain,
    ( spl0_1389
    | ~ spl0_24
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3568,f3498,f303,f34286]) ).

fof(f34286,plain,
    ( spl0_1389
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,composition_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).

fof(f3568,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,composition_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_24
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f305]) ).

fof(f34284,plain,
    ( spl0_1388
    | ~ spl0_21
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3563,f3498,f291,f34282]) ).

fof(f34282,plain,
    ( spl0_1388
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,compose(X1,X2))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).

fof(f3563,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,compose(X1,X2))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_21
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f292]) ).

fof(f34280,plain,
    ( spl0_1387
    | ~ spl0_22
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3550,f3498,f295,f34278]) ).

fof(f34278,plain,
    ( spl0_1387
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).

fof(f3550,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) )
    | ~ spl0_22
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f296]) ).

fof(f34276,plain,
    ( spl0_1386
    | ~ spl0_111
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3276,f3149,f823,f34274]) ).

fof(f34274,plain,
    ( spl0_1386
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).

fof(f823,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f3276,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_111
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f824]) ).

fof(f824,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f823]) ).

fof(f34272,plain,
    ( spl0_1385
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3267,f3145,f2310,f393,f34270]) ).

fof(f34270,plain,
    ( spl0_1385
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).

fof(f3145,plain,
    ( spl0_315
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f3267,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_315 ),
    inference(forward_demodulation,[],[f3265,f2312]) ).

fof(f3265,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_315 ),
    inference(superposition,[],[f3146,f395]) ).

fof(f3146,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3145]) ).

fof(f34268,plain,
    ( spl0_1384
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3266,f3145,f2310,f384,f34266]) ).

fof(f34266,plain,
    ( spl0_1384
  <=> ! [X0] :
        ( member(regular(X0),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).

fof(f3266,plain,
    ( ! [X0] :
        ( member(regular(X0),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | null_class = X0 )
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_315 ),
    inference(forward_demodulation,[],[f3264,f2312]) ).

fof(f3264,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_41
    | ~ spl0_315 ),
    inference(superposition,[],[f3146,f386]) ).

fof(f34264,plain,
    ( spl0_1383
    | ~ spl0_38
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f3133,f3118,f372,f34262]) ).

fof(f34262,plain,
    ( spl0_1383
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(X0,singleton_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).

fof(f3118,plain,
    ( spl0_312
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f3133,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(X0,singleton_relation)),X1) )
    | ~ spl0_38
    | ~ spl0_312 ),
    inference(resolution,[],[f3119,f373]) ).

fof(f3119,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f3118]) ).

fof(f34260,plain,
    ( spl0_1382
    | ~ spl0_38
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3126,f3092,f372,f34258]) ).

fof(f3126,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(subset_relation,X2)
        | member(not_subclass_element(X0,X1),X2) )
    | ~ spl0_38
    | ~ spl0_310 ),
    inference(resolution,[],[f3093,f373]) ).

fof(f34256,plain,
    ( spl0_1381
    | ~ spl0_38
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f3100,f2940,f372,f34254]) ).

fof(f34254,plain,
    ( spl0_1381
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(element_relation,X2)
        | member(not_subclass_element(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).

fof(f3100,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(element_relation,X2)
        | member(not_subclass_element(X0,X1),X2) )
    | ~ spl0_38
    | ~ spl0_302 ),
    inference(resolution,[],[f2941,f373]) ).

fof(f34252,plain,
    ( spl0_1380
    | ~ spl0_38
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f3088,f2930,f372,f34250]) ).

fof(f34250,plain,
    ( spl0_1380
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(X0,singleton_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).

fof(f2930,plain,
    ( spl0_300
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f3088,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(X0,singleton_relation)),X1) )
    | ~ spl0_38
    | ~ spl0_300 ),
    inference(resolution,[],[f2931,f373]) ).

fof(f2931,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f2930]) ).

fof(f34248,plain,
    ( spl0_1379
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f3045,f2822,f2310,f372,f34246]) ).

fof(f34246,plain,
    ( spl0_1379
  <=> ! [X0,X1] :
        ( member(regular(intersection(singleton_relation,X0)),X1)
        | null_class = intersection(singleton_relation,X0)
        | ~ subclass(subset_relation,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).

fof(f2822,plain,
    ( spl0_293
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f3045,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(singleton_relation,X0)),X1)
        | null_class = intersection(singleton_relation,X0)
        | ~ subclass(subset_relation,X1) )
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_293 ),
    inference(forward_demodulation,[],[f3029,f2312]) ).

fof(f3029,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(identity_relation,X0)),X1) )
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_293 ),
    inference(forward_demodulation,[],[f3022,f2312]) ).

fof(f3022,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(identity_relation,X0)),X1) )
    | ~ spl0_38
    | ~ spl0_293 ),
    inference(resolution,[],[f2823,f373]) ).

fof(f2823,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f2822]) ).

fof(f34244,plain,
    ( spl0_1378
    | ~ spl0_38
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3036,f2826,f372,f34242]) ).

fof(f34242,plain,
    ( spl0_1378
  <=> ! [X0,X1] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(singleton_relation,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).

fof(f2826,plain,
    ( spl0_294
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f3036,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(singleton_relation,X0)),X1) )
    | ~ spl0_38
    | ~ spl0_294 ),
    inference(resolution,[],[f2827,f373]) ).

fof(f2827,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_294 ),
    inference(avatar_component_clause,[],[f2826]) ).

fof(f34240,plain,
    ( spl0_1377
    | ~ spl0_30
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2969,f2818,f331,f34238]) ).

fof(f34238,plain,
    ( spl0_1377
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).

fof(f2969,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_30
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f332]) ).

fof(f34236,plain,
    ( spl0_1376
    | ~ spl0_29
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2968,f2818,f327,f34234]) ).

fof(f34234,plain,
    ( spl0_1376
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).

fof(f2968,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_29
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f328]) ).

fof(f34232,plain,
    ( spl0_1375
    | ~ spl0_31
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2795,f2739,f335,f34230]) ).

fof(f34230,plain,
    ( spl0_1375
  <=> ! [X0,X1] :
        ( subclass(universal_class,complement(intersection(X0,X1)))
        | member(not_subclass_element(universal_class,complement(intersection(X0,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).

fof(f335,plain,
    ( spl0_31
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f2739,plain,
    ( spl0_287
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f2795,plain,
    ( ! [X0,X1] :
        ( subclass(universal_class,complement(intersection(X0,X1)))
        | member(not_subclass_element(universal_class,complement(intersection(X0,X1))),X0) )
    | ~ spl0_31
    | ~ spl0_287 ),
    inference(resolution,[],[f2740,f336]) ).

fof(f336,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f335]) ).

fof(f2740,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f2739]) ).

fof(f34228,plain,
    ( spl0_1374
    | ~ spl0_32
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2794,f2739,f339,f34226]) ).

fof(f34226,plain,
    ( spl0_1374
  <=> ! [X0,X1] :
        ( subclass(universal_class,complement(intersection(X0,X1)))
        | member(not_subclass_element(universal_class,complement(intersection(X0,X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).

fof(f339,plain,
    ( spl0_32
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f2794,plain,
    ( ! [X0,X1] :
        ( subclass(universal_class,complement(intersection(X0,X1)))
        | member(not_subclass_element(universal_class,complement(intersection(X0,X1))),X1) )
    | ~ spl0_32
    | ~ spl0_287 ),
    inference(resolution,[],[f2740,f340]) ).

fof(f340,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f339]) ).

fof(f34223,plain,
    ( spl0_1373
    | ~ spl0_130
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f2613,f2529,f1012,f34221]) ).

fof(f34221,plain,
    ( spl0_1373
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).

fof(f2529,plain,
    ( spl0_273
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f2613,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_273 ),
    inference(resolution,[],[f2530,f1013]) ).

fof(f2530,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_273 ),
    inference(avatar_component_clause,[],[f2529]) ).

fof(f34217,plain,
    ( spl0_1372
    | ~ spl0_27
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f2596,f2529,f319,f34215]) ).

fof(f34215,plain,
    ( spl0_1372
  <=> ! [X0] :
        ( ~ member(not_subclass_element(compose(element_relation,complement(identity_relation)),X0),singleton_relation)
        | subclass(compose(element_relation,complement(identity_relation)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).

fof(f2596,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(compose(element_relation,complement(identity_relation)),X0),singleton_relation)
        | subclass(compose(element_relation,complement(identity_relation)),X0) )
    | ~ spl0_27
    | ~ spl0_273 ),
    inference(resolution,[],[f2530,f320]) ).

fof(f33900,plain,
    ( ~ spl0_1371
    | spl0_1253
    | ~ spl0_1342 ),
    inference(avatar_split_clause,[],[f32514,f32458,f28371,f33897]) ).

fof(f33897,plain,
    ( spl0_1371
  <=> one_to_one(domain_of(domain_of(flip(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).

fof(f28371,plain,
    ( spl0_1253
  <=> one_to_one(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).

fof(f32458,plain,
    ( spl0_1342
  <=> ! [X0] : null_class = cross_product(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).

fof(f32514,plain,
    ( ~ one_to_one(domain_of(domain_of(flip(null_class))))
    | spl0_1253
    | ~ spl0_1342 ),
    inference(superposition,[],[f28373,f32459]) ).

fof(f32459,plain,
    ( ! [X0] : null_class = cross_product(null_class,X0)
    | ~ spl0_1342 ),
    inference(avatar_component_clause,[],[f32458]) ).

fof(f28373,plain,
    ( ~ one_to_one(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
    | spl0_1253 ),
    inference(avatar_component_clause,[],[f28371]) ).

fof(f33242,plain,
    ( ~ spl0_1370
    | spl0_784
    | ~ spl0_1342 ),
    inference(avatar_split_clause,[],[f32506,f32458,f14692,f33239]) ).

fof(f33239,plain,
    ( spl0_1370
  <=> inductive(domain_of(domain_of(flip(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).

fof(f14692,plain,
    ( spl0_784
  <=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f32506,plain,
    ( ~ inductive(domain_of(domain_of(flip(null_class))))
    | spl0_784
    | ~ spl0_1342 ),
    inference(superposition,[],[f14694,f32459]) ).

fof(f14694,plain,
    ( ~ inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
    | spl0_784 ),
    inference(avatar_component_clause,[],[f14692]) ).

fof(f32794,plain,
    ( spl0_1369
    | ~ spl0_235
    | ~ spl0_1339 ),
    inference(avatar_split_clause,[],[f32448,f32445,f2310,f32792]) ).

fof(f32792,plain,
    ( spl0_1369
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).

fof(f32445,plain,
    ( spl0_1339
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).

fof(f32448,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_235
    | ~ spl0_1339 ),
    inference(forward_demodulation,[],[f32446,f2312]) ).

fof(f32446,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_1339 ),
    inference(avatar_component_clause,[],[f32445]) ).

fof(f32735,plain,
    ( spl0_1368
    | ~ spl0_268
    | ~ spl0_735 ),
    inference(avatar_split_clause,[],[f12814,f12598,f2499,f32733]) ).

fof(f32733,plain,
    ( spl0_1368
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).

fof(f12598,plain,
    ( spl0_735
  <=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f12814,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_735 ),
    inference(superposition,[],[f2500,f12600]) ).

fof(f12600,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_735 ),
    inference(avatar_component_clause,[],[f12598]) ).

fof(f32731,plain,
    ( spl0_1367
    | ~ spl0_268
    | ~ spl0_734 ),
    inference(avatar_split_clause,[],[f12736,f12593,f2499,f32729]) ).

fof(f32729,plain,
    ( spl0_1367
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).

fof(f12593,plain,
    ( spl0_734
  <=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f12736,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_734 ),
    inference(superposition,[],[f2500,f12595]) ).

fof(f12595,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_734 ),
    inference(avatar_component_clause,[],[f12593]) ).

fof(f32727,plain,
    ( spl0_1366
    | ~ spl0_68
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9590,f9579,f560,f32725]) ).

fof(f32725,plain,
    ( spl0_1366
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(first(unordered_pair(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).

fof(f9590,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(first(unordered_pair(X0,X1)),X2) )
    | ~ spl0_68
    | ~ spl0_630 ),
    inference(superposition,[],[f561,f9580]) ).

fof(f32723,plain,
    ( spl0_1365
    | ~ spl0_67
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9589,f9579,f556,f32721]) ).

fof(f32721,plain,
    ( spl0_1365
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(second(unordered_pair(X0,X1)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).

fof(f9589,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(second(unordered_pair(X0,X1)),X3) )
    | ~ spl0_67
    | ~ spl0_630 ),
    inference(superposition,[],[f557,f9580]) ).

fof(f32719,plain,
    ( spl0_1364
    | ~ spl0_327
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5073,f4790,f3210,f32717]) ).

fof(f32717,plain,
    ( spl0_1364
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).

fof(f3210,plain,
    ( spl0_327
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f5073,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2))))
    | ~ spl0_327
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5037]) ).

fof(f5037,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2))))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2)))) )
    | ~ spl0_327
    | ~ spl0_407 ),
    inference(resolution,[],[f4791,f3211]) ).

fof(f3211,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f3210]) ).

fof(f32715,plain,
    ( spl0_1363
    | ~ spl0_327
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5015,f4786,f3210,f32713]) ).

fof(f32713,plain,
    ( spl0_1363
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).

fof(f5015,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2))))
    | ~ spl0_327
    | ~ spl0_406 ),
    inference(duplicate_literal_removal,[],[f4979]) ).

fof(f4979,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2))))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2)))) )
    | ~ spl0_327
    | ~ spl0_406 ),
    inference(resolution,[],[f4787,f3211]) ).

fof(f32711,plain,
    ( ~ spl0_1362
    | spl0_990
    | ~ spl0_1342 ),
    inference(avatar_split_clause,[],[f32513,f32458,f20779,f32708]) ).

fof(f32708,plain,
    ( spl0_1362
  <=> operation(domain_of(flip(null_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).

fof(f20779,plain,
    ( spl0_990
  <=> operation(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f32513,plain,
    ( ~ operation(domain_of(flip(null_class)))
    | spl0_990
    | ~ spl0_1342 ),
    inference(superposition,[],[f20781,f32459]) ).

fof(f20781,plain,
    ( ~ operation(domain_of(flip(cross_product(null_class,universal_class))))
    | spl0_990 ),
    inference(avatar_component_clause,[],[f20779]) ).

fof(f32706,plain,
    ( spl0_1361
    | ~ spl0_327
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4956,f4782,f3210,f32704]) ).

fof(f32704,plain,
    ( spl0_1361
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).

fof(f4956,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2)))
    | ~ spl0_327
    | ~ spl0_405 ),
    inference(duplicate_literal_removal,[],[f4920]) ).

fof(f4920,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2))) )
    | ~ spl0_327
    | ~ spl0_405 ),
    inference(resolution,[],[f4783,f3211]) ).

fof(f32702,plain,
    ( spl0_1360
    | ~ spl0_327
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f4898,f4778,f3210,f32700]) ).

fof(f32700,plain,
    ( spl0_1360
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).

fof(f4898,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2)))
    | ~ spl0_327
    | ~ spl0_404 ),
    inference(duplicate_literal_removal,[],[f4862]) ).

fof(f4862,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2))) )
    | ~ spl0_327
    | ~ spl0_404 ),
    inference(resolution,[],[f4779,f3211]) ).

fof(f32698,plain,
    ( spl0_1359
    | ~ spl0_76
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4433,f4223,f608,f32696]) ).

fof(f32696,plain,
    ( spl0_1359
  <=> ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).

fof(f4433,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,subset_relation) )
    | ~ spl0_76
    | ~ spl0_387 ),
    inference(superposition,[],[f4224,f610]) ).

fof(f32694,plain,
    ( spl0_1358
    | ~ spl0_76
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4345,f4215,f608,f32692]) ).

fof(f32692,plain,
    ( spl0_1358
  <=> ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).

fof(f4345,plain,
    ( ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_385 ),
    inference(superposition,[],[f4216,f610]) ).

fof(f32690,plain,
    ( spl0_1357
    | ~ spl0_20
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f4153,f3830,f287,f32688]) ).

fof(f32688,plain,
    ( spl0_1357
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | ~ member(X0,compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).

fof(f3830,plain,
    ( spl0_379
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f4153,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | ~ member(X0,compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))) )
    | ~ spl0_20
    | ~ spl0_379 ),
    inference(resolution,[],[f3831,f288]) ).

fof(f3831,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_379 ),
    inference(avatar_component_clause,[],[f3830]) ).

fof(f32686,plain,
    ( spl0_1356
    | ~ spl0_14
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4012,f3785,f262,f32684]) ).

fof(f32684,plain,
    ( spl0_1356
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,domain_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).

fof(f262,plain,
    ( spl0_14
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f4012,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,domain_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_14
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f264]) ).

fof(f264,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f32682,plain,
    ( spl0_1355
    | ~ spl0_13
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4005,f3785,f258,f32680]) ).

fof(f4005,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,omega)
        | member(not_subclass_element(X0,X1),X2)
        | ~ inductive(X2) )
    | ~ spl0_13
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f259]) ).

fof(f32678,plain,
    ( spl0_1354
    | ~ spl0_11
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4004,f3785,f249,f32676]) ).

fof(f32676,plain,
    ( spl0_1354
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,successor_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).

fof(f249,plain,
    ( spl0_11
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f4004,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,successor_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f251]) ).

fof(f251,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f32674,plain,
    ( spl0_1353
    | ~ spl0_10
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f3996,f3785,f244,f32672]) ).

fof(f32672,plain,
    ( spl0_1353
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,element_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).

fof(f244,plain,
    ( spl0_10
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f3996,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,element_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_10
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f246]) ).

fof(f246,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f32503,plain,
    ( ~ spl0_4
    | spl0_1351 ),
    inference(avatar_contradiction_clause,[],[f32502]) ).

fof(f32502,plain,
    ( $false
    | ~ spl0_4
    | spl0_1351 ),
    inference(resolution,[],[f32496,f220]) ).

fof(f32496,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),universal_class)
    | spl0_1351 ),
    inference(avatar_component_clause,[],[f32494]) ).

fof(f32494,plain,
    ( spl0_1351
  <=> subclass(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).

fof(f32501,plain,
    ( ~ spl0_1351
    | spl0_1352
    | ~ spl0_355
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f3851,f3761,f3541,f32498,f32494]) ).

fof(f32498,plain,
    ( spl0_1352
  <=> subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).

fof(f3761,plain,
    ( spl0_362
  <=> ! [X0] :
        ( subclass(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f3851,plain,
    ( subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation))
    | ~ subclass(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ spl0_355
    | ~ spl0_362 ),
    inference(duplicate_literal_removal,[],[f3848]) ).

fof(f3848,plain,
    ( subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation))
    | subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation))
    | ~ subclass(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ spl0_355
    | ~ spl0_362 ),
    inference(resolution,[],[f3762,f3542]) ).

fof(f3762,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation)
        | subclass(complement(cross_product(universal_class,universal_class)),X0) )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f3761]) ).

fof(f32492,plain,
    ( spl0_1350
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3737,f3541,f2310,f761,f32490]) ).

fof(f32490,plain,
    ( spl0_1350
  <=> ! [X0] :
        ( member(not_subclass_element(X0,complement(singleton_relation)),subset_relation)
        | subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).

fof(f3737,plain,
    ( ! [X0] :
        ( member(not_subclass_element(X0,complement(singleton_relation)),subset_relation)
        | subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_355 ),
    inference(forward_demodulation,[],[f3736,f2312]) ).

fof(f3736,plain,
    ( ! [X0] :
        ( subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_235
    | ~ spl0_355 ),
    inference(forward_demodulation,[],[f3725,f2312]) ).

fof(f3725,plain,
    ( ! [X0] :
        ( subclass(X0,complement(identity_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_355 ),
    inference(resolution,[],[f3542,f762]) ).

fof(f32488,plain,
    ( spl0_1349
    | ~ spl0_97
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3727,f3541,f731,f32486]) ).

fof(f32486,plain,
    ( spl0_1349
  <=> ! [X0] :
        ( subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).

fof(f3727,plain,
    ( ! [X0] :
        ( subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(singleton_relation)),element_relation) )
    | ~ spl0_97
    | ~ spl0_355 ),
    inference(resolution,[],[f3542,f732]) ).

fof(f32484,plain,
    ( spl0_1348
    | ~ spl0_76
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3701,f3537,f608,f32482]) ).

fof(f32482,plain,
    ( spl0_1348
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).

fof(f3701,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_76
    | ~ spl0_354 ),
    inference(superposition,[],[f3538,f610]) ).

fof(f32480,plain,
    ( spl0_1347
    | ~ spl0_18
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3567,f3498,f279,f32478]) ).

fof(f32478,plain,
    ( spl0_1347
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).

fof(f3567,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_18
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f280]) ).

fof(f32476,plain,
    ( spl0_1346
    | ~ spl0_40
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3364,f3210,f380,f32474]) ).

fof(f32474,plain,
    ( spl0_1346
  <=> ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),null_class),X0)
        | subclass(regular(X0),null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).

fof(f3364,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),null_class),X0)
        | subclass(regular(X0),null_class)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_327 ),
    inference(superposition,[],[f3211,f381]) ).

fof(f32472,plain,
    ( spl0_1345
    | ~ spl0_111
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2971,f2818,f823,f32470]) ).

fof(f32470,plain,
    ( spl0_1345
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).

fof(f2971,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_111
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f824]) ).

fof(f32468,plain,
    ( spl0_1344
    | ~ spl0_143
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2872,f2310,f1163,f32466]) ).

fof(f32466,plain,
    ( spl0_1344
  <=> ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).

fof(f1163,plain,
    ( spl0_143
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f2872,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_143
    | ~ spl0_235 ),
    inference(superposition,[],[f1164,f2312]) ).

fof(f1164,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1163]) ).

fof(f32464,plain,
    ( spl0_1343
    | ~ spl0_38
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2791,f2739,f372,f32462]) ).

fof(f32462,plain,
    ( spl0_1343
  <=> ! [X0,X1] :
        ( subclass(universal_class,complement(X0))
        | ~ subclass(X0,X1)
        | member(not_subclass_element(universal_class,complement(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).

fof(f2791,plain,
    ( ! [X0,X1] :
        ( subclass(universal_class,complement(X0))
        | ~ subclass(X0,X1)
        | member(not_subclass_element(universal_class,complement(X0)),X1) )
    | ~ spl0_38
    | ~ spl0_287 ),
    inference(resolution,[],[f2740,f373]) ).

fof(f32460,plain,
    ( spl0_1342
    | ~ spl0_926
    | ~ spl0_1322 ),
    inference(avatar_split_clause,[],[f32134,f30146,f18166,f32458]) ).

fof(f30146,plain,
    ( spl0_1322
  <=> ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).

fof(f32134,plain,
    ( ! [X0] : null_class = cross_product(null_class,X0)
    | ~ spl0_926
    | ~ spl0_1322 ),
    inference(resolution,[],[f30147,f18167]) ).

fof(f30147,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_1322 ),
    inference(avatar_component_clause,[],[f30146]) ).

fof(f32456,plain,
    ( spl0_1341
    | ~ spl0_38
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2785,f2735,f372,f32454]) ).

fof(f32454,plain,
    ( spl0_1341
  <=> ! [X0,X1] :
        ( subclass(subset_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(not_subclass_element(subset_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).

fof(f2785,plain,
    ( ! [X0,X1] :
        ( subclass(subset_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(not_subclass_element(subset_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_286 ),
    inference(resolution,[],[f2736,f373]) ).

fof(f32452,plain,
    ( spl0_1340
    | ~ spl0_38
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2774,f2731,f372,f32450]) ).

fof(f32450,plain,
    ( spl0_1340
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).

fof(f2774,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_38
    | ~ spl0_285 ),
    inference(resolution,[],[f2732,f373]) ).

fof(f32447,plain,
    ( spl0_1339
    | ~ spl0_38
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2765,f2723,f372,f32445]) ).

fof(f2765,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_38
    | ~ spl0_283 ),
    inference(resolution,[],[f2724,f373]) ).

fof(f32442,plain,
    ( spl0_1338
    | ~ spl0_116
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f2609,f2529,f919,f32440]) ).

fof(f32440,plain,
    ( spl0_1338
  <=> ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).

fof(f2609,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_273 ),
    inference(resolution,[],[f2530,f920]) ).

fof(f32436,plain,
    ( ~ spl0_1337
    | ~ spl0_235
    | spl0_1335 ),
    inference(avatar_split_clause,[],[f32425,f32421,f2310,f32433]) ).

fof(f32433,plain,
    ( spl0_1337
  <=> member(regular(compose(element_relation,complement(singleton_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).

fof(f32421,plain,
    ( spl0_1335
  <=> member(regular(compose(element_relation,complement(identity_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).

fof(f32425,plain,
    ( ~ member(regular(compose(element_relation,complement(singleton_relation))),singleton_relation)
    | ~ spl0_235
    | spl0_1335 ),
    inference(forward_demodulation,[],[f32423,f2312]) ).

fof(f32423,plain,
    ( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
    | spl0_1335 ),
    inference(avatar_component_clause,[],[f32421]) ).

fof(f32431,plain,
    ( ~ spl0_1336
    | ~ spl0_235
    | spl0_1334 ),
    inference(avatar_split_clause,[],[f32426,f32417,f2310,f32428]) ).

fof(f32428,plain,
    ( spl0_1336
  <=> null_class = compose(element_relation,complement(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).

fof(f32417,plain,
    ( spl0_1334
  <=> null_class = compose(element_relation,complement(identity_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).

fof(f32426,plain,
    ( null_class != compose(element_relation,complement(singleton_relation))
    | ~ spl0_235
    | spl0_1334 ),
    inference(forward_demodulation,[],[f32418,f2312]) ).

fof(f32418,plain,
    ( null_class != compose(element_relation,complement(identity_relation))
    | spl0_1334 ),
    inference(avatar_component_clause,[],[f32417]) ).

fof(f32424,plain,
    ( spl0_1334
    | ~ spl0_1335
    | ~ spl0_23
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f2601,f2529,f299,f32421,f32417]) ).

fof(f299,plain,
    ( spl0_23
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f2601,plain,
    ( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
    | null_class = compose(element_relation,complement(identity_relation))
    | ~ spl0_23
    | ~ spl0_273 ),
    inference(resolution,[],[f2530,f300]) ).

fof(f300,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f299]) ).

fof(f32415,plain,
    ( spl0_1333
    | ~ spl0_186
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2582,f2499,f1578,f32413]) ).

fof(f32413,plain,
    ( spl0_1333
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(compose_class(X0)))
        | ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).

fof(f1578,plain,
    ( spl0_186
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f2582,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(compose_class(X0)))
        | ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_186
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f1579]) ).

fof(f1579,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1578]) ).

fof(f32308,plain,
    ( spl0_1331
    | ~ spl0_1332
    | ~ spl0_125
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2577,f2499,f959,f32305,f32302]) ).

fof(f32302,plain,
    ( spl0_1331
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).

fof(f32305,plain,
    ( spl0_1332
  <=> subclass(universal_class,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).

fof(f2577,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(unordered_pair(X0,X1),identity_relation) )
    | ~ spl0_125
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f960]) ).

fof(f32300,plain,
    ( ~ spl0_1330
    | ~ spl0_235
    | spl0_1329 ),
    inference(avatar_split_clause,[],[f32295,f32291,f2310,f32297]) ).

fof(f32297,plain,
    ( spl0_1330
  <=> subclass(universal_class,complement(complement(compose(element_relation,complement(singleton_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).

fof(f32291,plain,
    ( spl0_1329
  <=> subclass(universal_class,complement(complement(compose(element_relation,complement(identity_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).

fof(f32295,plain,
    ( ~ subclass(universal_class,complement(complement(compose(element_relation,complement(singleton_relation)))))
    | ~ spl0_235
    | spl0_1329 ),
    inference(forward_demodulation,[],[f32293,f2312]) ).

fof(f32293,plain,
    ( ~ subclass(universal_class,complement(complement(compose(element_relation,complement(identity_relation)))))
    | spl0_1329 ),
    inference(avatar_component_clause,[],[f32291]) ).

fof(f32294,plain,
    ( spl0_1255
    | ~ spl0_1329
    | ~ spl0_124
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2574,f2499,f955,f32291,f28380]) ).

fof(f28380,plain,
    ( spl0_1255
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).

fof(f2574,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(unordered_pair(X0,X1),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f956]) ).

fof(f32289,plain,
    ( spl0_1328
    | ~ spl0_30
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2567,f2499,f331,f32287]) ).

fof(f32287,plain,
    ( spl0_1328
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(X0,unordered_pair(X1,X2))))
        | ~ member(unordered_pair(X1,X2),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).

fof(f2567,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(X0,unordered_pair(X1,X2))))
        | ~ member(unordered_pair(X1,X2),universal_class) )
    | ~ spl0_30
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f332]) ).

fof(f32285,plain,
    ( spl0_1327
    | ~ spl0_29
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2566,f2499,f327,f32283]) ).

fof(f32283,plain,
    ( spl0_1327
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(unordered_pair(X0,X1),X2)))
        | ~ member(unordered_pair(X0,X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).

fof(f2566,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(unordered_pair(X0,X1),X2)))
        | ~ member(unordered_pair(X0,X1),universal_class) )
    | ~ spl0_29
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f328]) ).

fof(f32107,plain,
    ( spl0_1326
    | ~ spl0_926
    | ~ spl0_1321 ),
    inference(avatar_split_clause,[],[f32069,f30142,f18166,f32105]) ).

fof(f30142,plain,
    ( spl0_1321
  <=> ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).

fof(f32069,plain,
    ( ! [X0] : null_class = cross_product(X0,null_class)
    | ~ spl0_926
    | ~ spl0_1321 ),
    inference(resolution,[],[f30143,f18167]) ).

fof(f30143,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_1321 ),
    inference(avatar_component_clause,[],[f30142]) ).

fof(f30294,plain,
    ( spl0_1325
    | ~ spl0_1011
    | ~ spl0_1131 ),
    inference(avatar_split_clause,[],[f25639,f24394,f21316,f30292]) ).

fof(f21316,plain,
    ( spl0_1011
  <=> null_class = intersection(x,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f24394,plain,
    ( spl0_1131
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f25639,plain,
    ( ! [X0] : subclass(intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(x,X0)),null_class)
    | ~ spl0_1011
    | ~ spl0_1131 ),
    inference(superposition,[],[f24395,f21318]) ).

fof(f21318,plain,
    ( null_class = intersection(x,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ spl0_1011 ),
    inference(avatar_component_clause,[],[f21316]) ).

fof(f24395,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
    | ~ spl0_1131 ),
    inference(avatar_component_clause,[],[f24394]) ).

fof(f30156,plain,
    ( spl0_1324
    | ~ spl0_106
    | ~ spl0_735 ),
    inference(avatar_split_clause,[],[f12807,f12598,f802,f30154]) ).

fof(f30154,plain,
    ( spl0_1324
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).

fof(f12807,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106
    | ~ spl0_735 ),
    inference(superposition,[],[f803,f12600]) ).

fof(f30152,plain,
    ( spl0_1323
    | ~ spl0_106
    | ~ spl0_734 ),
    inference(avatar_split_clause,[],[f12729,f12593,f802,f30150]) ).

fof(f30150,plain,
    ( spl0_1323
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).

fof(f12729,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106
    | ~ spl0_734 ),
    inference(superposition,[],[f803,f12595]) ).

fof(f30148,plain,
    ( spl0_1322
    | ~ spl0_23
    | ~ spl0_492 ),
    inference(avatar_split_clause,[],[f6784,f6453,f299,f30146]) ).

fof(f6453,plain,
    ( spl0_492
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f6784,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_492 ),
    inference(duplicate_literal_removal,[],[f6779]) ).

fof(f6779,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_492 ),
    inference(resolution,[],[f6454,f300]) ).

fof(f6454,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_492 ),
    inference(avatar_component_clause,[],[f6453]) ).

fof(f30144,plain,
    ( spl0_1321
    | ~ spl0_23
    | ~ spl0_491 ),
    inference(avatar_split_clause,[],[f6777,f6449,f299,f30142]) ).

fof(f6449,plain,
    ( spl0_491
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f6777,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_491 ),
    inference(duplicate_literal_removal,[],[f6772]) ).

fof(f6772,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_491 ),
    inference(resolution,[],[f6450,f300]) ).

fof(f6450,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_491 ),
    inference(avatar_component_clause,[],[f6449]) ).

fof(f30140,plain,
    ( spl0_1320
    | ~ spl0_1011
    | ~ spl0_1130 ),
    inference(avatar_split_clause,[],[f25546,f24390,f21316,f30138]) ).

fof(f24390,plain,
    ( spl0_1130
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f25546,plain,
    ( ! [X0] : subclass(intersection(cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class),intersection(X0,x)),null_class)
    | ~ spl0_1011
    | ~ spl0_1130 ),
    inference(superposition,[],[f24391,f21318]) ).

fof(f24391,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
    | ~ spl0_1130 ),
    inference(avatar_component_clause,[],[f24390]) ).

fof(f30136,plain,
    ( spl0_1319
    | ~ spl0_32
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f6198,f6191,f339,f30133]) ).

fof(f30133,plain,
    ( spl0_1319
  <=> member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).

fof(f6191,plain,
    ( spl0_470
  <=> member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f6198,plain,
    ( member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_32
    | ~ spl0_470 ),
    inference(resolution,[],[f6193,f340]) ).

fof(f6193,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_470 ),
    inference(avatar_component_clause,[],[f6191]) ).

fof(f30131,plain,
    ( ~ spl0_1316
    | spl0_1317
    | spl0_1318
    | ~ spl0_9
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f5613,f5510,f240,f30129,f30125,f30121]) ).

fof(f30121,plain,
    ( spl0_1316
  <=> subclass(universal_class,regular(universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).

fof(f30125,plain,
    ( spl0_1317
  <=> universal_class = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).

fof(f5613,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | universal_class = null_class
        | ~ subclass(universal_class,regular(universal_class)) )
    | ~ spl0_9
    | ~ spl0_434 ),
    inference(resolution,[],[f5511,f241]) ).

fof(f30118,plain,
    ( spl0_231
    | spl0_1315
    | ~ spl0_389
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5358,f4849,f4231,f30116,f2282]) ).

fof(f30116,plain,
    ( spl0_1315
  <=> ! [X0] : subclass(intersection(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).

fof(f4849,plain,
    ( spl0_419
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f5358,plain,
    ( ! [X0] :
        ( subclass(intersection(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = singleton_relation )
    | ~ spl0_389
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5349]) ).

fof(f5349,plain,
    ( ! [X0] :
        ( subclass(intersection(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = singleton_relation )
    | ~ spl0_389
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4232]) ).

fof(f4850,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_419 ),
    inference(avatar_component_clause,[],[f4849]) ).

fof(f30113,plain,
    ( spl0_231
    | spl0_1314
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5357,f4849,f4239,f30111,f2282]) ).

fof(f30111,plain,
    ( spl0_1314
  <=> ! [X0] : subclass(intersection(X0,null_class),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).

fof(f5357,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,null_class),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = singleton_relation )
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5350]) ).

fof(f5350,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,null_class),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,null_class),domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = singleton_relation )
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4240]) ).

fof(f30109,plain,
    ( spl0_1313
    | ~ spl0_390
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5355,f4849,f4235,f30107]) ).

fof(f30107,plain,
    ( spl0_1313
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X1,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).

fof(f5355,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X1,singleton_relation) )
    | ~ spl0_390
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5352]) ).

fof(f5352,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X1,singleton_relation)
        | subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_390
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4236]) ).

fof(f30105,plain,
    ( spl0_1312
    | ~ spl0_388
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5354,f4849,f4227,f30103]) ).

fof(f30103,plain,
    ( spl0_1312
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).

fof(f5354,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_388
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5353]) ).

fof(f5353,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_388
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4228]) ).

fof(f30100,plain,
    ( spl0_231
    | spl0_1311
    | ~ spl0_389
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5334,f4845,f4231,f30098,f2282]) ).

fof(f30098,plain,
    ( spl0_1311
  <=> ! [X0] : subclass(intersection(null_class,X0),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).

fof(f4845,plain,
    ( spl0_418
  <=> ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f5334,plain,
    ( ! [X0] :
        ( subclass(intersection(null_class,X0),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = singleton_relation )
    | ~ spl0_389
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5325]) ).

fof(f5325,plain,
    ( ! [X0] :
        ( subclass(intersection(null_class,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(null_class,X0),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = singleton_relation )
    | ~ spl0_389
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4232]) ).

fof(f4846,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_418 ),
    inference(avatar_component_clause,[],[f4845]) ).

fof(f30095,plain,
    ( spl0_231
    | spl0_1310
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5333,f4845,f4239,f30093,f2282]) ).

fof(f30093,plain,
    ( spl0_1310
  <=> ! [X0] : subclass(intersection(X0,null_class),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).

fof(f5333,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,null_class),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = singleton_relation )
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5326]) ).

fof(f5326,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,null_class),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,null_class),complement(compose(element_relation,complement(singleton_relation))))
        | null_class = singleton_relation )
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4240]) ).

fof(f30091,plain,
    ( spl0_1309
    | ~ spl0_1011
    | ~ spl0_1129 ),
    inference(avatar_split_clause,[],[f25456,f24386,f21316,f30089]) ).

fof(f24386,plain,
    ( spl0_1129
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f25456,plain,
    ( ! [X0] : subclass(intersection(intersection(x,X0),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)),null_class)
    | ~ spl0_1011
    | ~ spl0_1129 ),
    inference(superposition,[],[f24387,f21318]) ).

fof(f24387,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
    | ~ spl0_1129 ),
    inference(avatar_component_clause,[],[f24386]) ).

fof(f30087,plain,
    ( spl0_1308
    | ~ spl0_390
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5331,f4845,f4235,f30085]) ).

fof(f30085,plain,
    ( spl0_1308
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X1,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).

fof(f5331,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X1,singleton_relation) )
    | ~ spl0_390
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5328]) ).

fof(f5328,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X1,singleton_relation)
        | subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_390
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4236]) ).

fof(f30083,plain,
    ( spl0_1307
    | ~ spl0_388
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5330,f4845,f4227,f30081]) ).

fof(f30081,plain,
    ( spl0_1307
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).

fof(f5330,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_388
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5329]) ).

fof(f5329,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_388
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4228]) ).

fof(f30079,plain,
    ( spl0_1306
    | ~ spl0_130
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5298,f4832,f1012,f30077]) ).

fof(f30077,plain,
    ( spl0_1306
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).

fof(f4832,plain,
    ( spl0_417
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f5298,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_130
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5257]) ).

fof(f5257,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_130
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f1013]) ).

fof(f4833,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_417 ),
    inference(avatar_component_clause,[],[f4832]) ).

fof(f30075,plain,
    ( spl0_1305
    | ~ spl0_302
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5292,f4832,f2940,f30073]) ).

fof(f30073,plain,
    ( spl0_1305
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).

fof(f5292,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5264]) ).

fof(f5264,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X0))
        | subclass(intersection(X0,X1),intersection(element_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f2941]) ).

fof(f30071,plain,
    ( spl0_1304
    | ~ spl0_310
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5289,f4832,f3092,f30069]) ).

fof(f30069,plain,
    ( spl0_1304
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).

fof(f5289,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5276]) ).

fof(f5276,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f3093]) ).

fof(f30067,plain,
    ( spl0_1303
    | ~ spl0_130
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5233,f4828,f1012,f30065]) ).

fof(f30065,plain,
    ( spl0_1303
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).

fof(f4828,plain,
    ( spl0_416
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f5233,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_130
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5192]) ).

fof(f5192,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_130
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f1013]) ).

fof(f4829,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_416 ),
    inference(avatar_component_clause,[],[f4828]) ).

fof(f30063,plain,
    ( spl0_1302
    | ~ spl0_302
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5227,f4828,f2940,f30061]) ).

fof(f30061,plain,
    ( spl0_1302
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).

fof(f5227,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5199]) ).

fof(f5199,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X1))
        | subclass(intersection(X0,X1),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f2941]) ).

fof(f30059,plain,
    ( spl0_1301
    | ~ spl0_310
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5224,f4828,f3092,f30057]) ).

fof(f30057,plain,
    ( spl0_1301
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).

fof(f5224,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5211]) ).

fof(f5211,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f3093]) ).

fof(f30055,plain,
    ( spl0_1300
    | ~ spl0_134
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4724,f4270,f1083,f30053]) ).

fof(f30053,plain,
    ( spl0_1300
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X2))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).

fof(f1083,plain,
    ( spl0_134
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f4724,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X2))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_134
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4674]) ).

fof(f4674,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X2))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X0,X2)) )
    | ~ spl0_134
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f1084]) ).

fof(f1084,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1083]) ).

fof(f30051,plain,
    ( spl0_1299
    | ~ spl0_135
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4723,f4270,f1087,f30049]) ).

fof(f30049,plain,
    ( spl0_1299
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X2))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).

fof(f1087,plain,
    ( spl0_135
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f4723,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X2))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_135
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4675]) ).

fof(f4675,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X2))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X1,X2)) )
    | ~ spl0_135
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f1088]) ).

fof(f1088,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1087]) ).

fof(f30046,plain,
    ( spl0_1298
    | ~ spl0_320
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4714,f4270,f3172,f30044]) ).

fof(f30044,plain,
    ( spl0_1298
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).

fof(f4714,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_320
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4685]) ).

fof(f4685,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,X1)) )
    | ~ spl0_320
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3173]) ).

fof(f30042,plain,
    ( spl0_1297
    | ~ spl0_324
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4713,f4270,f3193,f30040]) ).

fof(f30040,plain,
    ( spl0_1297
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).

fof(f4713,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_324
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4686]) ).

fof(f4686,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,X1)) )
    | ~ spl0_324
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3194]) ).

fof(f30038,plain,
    ( spl0_1296
    | ~ spl0_333
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4712,f4270,f3324,f30036]) ).

fof(f30036,plain,
    ( spl0_1296
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).

fof(f4712,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_333
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4689]) ).

fof(f4689,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0)) )
    | ~ spl0_333
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3325]) ).

fof(f30034,plain,
    ( spl0_1295
    | ~ spl0_334
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4711,f4270,f3328,f30032]) ).

fof(f30032,plain,
    ( spl0_1295
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).

fof(f4711,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_334
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4694]) ).

fof(f4694,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)) )
    | ~ spl0_334
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3329]) ).

fof(f30030,plain,
    ( spl0_1294
    | ~ spl0_332
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4708,f4270,f3310,f30028]) ).

fof(f30028,plain,
    ( spl0_1294
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).

fof(f4708,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_332
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4699]) ).

fof(f4699,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1)) )
    | ~ spl0_332
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3311]) ).

fof(f30026,plain,
    ( spl0_1293
    | ~ spl0_335
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4707,f4270,f3332,f30024]) ).

fof(f30024,plain,
    ( spl0_1293
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).

fof(f4707,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_335
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4700]) ).

fof(f4700,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1)) )
    | ~ spl0_335
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3333]) ).

fof(f30021,plain,
    ( spl0_1292
    | ~ spl0_327
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4630,f4239,f3210,f30019]) ).

fof(f30019,plain,
    ( spl0_1292
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class)))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).

fof(f4630,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class)))
        | null_class = X1 )
    | ~ spl0_327
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4602]) ).

fof(f4602,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class)))
        | null_class = X1
        | subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class))) )
    | ~ spl0_327
    | ~ spl0_391 ),
    inference(resolution,[],[f4240,f3211]) ).

fof(f30017,plain,
    ( spl0_1291
    | ~ spl0_327
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4586,f4235,f3210,f30015]) ).

fof(f30015,plain,
    ( spl0_1291
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).

fof(f4586,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0))) )
    | ~ spl0_327
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4553]) ).

fof(f4553,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0)))
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0))) )
    | ~ spl0_327
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f3211]) ).

fof(f30012,plain,
    ( spl0_1290
    | ~ spl0_327
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f4537,f4231,f3210,f30010]) ).

fof(f30010,plain,
    ( spl0_1290
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0)))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).

fof(f4537,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0)))
        | null_class = X1 )
    | ~ spl0_327
    | ~ spl0_389 ),
    inference(duplicate_literal_removal,[],[f4509]) ).

fof(f4509,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0)))
        | null_class = X1
        | subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0))) )
    | ~ spl0_327
    | ~ spl0_389 ),
    inference(resolution,[],[f4232,f3211]) ).

fof(f30008,plain,
    ( spl0_1289
    | ~ spl0_327
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4490,f4227,f3210,f30006]) ).

fof(f30006,plain,
    ( spl0_1289
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).

fof(f4490,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2))) )
    | ~ spl0_327
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4457]) ).

fof(f4457,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2)))
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2))) )
    | ~ spl0_327
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f3211]) ).

fof(f30003,plain,
    ( spl0_1288
    | ~ spl0_130
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f4074,f3806,f1012,f30001]) ).

fof(f30001,plain,
    ( spl0_1288
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ subclass(intersection(X0,complement(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).

fof(f3806,plain,
    ( spl0_373
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f4074,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ subclass(intersection(X0,complement(X1)),X1) )
    | ~ spl0_130
    | ~ spl0_373 ),
    inference(duplicate_literal_removal,[],[f4055]) ).

fof(f4055,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ subclass(intersection(X0,complement(X1)),X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_130
    | ~ spl0_373 ),
    inference(resolution,[],[f3807,f1013]) ).

fof(f3807,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_373 ),
    inference(avatar_component_clause,[],[f3806]) ).

fof(f29999,plain,
    ( spl0_1287
    | ~ spl0_302
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f4072,f3806,f2940,f29997]) ).

fof(f29997,plain,
    ( spl0_1287
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,complement(element_relation)),X1)
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).

fof(f4072,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(element_relation)),X1)
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_373 ),
    inference(duplicate_literal_removal,[],[f4058]) ).

fof(f4058,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(element_relation)),X1)
        | subclass(intersection(X0,complement(element_relation)),X1)
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_373 ),
    inference(resolution,[],[f3807,f2941]) ).

fof(f29995,plain,
    ( spl0_1286
    | ~ spl0_310
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f4070,f3806,f3092,f29993]) ).

fof(f29993,plain,
    ( spl0_1286
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,complement(subset_relation)),X1)
        | ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).

fof(f4070,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(subset_relation)),X1)
        | ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_373 ),
    inference(duplicate_literal_removal,[],[f4067]) ).

fof(f4067,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(subset_relation)),X1)
        | subclass(intersection(X0,complement(subset_relation)),X1)
        | ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_373 ),
    inference(resolution,[],[f3807,f3093]) ).

fof(f29991,plain,
    ( spl0_1285
    | ~ spl0_130
    | ~ spl0_372 ),
    inference(avatar_split_clause,[],[f4042,f3802,f1012,f29989]) ).

fof(f29989,plain,
    ( spl0_1285
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ subclass(intersection(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).

fof(f3802,plain,
    ( spl0_372
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f4042,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ subclass(intersection(complement(X0),X1),X0) )
    | ~ spl0_130
    | ~ spl0_372 ),
    inference(duplicate_literal_removal,[],[f4021]) ).

fof(f4021,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ subclass(intersection(complement(X0),X1),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_130
    | ~ spl0_372 ),
    inference(resolution,[],[f3803,f1013]) ).

fof(f3803,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_372 ),
    inference(avatar_component_clause,[],[f3802]) ).

fof(f29987,plain,
    ( spl0_1284
    | ~ spl0_302
    | ~ spl0_372 ),
    inference(avatar_split_clause,[],[f4040,f3802,f2940,f29985]) ).

fof(f29985,plain,
    ( spl0_1284
  <=> ! [X0,X1] :
        ( subclass(intersection(complement(element_relation),X0),X1)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).

fof(f4040,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(element_relation),X0),X1)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_372 ),
    inference(duplicate_literal_removal,[],[f4024]) ).

fof(f4024,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(element_relation),X0),X1)
        | subclass(intersection(complement(element_relation),X0),X1)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_302
    | ~ spl0_372 ),
    inference(resolution,[],[f3803,f2941]) ).

fof(f29983,plain,
    ( spl0_1283
    | ~ spl0_310
    | ~ spl0_372 ),
    inference(avatar_split_clause,[],[f4038,f3802,f3092,f29981]) ).

fof(f29981,plain,
    ( spl0_1283
  <=> ! [X0,X1] :
        ( subclass(intersection(complement(subset_relation),X0),X1)
        | ~ subclass(intersection(complement(subset_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).

fof(f4038,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(subset_relation),X0),X1)
        | ~ subclass(intersection(complement(subset_relation),X0),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_372 ),
    inference(duplicate_literal_removal,[],[f4033]) ).

fof(f4033,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(subset_relation),X0),X1)
        | subclass(intersection(complement(subset_relation),X0),X1)
        | ~ subclass(intersection(complement(subset_relation),X0),singleton_relation) )
    | ~ spl0_310
    | ~ spl0_372 ),
    inference(resolution,[],[f3803,f3093]) ).

fof(f29979,plain,
    ( spl0_1282
    | ~ spl0_13
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3697,f3537,f258,f29977]) ).

fof(f29977,plain,
    ( spl0_1282
  <=> ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).

fof(f3697,plain,
    ( ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X1,X2)) )
    | ~ spl0_13
    | ~ spl0_354 ),
    inference(resolution,[],[f3538,f259]) ).

fof(f29975,plain,
    ( spl0_1281
    | ~ spl0_13
    | ~ spl0_353 ),
    inference(avatar_split_clause,[],[f3682,f3533,f258,f29973]) ).

fof(f29973,plain,
    ( spl0_1281
  <=> ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).

fof(f3533,plain,
    ( spl0_353
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f3682,plain,
    ( ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X2,X1)) )
    | ~ spl0_13
    | ~ spl0_353 ),
    inference(resolution,[],[f3534,f259]) ).

fof(f3534,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f3533]) ).

fof(f29971,plain,
    ( spl0_1280
    | ~ spl0_235
    | ~ spl0_283
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3674,f3529,f2723,f2310,f29969]) ).

fof(f29969,plain,
    ( spl0_1280
  <=> ! [X0] :
        ( ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation)
        | null_class = intersection(X0,complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).

fof(f3529,plain,
    ( spl0_352
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f3674,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation)
        | null_class = intersection(X0,complement(subset_relation)) )
    | ~ spl0_235
    | ~ spl0_283
    | ~ spl0_352 ),
    inference(forward_demodulation,[],[f3663,f2312]) ).

fof(f3663,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
    | ~ spl0_283
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3660]) ).

fof(f3660,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(subset_relation))
        | null_class = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
    | ~ spl0_283
    | ~ spl0_352 ),
    inference(resolution,[],[f3530,f2724]) ).

fof(f3530,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,complement(X1))),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_352 ),
    inference(avatar_component_clause,[],[f3529]) ).

fof(f29967,plain,
    ( spl0_1279
    | ~ spl0_116
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3667,f3529,f919,f29965]) ).

fof(f29965,plain,
    ( spl0_1279
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).

fof(f3667,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1) )
    | ~ spl0_116
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3648]) ).

fof(f3648,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_116
    | ~ spl0_352 ),
    inference(resolution,[],[f3530,f920]) ).

fof(f29963,plain,
    ( ~ spl0_1278
    | ~ spl0_1162
    | spl0_1266 ),
    inference(avatar_split_clause,[],[f29906,f29902,f25903,f29960]) ).

fof(f29960,plain,
    ( spl0_1278
  <=> member(not_subclass_element(subset_relation,singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).

fof(f25903,plain,
    ( spl0_1162
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f29902,plain,
    ( spl0_1266
  <=> member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).

fof(f29906,plain,
    ( ~ member(not_subclass_element(subset_relation,singleton_relation),singleton_relation)
    | ~ spl0_1162
    | spl0_1266 ),
    inference(resolution,[],[f29904,f25904]) ).

fof(f25904,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_1162 ),
    inference(avatar_component_clause,[],[f25903]) ).

fof(f29904,plain,
    ( ~ member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | spl0_1266 ),
    inference(avatar_component_clause,[],[f29902]) ).

fof(f29958,plain,
    ( spl0_1277
    | ~ spl0_285
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3665,f3529,f2731,f29956]) ).

fof(f29956,plain,
    ( spl0_1277
  <=> ! [X0] :
        ( null_class = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).

fof(f3665,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_285
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3651]) ).

fof(f3651,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(element_relation))
        | null_class = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_285
    | ~ spl0_352 ),
    inference(resolution,[],[f3530,f2732]) ).

fof(f29954,plain,
    ( spl0_1276
    | ~ spl0_235
    | ~ spl0_283
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3645,f3525,f2723,f2310,f29952]) ).

fof(f29952,plain,
    ( spl0_1276
  <=> ! [X0] :
        ( ~ subclass(intersection(complement(subset_relation),X0),singleton_relation)
        | null_class = intersection(complement(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).

fof(f3525,plain,
    ( spl0_351
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f3645,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(complement(subset_relation),X0),singleton_relation)
        | null_class = intersection(complement(subset_relation),X0) )
    | ~ spl0_235
    | ~ spl0_283
    | ~ spl0_351 ),
    inference(forward_demodulation,[],[f3635,f2312]) ).

fof(f3635,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
    | ~ spl0_283
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3630]) ).

fof(f3630,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(subset_relation),X0)
        | null_class = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
    | ~ spl0_283
    | ~ spl0_351 ),
    inference(resolution,[],[f3526,f2724]) ).

fof(f3526,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(complement(X0),X1)),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_351 ),
    inference(avatar_component_clause,[],[f3525]) ).

fof(f29950,plain,
    ( spl0_1275
    | ~ spl0_116
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3639,f3525,f919,f29948]) ).

fof(f29948,plain,
    ( spl0_1275
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).

fof(f3639,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0) )
    | ~ spl0_116
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3618]) ).

fof(f3618,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_351 ),
    inference(resolution,[],[f3526,f920]) ).

fof(f29946,plain,
    ( spl0_1274
    | ~ spl0_285
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3637,f3525,f2731,f29944]) ).

fof(f29944,plain,
    ( spl0_1274
  <=> ! [X0] :
        ( null_class = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).

fof(f3637,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_285
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3621]) ).

fof(f3621,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(element_relation),X0)
        | null_class = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_285
    | ~ spl0_351 ),
    inference(resolution,[],[f3526,f2732]) ).

fof(f29942,plain,
    ( spl0_1273
    | ~ spl0_14
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3569,f3498,f262,f29940]) ).

fof(f29940,plain,
    ( spl0_1273
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).

fof(f3569,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_14
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f264]) ).

fof(f29938,plain,
    ( spl0_1272
    | ~ spl0_13
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3562,f3498,f258,f29936]) ).

fof(f29936,plain,
    ( spl0_1272
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).

fof(f3562,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) )
    | ~ spl0_13
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f259]) ).

fof(f29934,plain,
    ( spl0_1271
    | ~ spl0_11
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3561,f3498,f249,f29932]) ).

fof(f29932,plain,
    ( spl0_1271
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).

fof(f3561,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f251]) ).

fof(f29930,plain,
    ( spl0_1270
    | ~ spl0_10
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3553,f3498,f244,f29928]) ).

fof(f29928,plain,
    ( spl0_1270
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).

fof(f3553,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_10
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f246]) ).

fof(f29926,plain,
    ( spl0_344
    | ~ spl0_1269
    | ~ spl0_235
    | ~ spl0_283
    | spl0_343 ),
    inference(avatar_split_clause,[],[f3496,f3486,f2723,f2310,f29923,f3490]) ).

fof(f3490,plain,
    ( spl0_344
  <=> null_class = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f29923,plain,
    ( spl0_1269
  <=> subclass(complement(cross_product(universal_class,universal_class)),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).

fof(f3486,plain,
    ( spl0_343
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f3496,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),singleton_relation)
    | null_class = complement(cross_product(universal_class,universal_class))
    | ~ spl0_235
    | ~ spl0_283
    | spl0_343 ),
    inference(forward_demodulation,[],[f3494,f2312]) ).

fof(f3494,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ subclass(complement(cross_product(universal_class,universal_class)),identity_relation)
    | ~ spl0_283
    | spl0_343 ),
    inference(resolution,[],[f3488,f2724]) ).

fof(f3488,plain,
    ( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | spl0_343 ),
    inference(avatar_component_clause,[],[f3486]) ).

fof(f29921,plain,
    ( ~ spl0_1268
    | ~ spl0_1153
    | spl0_1265 ),
    inference(avatar_split_clause,[],[f29898,f29894,f25866,f29918]) ).

fof(f29918,plain,
    ( spl0_1268
  <=> member(not_subclass_element(element_relation,singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).

fof(f25866,plain,
    ( spl0_1153
  <=> ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f29894,plain,
    ( spl0_1265
  <=> member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).

fof(f29898,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),singleton_relation)
    | ~ spl0_1153
    | spl0_1265 ),
    inference(resolution,[],[f29896,f25867]) ).

fof(f25867,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_1153 ),
    inference(avatar_component_clause,[],[f25866]) ).

fof(f29896,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | spl0_1265 ),
    inference(avatar_component_clause,[],[f29894]) ).

fof(f29916,plain,
    ( spl0_344
    | ~ spl0_1267
    | ~ spl0_116
    | spl0_343 ),
    inference(avatar_split_clause,[],[f3495,f3486,f919,f29913,f3490]) ).

fof(f29913,plain,
    ( spl0_1267
  <=> subclass(complement(cross_product(universal_class,universal_class)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).

fof(f3495,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),subset_relation)
    | null_class = complement(cross_product(universal_class,universal_class))
    | ~ spl0_116
    | spl0_343 ),
    inference(resolution,[],[f3488,f920]) ).

fof(f29905,plain,
    ( ~ spl0_1266
    | spl0_796
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3389,f3210,f2310,f393,f15001,f29902]) ).

fof(f15001,plain,
    ( spl0_796
  <=> subclass(subset_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f3389,plain,
    ( subclass(subset_relation,singleton_relation)
    | ~ member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_327 ),
    inference(forward_demodulation,[],[f3388,f2312]) ).

fof(f3388,plain,
    ( ~ member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | subclass(subset_relation,identity_relation)
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_327 ),
    inference(forward_demodulation,[],[f3369,f2312]) ).

fof(f3369,plain,
    ( ~ member(not_subclass_element(subset_relation,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | subclass(subset_relation,identity_relation)
    | ~ spl0_43
    | ~ spl0_327 ),
    inference(superposition,[],[f3211,f395]) ).

fof(f29897,plain,
    ( spl0_770
    | ~ spl0_1265
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3387,f3210,f2310,f384,f29894,f14248]) ).

fof(f14248,plain,
    ( spl0_770
  <=> subclass(element_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f3387,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | subclass(element_relation,singleton_relation)
    | ~ spl0_41
    | ~ spl0_235
    | ~ spl0_327 ),
    inference(forward_demodulation,[],[f3368,f2312]) ).

fof(f3368,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | subclass(element_relation,singleton_relation)
    | ~ spl0_41
    | ~ spl0_327 ),
    inference(superposition,[],[f3211,f386]) ).

fof(f29892,plain,
    ( spl0_1264
    | ~ spl0_76
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3263,f3145,f608,f29890]) ).

fof(f29890,plain,
    ( spl0_1264
  <=> ! [X0] :
        ( ~ subclass(X0,subset_relation)
        | null_class = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).

fof(f3263,plain,
    ( ! [X0] :
        ( ~ subclass(X0,subset_relation)
        | null_class = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_76
    | ~ spl0_315 ),
    inference(superposition,[],[f3146,f610]) ).

fof(f29888,plain,
    ( spl0_1263
    | ~ spl0_20
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2797,f2739,f287,f29886]) ).

fof(f29886,plain,
    ( spl0_1263
  <=> ! [X0] :
        ( subclass(universal_class,complement(complement(X0)))
        | ~ member(not_subclass_element(universal_class,complement(complement(X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).

fof(f2797,plain,
    ( ! [X0] :
        ( subclass(universal_class,complement(complement(X0)))
        | ~ member(not_subclass_element(universal_class,complement(complement(X0))),X0) )
    | ~ spl0_20
    | ~ spl0_287 ),
    inference(resolution,[],[f2740,f288]) ).

fof(f29884,plain,
    ( spl0_1262
    | ~ spl0_77
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2568,f2499,f613,f29882]) ).

fof(f29882,plain,
    ( spl0_1262
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,complement(cross_product(X0,X1)))
        | ~ member(X2,X1)
        | ~ member(X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).

fof(f2568,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,complement(cross_product(X0,X1)))
        | ~ member(X2,X1)
        | ~ member(X3,X0) )
    | ~ spl0_77
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f614]) ).

fof(f29878,plain,
    ( spl0_1261
    | ~ spl0_164
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2474,f2364,f1365,f29876]) ).

fof(f29876,plain,
    ( spl0_1261
  <=> ! [X0] :
        ( subclass(identity_relation,intersection(X0,subset_relation))
        | ~ member(not_subclass_element(identity_relation,intersection(X0,subset_relation)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).

fof(f2474,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(X0,subset_relation))
        | ~ member(not_subclass_element(identity_relation,intersection(X0,subset_relation)),X0) )
    | ~ spl0_164
    | ~ spl0_244 ),
    inference(duplicate_literal_removal,[],[f2471]) ).

fof(f2471,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(X0,subset_relation))
        | ~ member(not_subclass_element(identity_relation,intersection(X0,subset_relation)),X0)
        | subclass(identity_relation,intersection(X0,subset_relation)) )
    | ~ spl0_164
    | ~ spl0_244 ),
    inference(resolution,[],[f2365,f1366]) ).

fof(f29862,plain,
    ( spl0_1260
    | ~ spl0_164
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f2463,f2360,f1365,f29860]) ).

fof(f29860,plain,
    ( spl0_1260
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(X0,element_relation))
        | ~ member(not_subclass_element(singleton_relation,intersection(X0,element_relation)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).

fof(f2360,plain,
    ( spl0_243
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f2463,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(X0,element_relation))
        | ~ member(not_subclass_element(singleton_relation,intersection(X0,element_relation)),X0) )
    | ~ spl0_164
    | ~ spl0_243 ),
    inference(duplicate_literal_removal,[],[f2460]) ).

fof(f2460,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(X0,element_relation))
        | ~ member(not_subclass_element(singleton_relation,intersection(X0,element_relation)),X0)
        | subclass(singleton_relation,intersection(X0,element_relation)) )
    | ~ spl0_164
    | ~ spl0_243 ),
    inference(resolution,[],[f2361,f1366]) ).

fof(f2361,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f2360]) ).

fof(f29858,plain,
    ( spl0_1259
    | ~ spl0_114
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2244,f2227,f892,f29856]) ).

fof(f29856,plain,
    ( spl0_1259
  <=> ! [X0] :
        ( function(intersection(X0,cross_product(universal_class,universal_class)))
        | ~ single_valued_class(intersection(X0,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).

fof(f892,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f2244,plain,
    ( ! [X0] :
        ( function(intersection(X0,cross_product(universal_class,universal_class)))
        | ~ single_valued_class(intersection(X0,cross_product(universal_class,universal_class))) )
    | ~ spl0_114
    | ~ spl0_224 ),
    inference(resolution,[],[f2228,f893]) ).

fof(f893,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f892]) ).

fof(f29854,plain,
    ( spl0_1258
    | ~ spl0_114
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2233,f2223,f892,f29852]) ).

fof(f29852,plain,
    ( spl0_1258
  <=> ! [X0] :
        ( function(intersection(cross_product(universal_class,universal_class),X0))
        | ~ single_valued_class(intersection(cross_product(universal_class,universal_class),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).

fof(f2223,plain,
    ( spl0_223
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f2233,plain,
    ( ! [X0] :
        ( function(intersection(cross_product(universal_class,universal_class),X0))
        | ~ single_valued_class(intersection(cross_product(universal_class,universal_class),X0)) )
    | ~ spl0_114
    | ~ spl0_223 ),
    inference(resolution,[],[f2224,f893]) ).

fof(f2224,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2223]) ).

fof(f28488,plain,
    ( spl0_1257
    | ~ spl0_1054
    | ~ spl0_1191 ),
    inference(avatar_split_clause,[],[f27901,f27199,f22038,f28485]) ).

fof(f28485,plain,
    ( spl0_1257
  <=> subclass(singleton_relation,intersection(element_relation,subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).

fof(f22038,plain,
    ( spl0_1054
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f27199,plain,
    ( spl0_1191
  <=> singleton_relation = intersection(subset_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f27901,plain,
    ( subclass(singleton_relation,intersection(element_relation,subset_relation))
    | ~ spl0_1054
    | ~ spl0_1191 ),
    inference(superposition,[],[f22039,f27201]) ).

fof(f27201,plain,
    ( singleton_relation = intersection(subset_relation,singleton_relation)
    | ~ spl0_1191 ),
    inference(avatar_component_clause,[],[f27199]) ).

fof(f22039,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
    | ~ spl0_1054 ),
    inference(avatar_component_clause,[],[f22038]) ).

fof(f28386,plain,
    ( spl0_1255
    | ~ spl0_1256
    | ~ spl0_106
    | ~ spl0_235
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f22990,f2529,f2310,f802,f28383,f28380]) ).

fof(f28383,plain,
    ( spl0_1256
  <=> subclass(universal_class,compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).

fof(f22990,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,compose(element_relation,complement(singleton_relation)))
        | ~ member(unordered_pair(X0,X1),singleton_relation) )
    | ~ spl0_106
    | ~ spl0_235
    | ~ spl0_273 ),
    inference(forward_demodulation,[],[f2611,f2312]) ).

fof(f2611,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),singleton_relation)
        | ~ subclass(universal_class,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_106
    | ~ spl0_273 ),
    inference(resolution,[],[f2530,f803]) ).

fof(f28378,plain,
    ( ~ spl0_1253
    | spl0_1254
    | ~ spl0_37
    | ~ spl0_786 ),
    inference(avatar_split_clause,[],[f14714,f14704,f359,f28375,f28371]) ).

fof(f28375,plain,
    ( spl0_1254
  <=> function(domain_of(flip(null_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).

fof(f14704,plain,
    ( spl0_786
  <=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f14714,plain,
    ( function(domain_of(flip(null_class)))
    | ~ one_to_one(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
    | ~ spl0_37
    | ~ spl0_786 ),
    inference(superposition,[],[f360,f14706]) ).

fof(f14706,plain,
    ( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_786 ),
    inference(avatar_component_clause,[],[f14704]) ).

fof(f28369,plain,
    ( spl0_1252
    | ~ spl0_268
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f10988,f10793,f2499,f28367]) ).

fof(f28367,plain,
    ( spl0_1252
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).

fof(f10988,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_686 ),
    inference(superposition,[],[f2500,f10795]) ).

fof(f28365,plain,
    ( spl0_1251
    | ~ spl0_268
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10914,f10783,f2499,f28363]) ).

fof(f28363,plain,
    ( spl0_1251
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).

fof(f10914,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_684 ),
    inference(superposition,[],[f2500,f10785]) ).

fof(f28361,plain,
    ( spl0_1250
    | ~ spl0_268
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f10840,f10778,f2499,f28359]) ).

fof(f28359,plain,
    ( spl0_1250
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).

fof(f10840,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_683 ),
    inference(superposition,[],[f2500,f10780]) ).

fof(f28357,plain,
    ( spl0_1249
    | ~ spl0_361
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9613,f9579,f3757,f28355]) ).

fof(f28355,plain,
    ( spl0_1249
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(second(unordered_pair(X0,X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).

fof(f3757,plain,
    ( spl0_361
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f9613,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(second(unordered_pair(X0,X1)),universal_class) )
    | ~ spl0_361
    | ~ spl0_630 ),
    inference(superposition,[],[f3758,f9580]) ).

fof(f3758,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_361 ),
    inference(avatar_component_clause,[],[f3757]) ).

fof(f28353,plain,
    ( spl0_1248
    | ~ spl0_1052
    | ~ spl0_1188 ),
    inference(avatar_split_clause,[],[f27691,f26731,f22030,f28350]) ).

fof(f28350,plain,
    ( spl0_1248
  <=> subclass(singleton_relation,intersection(subset_relation,element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).

fof(f22030,plain,
    ( spl0_1052
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f26731,plain,
    ( spl0_1188
  <=> singleton_relation = intersection(element_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f27691,plain,
    ( subclass(singleton_relation,intersection(subset_relation,element_relation))
    | ~ spl0_1052
    | ~ spl0_1188 ),
    inference(superposition,[],[f22031,f26733]) ).

fof(f26733,plain,
    ( singleton_relation = intersection(element_relation,singleton_relation)
    | ~ spl0_1188 ),
    inference(avatar_component_clause,[],[f26731]) ).

fof(f22031,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
    | ~ spl0_1052 ),
    inference(avatar_component_clause,[],[f22030]) ).

fof(f28348,plain,
    ( spl0_1247
    | ~ spl0_360
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9612,f9579,f3753,f28346]) ).

fof(f28346,plain,
    ( spl0_1247
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(first(unordered_pair(X0,X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).

fof(f9612,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(first(unordered_pair(X0,X1)),universal_class) )
    | ~ spl0_360
    | ~ spl0_630 ),
    inference(superposition,[],[f3754,f9580]) ).

fof(f28143,plain,
    ( spl0_1245
    | spl0_1246
    | ~ spl0_276
    | ~ spl0_588 ),
    inference(avatar_split_clause,[],[f9008,f8985,f2558,f28141,f28138]) ).

fof(f28138,plain,
    ( spl0_1245
  <=> ! [X2,X3] :
        ( ~ member(X2,X3)
        | member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f28141,plain,
    ( spl0_1246
  <=> ! [X0,X1] : ~ subclass(universal_class,compose(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f2558,plain,
    ( spl0_276
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f8985,plain,
    ( spl0_588
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f9008,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | ~ member(X2,X3)
        | member(X2,universal_class) )
    | ~ spl0_276
    | ~ spl0_588 ),
    inference(resolution,[],[f8986,f2559]) ).

fof(f2559,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,universal_class) )
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f2558]) ).

fof(f8986,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(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class)))))
        | ~ subclass(universal_class,compose(X0,X1)) )
    | ~ spl0_588 ),
    inference(avatar_component_clause,[],[f8985]) ).

fof(f28136,plain,
    ( ~ spl0_1244
    | spl0_1243
    | ~ spl0_489
    | ~ spl0_562 ),
    inference(avatar_split_clause,[],[f8334,f8322,f6441,f28129,f28133]) ).

fof(f28133,plain,
    ( spl0_1244
  <=> subclass(domain_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).

fof(f28129,plain,
    ( spl0_1243
  <=> ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).

fof(f6441,plain,
    ( spl0_489
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f8322,plain,
    ( spl0_562
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ member(X0,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f8334,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(element_relation)) )
    | ~ spl0_489
    | ~ spl0_562 ),
    inference(duplicate_literal_removal,[],[f8325]) ).

fof(f8325,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(element_relation)) )
    | ~ spl0_489
    | ~ spl0_562 ),
    inference(resolution,[],[f8323,f6442]) ).

fof(f6442,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | ~ member(X1,universal_class)
        | ~ subclass(domain_relation,complement(X0)) )
    | ~ spl0_489 ),
    inference(avatar_component_clause,[],[f6441]) ).

fof(f8323,plain,
    ( ! [X0] :
        ( 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))
        | ~ member(X0,universal_class) )
    | ~ spl0_562 ),
    inference(avatar_component_clause,[],[f8322]) ).

fof(f28131,plain,
    ( ~ spl0_1242
    | spl0_1243
    | ~ spl0_268
    | ~ spl0_562 ),
    inference(avatar_split_clause,[],[f8330,f8322,f2499,f28129,f28125]) ).

fof(f28125,plain,
    ( spl0_1242
  <=> subclass(universal_class,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).

fof(f8330,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ subclass(universal_class,complement(element_relation)) )
    | ~ spl0_268
    | ~ spl0_562 ),
    inference(resolution,[],[f8323,f2500]) ).

fof(f28123,plain,
    ( spl0_1241
    | ~ spl0_23
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f6004,f5892,f299,f28121]) ).

fof(f28121,plain,
    ( spl0_1241
  <=> ! [X0] :
        ( member(regular(X0),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f6004,plain,
    ( ! [X0] :
        ( member(regular(X0),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0)) )
    | ~ spl0_23
    | ~ spl0_455 ),
    inference(duplicate_literal_removal,[],[f5939]) ).

fof(f5939,plain,
    ( ! [X0] :
        ( member(regular(X0),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0))
        | null_class = X0
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_455 ),
    inference(resolution,[],[f5893,f300]) ).

fof(f28119,plain,
    ( spl0_1240
    | ~ spl0_405
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5363,f4849,f4782,f28117]) ).

fof(f28117,plain,
    ( spl0_1240
  <=> ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f5363,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_405
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5344]) ).

fof(f5344,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_405
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4783]) ).

fof(f28115,plain,
    ( spl0_1239
    | ~ spl0_407
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5361,f4849,f4790,f28113]) ).

fof(f28113,plain,
    ( spl0_1239
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f5361,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_407
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5346]) ).

fof(f5346,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_407
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4791]) ).

fof(f28111,plain,
    ( spl0_1238
    | ~ spl0_1144
    | ~ spl0_1158 ),
    inference(avatar_split_clause,[],[f26066,f25886,f25808,f28108]) ).

fof(f28108,plain,
    ( spl0_1238
  <=> singleton_relation = intersection(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f25808,plain,
    ( spl0_1144
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f25886,plain,
    ( spl0_1158
  <=> subclass(singleton_relation,intersection(singleton_relation,subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f26066,plain,
    ( singleton_relation = intersection(singleton_relation,subset_relation)
    | ~ spl0_1144
    | ~ spl0_1158 ),
    inference(resolution,[],[f25809,f25888]) ).

fof(f25888,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,subset_relation))
    | ~ spl0_1158 ),
    inference(avatar_component_clause,[],[f25886]) ).

fof(f25809,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 )
    | ~ spl0_1144 ),
    inference(avatar_component_clause,[],[f25808]) ).

fof(f28106,plain,
    ( spl0_1237
    | ~ spl0_404
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5360,f4849,f4778,f28104]) ).

fof(f28104,plain,
    ( spl0_1237
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f5360,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_404
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5347]) ).

fof(f5347,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_404
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4779]) ).

fof(f28102,plain,
    ( spl0_1236
    | ~ spl0_406
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5356,f4849,f4786,f28100]) ).

fof(f28100,plain,
    ( spl0_1236
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f5356,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_406
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5351]) ).

fof(f5351,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_406
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f4787]) ).

fof(f28098,plain,
    ( spl0_1235
    | ~ spl0_405
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5339,f4845,f4782,f28096]) ).

fof(f28096,plain,
    ( spl0_1235
  <=> ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f5339,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_405
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5320]) ).

fof(f5320,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_405
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4783]) ).

fof(f28094,plain,
    ( spl0_1234
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5337,f4845,f4790,f28092]) ).

fof(f28092,plain,
    ( spl0_1234
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f5337,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5322]) ).

fof(f5322,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4791]) ).

fof(f28090,plain,
    ( spl0_1233
    | ~ spl0_404
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5336,f4845,f4778,f28088]) ).

fof(f28088,plain,
    ( spl0_1233
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f5336,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_404
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5323]) ).

fof(f5323,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_404
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4779]) ).

fof(f28086,plain,
    ( spl0_1232
    | ~ spl0_406
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5332,f4845,f4786,f28084]) ).

fof(f28084,plain,
    ( spl0_1232
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f5332,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_406
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5327]) ).

fof(f5327,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_406
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f4787]) ).

fof(f28081,plain,
    ( spl0_1231
    | ~ spl0_405
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5305,f4832,f4782,f28079]) ).

fof(f28079,plain,
    ( spl0_1231
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f5305,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1)))
    | ~ spl0_405
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5250]) ).

fof(f5250,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1))) )
    | ~ spl0_405
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4783]) ).

fof(f28076,plain,
    ( spl0_1230
    | ~ spl0_404
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5301,f4832,f4778,f28074]) ).

fof(f28074,plain,
    ( spl0_1230
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f5301,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1)))
    | ~ spl0_404
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5254]) ).

fof(f5254,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1))) )
    | ~ spl0_404
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4779]) ).

fof(f28071,plain,
    ( spl0_1229
    | ~ spl0_407
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5237,f4828,f4790,f28069]) ).

fof(f28069,plain,
    ( spl0_1229
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f5237,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2)))
    | ~ spl0_407
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5188]) ).

fof(f5188,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2)))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2))) )
    | ~ spl0_407
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4791]) ).

fof(f28066,plain,
    ( spl0_1228
    | ~ spl0_406
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5232,f4828,f4786,f28064]) ).

fof(f28064,plain,
    ( spl0_1228
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f5232,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2)))
    | ~ spl0_406
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5193]) ).

fof(f5193,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2)))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2))) )
    | ~ spl0_406
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4787]) ).

fof(f28062,plain,
    ( spl0_1227
    | ~ spl0_1143
    | ~ spl0_1144 ),
    inference(avatar_split_clause,[],[f26065,f25808,f25767,f28059]) ).

fof(f28059,plain,
    ( spl0_1227
  <=> singleton_relation = intersection(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f25767,plain,
    ( spl0_1143
  <=> subclass(singleton_relation,intersection(singleton_relation,element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f26065,plain,
    ( singleton_relation = intersection(singleton_relation,element_relation)
    | ~ spl0_1143
    | ~ spl0_1144 ),
    inference(resolution,[],[f25809,f25769]) ).

fof(f25769,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,element_relation))
    | ~ spl0_1143 ),
    inference(avatar_component_clause,[],[f25767]) ).

fof(f28055,plain,
    ( spl0_1226
    | ~ spl0_347
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5069,f4790,f3506,f28053]) ).

fof(f28053,plain,
    ( spl0_1226
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(null_class,X1)),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f3506,plain,
    ( spl0_347
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f5069,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(null_class,X1)),regular(X2))
        | null_class = X2 )
    | ~ spl0_347
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5041]) ).

fof(f5041,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(null_class,X1)),regular(X2))
        | null_class = X2
        | subclass(intersection(X0,intersection(null_class,X1)),regular(X2)) )
    | ~ spl0_347
    | ~ spl0_407 ),
    inference(resolution,[],[f4791,f3507]) ).

fof(f3507,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_347 ),
    inference(avatar_component_clause,[],[f3506]) ).

fof(f28049,plain,
    ( spl0_1225
    | ~ spl0_347
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5011,f4786,f3506,f28047]) ).

fof(f28047,plain,
    ( spl0_1225
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,null_class)),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f5011,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,null_class)),regular(X2))
        | null_class = X2 )
    | ~ spl0_347
    | ~ spl0_406 ),
    inference(duplicate_literal_removal,[],[f4983]) ).

fof(f4983,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,null_class)),regular(X2))
        | null_class = X2
        | subclass(intersection(X0,intersection(X1,null_class)),regular(X2)) )
    | ~ spl0_347
    | ~ spl0_406 ),
    inference(resolution,[],[f4787,f3507]) ).

fof(f28043,plain,
    ( spl0_1224
    | ~ spl0_347
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4952,f4782,f3506,f28041]) ).

fof(f28041,plain,
    ( spl0_1224
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(intersection(null_class,X0),X1),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f4952,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(null_class,X0),X1),regular(X2))
        | null_class = X2 )
    | ~ spl0_347
    | ~ spl0_405 ),
    inference(duplicate_literal_removal,[],[f4924]) ).

fof(f4924,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(null_class,X0),X1),regular(X2))
        | null_class = X2
        | subclass(intersection(intersection(null_class,X0),X1),regular(X2)) )
    | ~ spl0_347
    | ~ spl0_405 ),
    inference(resolution,[],[f4783,f3507]) ).

fof(f28037,plain,
    ( spl0_1223
    | ~ spl0_347
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f4894,f4778,f3506,f28035]) ).

fof(f28035,plain,
    ( spl0_1223
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,null_class),X1),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f4894,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,null_class),X1),regular(X2))
        | null_class = X2 )
    | ~ spl0_347
    | ~ spl0_404 ),
    inference(duplicate_literal_removal,[],[f4866]) ).

fof(f4866,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,null_class),X1),regular(X2))
        | null_class = X2
        | subclass(intersection(intersection(X0,null_class),X1),regular(X2)) )
    | ~ spl0_347
    | ~ spl0_404 ),
    inference(resolution,[],[f4779,f3507]) ).

fof(f28033,plain,
    ( spl0_1222
    | ~ spl0_130
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4722,f4270,f1012,f28031]) ).

fof(f28031,plain,
    ( spl0_1222
  <=> ! [X2,X0,X1] :
        ( subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f4722,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | ~ subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4676]) ).

fof(f4676,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_130
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f1013]) ).

fof(f28029,plain,
    ( spl0_1221
    | ~ spl0_302
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4715,f4270,f2940,f28027]) ).

fof(f28027,plain,
    ( spl0_1221
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f4715,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4684]) ).

fof(f4684,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f2941]) ).

fof(f28025,plain,
    ( spl0_1220
    | ~ spl0_310
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4709,f4270,f3092,f28023]) ).

fof(f28023,plain,
    ( spl0_1220
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f4709,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4698]) ).

fof(f4698,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f3093]) ).

fof(f28021,plain,
    ( spl0_1219
    | ~ spl0_377 ),
    inference(avatar_split_clause,[],[f4151,f3822,f28019]) ).

fof(f28019,plain,
    ( spl0_1219
  <=> ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f3822,plain,
    ( spl0_377
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f4151,plain,
    ( ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = null_class )
    | ~ spl0_377 ),
    inference(equality_resolution,[],[f3823]) ).

fof(f3823,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_377 ),
    inference(avatar_component_clause,[],[f3822]) ).

fof(f28017,plain,
    ( spl0_1218
    | ~ spl0_4
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f3991,f3785,f219,f28015]) ).

fof(f28015,plain,
    ( spl0_1218
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,X2)
        | member(not_subclass_element(X0,X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f3991,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,X2)
        | member(not_subclass_element(X0,X1),universal_class) )
    | ~ spl0_4
    | ~ spl0_368 ),
    inference(resolution,[],[f3786,f220]) ).

fof(f28013,plain,
    ( spl0_1217
    | ~ spl0_316
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3451,f3332,f3149,f28011]) ).

fof(f28011,plain,
    ( spl0_1217
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f3451,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_316
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3440]) ).

fof(f3440,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_316
    | ~ spl0_335 ),
    inference(resolution,[],[f3333,f3150]) ).

fof(f27878,plain,
    ( spl0_1216
    | ~ spl0_20
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f3418,f3324,f287,f27876]) ).

fof(f27876,plain,
    ( spl0_1216
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ member(not_subclass_element(singleton_relation,X0),compose(element_relation,complement(singleton_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f3418,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ member(not_subclass_element(singleton_relation,X0),compose(element_relation,complement(singleton_relation))) )
    | ~ spl0_20
    | ~ spl0_333 ),
    inference(resolution,[],[f3325,f288]) ).

fof(f27874,plain,
    ( spl0_1215
    | ~ spl0_316
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3412,f3310,f3149,f27872]) ).

fof(f27872,plain,
    ( spl0_1215
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f3412,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(subset_relation)) )
    | ~ spl0_316
    | ~ spl0_332 ),
    inference(duplicate_literal_removal,[],[f3401]) ).

fof(f3401,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(subset_relation)) )
    | ~ spl0_316
    | ~ spl0_332 ),
    inference(resolution,[],[f3311,f3150]) ).

fof(f27870,plain,
    ( spl0_1214
    | ~ spl0_316
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f3343,f3193,f3149,f27868]) ).

fof(f27868,plain,
    ( spl0_1214
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f3343,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_316
    | ~ spl0_324 ),
    inference(duplicate_literal_removal,[],[f3336]) ).

fof(f3336,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_316
    | ~ spl0_324 ),
    inference(resolution,[],[f3194,f3150]) ).

fof(f27866,plain,
    ( spl0_1213
    | ~ spl0_316
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f3321,f3172,f3149,f27864]) ).

fof(f27864,plain,
    ( spl0_1213
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f3321,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_316
    | ~ spl0_320 ),
    inference(duplicate_literal_removal,[],[f3314]) ).

fof(f3314,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_316
    | ~ spl0_320 ),
    inference(resolution,[],[f3173,f3150]) ).

fof(f27862,plain,
    ( spl0_1212
    | ~ spl0_134
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3296,f3149,f1083,f27860]) ).

fof(f27860,plain,
    ( spl0_1212
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f3296,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X0)) )
    | ~ spl0_134
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f3269]) ).

fof(f3269,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X0))
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_134
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f1084]) ).

fof(f27858,plain,
    ( spl0_1211
    | ~ spl0_135
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3294,f3149,f1087,f27856]) ).

fof(f27856,plain,
    ( spl0_1211
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f3294,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f3271]) ).

fof(f3271,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X1))
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f1088]) ).

fof(f27830,plain,
    ( spl0_1210
    | spl0_1142
    | ~ spl0_13
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3259,f3145,f258,f24444,f27828]) ).

fof(f27828,plain,
    ( spl0_1210
  <=> ! [X0,X1] :
        ( member(regular(omega),X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f3259,plain,
    ( ! [X0,X1] :
        ( null_class = omega
        | member(regular(omega),X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_315 ),
    inference(resolution,[],[f3146,f259]) ).

fof(f27802,plain,
    ( spl0_1209
    | spl0_1142
    | ~ spl0_13
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f3245,f3141,f258,f24444,f27800]) ).

fof(f27800,plain,
    ( spl0_1209
  <=> ! [X0,X1] :
        ( member(regular(omega),X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).

fof(f3141,plain,
    ( spl0_314
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f3245,plain,
    ( ! [X0,X1] :
        ( null_class = omega
        | member(regular(omega),X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_13
    | ~ spl0_314 ),
    inference(resolution,[],[f3142,f259]) ).

fof(f3142,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f3141]) ).

fof(f27672,plain,
    ( spl0_1208
    | ~ spl0_292
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f3135,f3118,f2818,f27670]) ).

fof(f27670,plain,
    ( spl0_1208
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).

fof(f3135,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_292
    | ~ spl0_312 ),
    inference(duplicate_literal_removal,[],[f3130]) ).

fof(f3130,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_292
    | ~ spl0_312 ),
    inference(resolution,[],[f3119,f2819]) ).

fof(f27668,plain,
    ( spl0_1207
    | ~ spl0_292
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f3090,f2930,f2818,f27666]) ).

fof(f27666,plain,
    ( spl0_1207
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).

fof(f3090,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_292
    | ~ spl0_300 ),
    inference(duplicate_literal_removal,[],[f3085]) ).

fof(f3085,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_292
    | ~ spl0_300 ),
    inference(resolution,[],[f2931,f2819]) ).

fof(f27664,plain,
    ( spl0_1206
    | ~ spl0_38
    | ~ spl0_309 ),
    inference(avatar_split_clause,[],[f3083,f3070,f372,f27662]) ).

fof(f27662,plain,
    ( spl0_1206
  <=> ! [X0] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).

fof(f3070,plain,
    ( spl0_309
  <=> member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f3083,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_38
    | ~ spl0_309 ),
    inference(resolution,[],[f3072,f373]) ).

fof(f3072,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_309 ),
    inference(avatar_component_clause,[],[f3070]) ).

fof(f27660,plain,
    ( ~ spl0_1205
    | spl0_231
    | ~ spl0_292
    | ~ spl0_309 ),
    inference(avatar_split_clause,[],[f3079,f3070,f2818,f2282,f27657]) ).

fof(f27657,plain,
    ( spl0_1205
  <=> subclass(singleton_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).

fof(f3079,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
    | ~ spl0_292
    | ~ spl0_309 ),
    inference(resolution,[],[f3072,f2819]) ).

fof(f27655,plain,
    ( spl0_1204
    | ~ spl0_38
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f3078,f3065,f372,f27653]) ).

fof(f27653,plain,
    ( spl0_1204
  <=> ! [X0] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).

fof(f3065,plain,
    ( spl0_308
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f3078,plain,
    ( ! [X0] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_38
    | ~ spl0_308 ),
    inference(resolution,[],[f3067,f373]) ).

fof(f3067,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_308 ),
    inference(avatar_component_clause,[],[f3065]) ).

fof(f27651,plain,
    ( ~ spl0_1203
    | spl0_231
    | ~ spl0_292
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f3074,f3065,f2818,f2282,f27648]) ).

fof(f27648,plain,
    ( spl0_1203
  <=> subclass(singleton_relation,complement(complement(compose(element_relation,complement(singleton_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).

fof(f3074,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(complement(compose(element_relation,complement(singleton_relation)))))
    | ~ spl0_292
    | ~ spl0_308 ),
    inference(resolution,[],[f3067,f2819]) ).

fof(f27646,plain,
    ( spl0_1202
    | ~ spl0_235
    | ~ spl0_292
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f3046,f2822,f2818,f2310,f27644]) ).

fof(f27644,plain,
    ( spl0_1202
  <=> ! [X0] :
        ( ~ subclass(intersection(singleton_relation,X0),complement(subset_relation))
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).

fof(f3046,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(singleton_relation,X0),complement(subset_relation))
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_292
    | ~ spl0_293 ),
    inference(forward_demodulation,[],[f3026,f2312]) ).

fof(f3026,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_235
    | ~ spl0_292
    | ~ spl0_293 ),
    inference(forward_demodulation,[],[f3025,f2312]) ).

fof(f3025,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_292
    | ~ spl0_293 ),
    inference(duplicate_literal_removal,[],[f3019]) ).

fof(f3019,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | null_class = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_292
    | ~ spl0_293 ),
    inference(resolution,[],[f2823,f2819]) ).

fof(f27642,plain,
    ( spl0_1201
    | ~ spl0_292
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3038,f2826,f2818,f27640]) ).

fof(f27640,plain,
    ( spl0_1201
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).

fof(f3038,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_292
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f3033]) ).

fof(f3033,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_292
    | ~ spl0_294 ),
    inference(resolution,[],[f2827,f2819]) ).

fof(f27239,plain,
    ( spl0_1200
    | ~ spl0_235
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f3023,f2822,f2310,f27237]) ).

fof(f27237,plain,
    ( spl0_1200
  <=> ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),subset_relation)
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).

fof(f3023,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),subset_relation)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_293 ),
    inference(superposition,[],[f2823,f2312]) ).

fof(f27235,plain,
    ( spl0_1199
    | ~ spl0_128
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2991,f2818,f1004,f27233]) ).

fof(f27233,plain,
    ( spl0_1199
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f1004,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f2991,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X0)) )
    | ~ spl0_128
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f2965]) ).

fof(f2965,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X0))
        | intersection(X0,X1) = null_class )
    | ~ spl0_128
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f1005]) ).

fof(f1005,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1004]) ).

fof(f27231,plain,
    ( spl0_1198
    | ~ spl0_129
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2989,f2818,f1008,f27229]) ).

fof(f27229,plain,
    ( spl0_1198
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f1008,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f2989,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X1)) )
    | ~ spl0_129
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f2967]) ).

fof(f2967,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X1))
        | intersection(X0,X1) = null_class )
    | ~ spl0_129
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f1009]) ).

fof(f1009,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1008]) ).

fof(f27227,plain,
    ( spl0_1197
    | ~ spl0_53
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2868,f2310,f464,f27225]) ).

fof(f27225,plain,
    ( spl0_1197
  <=> ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f464,plain,
    ( spl0_53
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f2868,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | single_valued_class(X0) )
    | ~ spl0_53
    | ~ spl0_235 ),
    inference(superposition,[],[f465,f2312]) ).

fof(f465,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f464]) ).

fof(f27223,plain,
    ( spl0_1196
    | ~ spl0_52
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2867,f2310,f460,f27221]) ).

fof(f27221,plain,
    ( spl0_1196
  <=> ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f460,plain,
    ( spl0_52
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f2867,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_235 ),
    inference(superposition,[],[f461,f2312]) ).

fof(f461,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f460]) ).

fof(f27219,plain,
    ( spl0_1195
    | ~ spl0_51
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2866,f2310,f456,f27217]) ).

fof(f27217,plain,
    ( spl0_1195
  <=> ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f456,plain,
    ( spl0_51
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f2866,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_235 ),
    inference(superposition,[],[f457,f2312]) ).

fof(f457,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f456]) ).

fof(f27215,plain,
    ( spl0_1193
    | ~ spl0_1194
    | ~ spl0_111
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2569,f2499,f823,f27212,f27209]) ).

fof(f27209,plain,
    ( spl0_1193
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f27212,plain,
    ( spl0_1194
  <=> subclass(universal_class,complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f2569,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(cross_product(universal_class,universal_class)))
        | ~ member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_111
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f824]) ).

fof(f27207,plain,
    ( ~ spl0_1192
    | spl0_344
    | ~ spl0_22
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f2485,f2452,f295,f3490,f27204]) ).

fof(f27204,plain,
    ( spl0_1192
  <=> function(complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

fof(f2452,plain,
    ( spl0_262
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f2485,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ function(complement(cross_product(universal_class,universal_class)))
    | ~ spl0_22
    | ~ spl0_262 ),
    inference(resolution,[],[f2453,f296]) ).

fof(f2453,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f2452]) ).

fof(f27202,plain,
    ( spl0_1191
    | ~ spl0_428
    | ~ spl0_1145 ),
    inference(avatar_split_clause,[],[f26124,f25812,f5479,f27199]) ).

fof(f5479,plain,
    ( spl0_428
  <=> subclass(singleton_relation,intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f25812,plain,
    ( spl0_1145
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f26124,plain,
    ( singleton_relation = intersection(subset_relation,singleton_relation)
    | ~ spl0_428
    | ~ spl0_1145 ),
    inference(resolution,[],[f25813,f5481]) ).

fof(f5481,plain,
    ( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
    | ~ spl0_428 ),
    inference(avatar_component_clause,[],[f5479]) ).

fof(f25813,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 )
    | ~ spl0_1145 ),
    inference(avatar_component_clause,[],[f25812]) ).

fof(f27195,plain,
    ( spl0_1190
    | ~ spl0_38
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2473,f2364,f372,f27193]) ).

fof(f27193,plain,
    ( spl0_1190
  <=> ! [X0,X1] :
        ( subclass(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(not_subclass_element(identity_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f2473,plain,
    ( ! [X0,X1] :
        ( subclass(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(not_subclass_element(identity_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_244 ),
    inference(resolution,[],[f2365,f373]) ).

fof(f27191,plain,
    ( spl0_1189
    | ~ spl0_38
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f2462,f2360,f372,f27189]) ).

fof(f27189,plain,
    ( spl0_1189
  <=> ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(not_subclass_element(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f2462,plain,
    ( ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(not_subclass_element(singleton_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_243 ),
    inference(resolution,[],[f2361,f373]) ).

fof(f26734,plain,
    ( spl0_1188
    | ~ spl0_420
    | ~ spl0_1145 ),
    inference(avatar_split_clause,[],[f26121,f25812,f4853,f26731]) ).

fof(f4853,plain,
    ( spl0_420
  <=> subclass(singleton_relation,intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f26121,plain,
    ( singleton_relation = intersection(element_relation,singleton_relation)
    | ~ spl0_420
    | ~ spl0_1145 ),
    inference(resolution,[],[f25813,f4855]) ).

fof(f4855,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_420 ),
    inference(avatar_component_clause,[],[f4853]) ).

fof(f26364,plain,
    ( spl0_1187
    | ~ spl0_423
    | ~ spl0_1144 ),
    inference(avatar_split_clause,[],[f26044,f25808,f5170,f26362]) ).

fof(f26362,plain,
    ( spl0_1187
  <=> ! [X0] : intersection(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f5170,plain,
    ( spl0_423
  <=> ! [X0] : subclass(X0,intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f26044,plain,
    ( ! [X0] : intersection(X0,X0) = X0
    | ~ spl0_423
    | ~ spl0_1144 ),
    inference(resolution,[],[f25809,f5171]) ).

fof(f5171,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_423 ),
    inference(avatar_component_clause,[],[f5170]) ).

fof(f26043,plain,
    ( spl0_1186
    | ~ spl0_1011
    | ~ spl0_1127 ),
    inference(avatar_split_clause,[],[f25324,f24378,f21316,f26041]) ).

fof(f24378,plain,
    ( spl0_1127
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f25324,plain,
    ( ! [X0] : subclass(intersection(intersection(X0,x),cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)),null_class)
    | ~ spl0_1011
    | ~ spl0_1127 ),
    inference(superposition,[],[f24379,f21318]) ).

fof(f24379,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
    | ~ spl0_1127 ),
    inference(avatar_component_clause,[],[f24378]) ).

fof(f26039,plain,
    ( spl0_1185
    | ~ spl0_106
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f10981,f10793,f802,f26037]) ).

fof(f26037,plain,
    ( spl0_1185
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f10981,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106
    | ~ spl0_686 ),
    inference(superposition,[],[f803,f10795]) ).

fof(f26035,plain,
    ( spl0_1184
    | ~ spl0_106
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10907,f10783,f802,f26033]) ).

fof(f26033,plain,
    ( spl0_1184
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f10907,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106
    | ~ spl0_684 ),
    inference(superposition,[],[f803,f10785]) ).

fof(f26031,plain,
    ( spl0_1183
    | ~ spl0_106
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f10833,f10778,f802,f26029]) ).

fof(f26029,plain,
    ( spl0_1183
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f10833,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106
    | ~ spl0_683 ),
    inference(superposition,[],[f803,f10780]) ).

fof(f26025,plain,
    ( spl0_1182
    | spl0_652
    | ~ spl0_165
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6766,f6441,f1369,f9912,f26023]) ).

fof(f26023,plain,
    ( spl0_1182
  <=> ! [X1] :
        ( ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f1369,plain,
    ( spl0_165
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f6766,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1) )
    | ~ spl0_165
    | ~ spl0_489 ),
    inference(duplicate_literal_removal,[],[f6742]) ).

fof(f6742,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_165
    | ~ spl0_489 ),
    inference(resolution,[],[f6442,f1370]) ).

fof(f1370,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
        | ~ subclass(domain_relation,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1369]) ).

fof(f26019,plain,
    ( spl0_1181
    | spl0_652
    | ~ spl0_106
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6743,f6441,f802,f9912,f26017]) ).

fof(f26017,plain,
    ( spl0_1181
  <=> ! [X1] :
        ( ~ subclass(domain_relation,complement(X1))
        | ~ subclass(universal_class,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f6743,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(universal_class,X1) )
    | ~ spl0_106
    | ~ spl0_489 ),
    inference(resolution,[],[f6442,f803]) ).

fof(f26006,plain,
    ( ~ spl0_275
    | spl0_1180
    | ~ spl0_185
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f6197,f6191,f1556,f26003,f2539]) ).

fof(f2539,plain,
    ( spl0_275
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f26003,plain,
    ( spl0_1180
  <=> member(regular(subset_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f1556,plain,
    ( spl0_185
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f6197,plain,
    ( member(regular(subset_relation),subset_relation)
    | ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_185
    | ~ spl0_470 ),
    inference(resolution,[],[f6193,f1557]) ).

fof(f1557,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1556]) ).

fof(f26001,plain,
    ( spl0_1179
    | ~ spl0_130
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5359,f4849,f1012,f25999]) ).

fof(f25999,plain,
    ( spl0_1179
  <=> ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f5359,plain,
    ( ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_130
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5348]) ).

fof(f5348,plain,
    ( ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_130
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f1013]) ).

fof(f25985,plain,
    ( spl0_1178
    | ~ spl0_130
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5335,f4845,f1012,f25983]) ).

fof(f25983,plain,
    ( spl0_1178
  <=> ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f5335,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_130
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5324]) ).

fof(f5324,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_130
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f1013]) ).

fof(f25980,plain,
    ( spl0_1177
    | ~ spl0_389
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5300,f4832,f4231,f25978]) ).

fof(f25978,plain,
    ( spl0_1177
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,null_class))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f5300,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_389
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5255]) ).

fof(f5255,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,null_class))
        | subclass(intersection(null_class,X0),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_389
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4232]) ).

fof(f25975,plain,
    ( spl0_1176
    | ~ spl0_391
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5299,f4832,f4239,f25973]) ).

fof(f25973,plain,
    ( spl0_1176
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X0))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f5299,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_391
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5256]) ).

fof(f5256,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X0))
        | subclass(intersection(X0,null_class),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_391
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4240]) ).

fof(f25971,plain,
    ( spl0_1175
    | ~ spl0_390
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5296,f4832,f4235,f25969]) ).

fof(f25969,plain,
    ( spl0_1175
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f5296,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2) )
    | ~ spl0_390
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5259]) ).

fof(f5259,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_390
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4236]) ).

fof(f25967,plain,
    ( spl0_1174
    | ~ spl0_388
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5295,f4832,f4227,f25965]) ).

fof(f25965,plain,
    ( spl0_1174
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f5295,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2) )
    | ~ spl0_388
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5260]) ).

fof(f5260,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_388
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4228]) ).

fof(f25962,plain,
    ( spl0_1173
    | ~ spl0_389
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5235,f4828,f4231,f25960]) ).

fof(f25960,plain,
    ( spl0_1173
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X0))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f5235,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_389
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5190]) ).

fof(f5190,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X0))
        | subclass(intersection(null_class,X0),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_389
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4232]) ).

fof(f25957,plain,
    ( spl0_1172
    | ~ spl0_391
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5234,f4828,f4239,f25955]) ).

fof(f25955,plain,
    ( spl0_1172
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,null_class))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f5234,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_391
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5191]) ).

fof(f5191,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,null_class))
        | subclass(intersection(X0,null_class),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_391
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4240]) ).

fof(f25953,plain,
    ( spl0_1171
    | ~ spl0_390
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5231,f4828,f4235,f25951]) ).

fof(f25951,plain,
    ( spl0_1171
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f5231,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2) )
    | ~ spl0_390
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5194]) ).

fof(f5194,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_390
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4236]) ).

fof(f25949,plain,
    ( spl0_1170
    | ~ spl0_388
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5230,f4828,f4227,f25947]) ).

fof(f25947,plain,
    ( spl0_1170
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f5230,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2) )
    | ~ spl0_388
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5195]) ).

fof(f5195,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_388
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4228]) ).

fof(f25945,plain,
    ( spl0_1169
    | ~ spl0_286
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4717,f4270,f2735,f25943]) ).

fof(f25943,plain,
    ( spl0_1169
  <=> ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f4717,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0) )
    | ~ spl0_286
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4681]) ).

fof(f4681,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0)
        | subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0)) )
    | ~ spl0_286
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f2736]) ).

fof(f25929,plain,
    ( spl0_1168
    | ~ spl0_373
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4589,f4235,f3806,f25927]) ).

fof(f25927,plain,
    ( spl0_1168
  <=> ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f4589,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2) )
    | ~ spl0_373
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4550]) ).

fof(f4550,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2)
        | subclass(intersection(X1,complement(X0)),X2) )
    | ~ spl0_373
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f3807]) ).

fof(f25925,plain,
    ( spl0_1167
    | ~ spl0_313
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4588,f4235,f3137,f25923]) ).

fof(f25923,plain,
    ( spl0_1167
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f3137,plain,
    ( spl0_313
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f4588,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4551]) ).

fof(f4551,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f3138]) ).

fof(f3138,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f3137]) ).

fof(f25921,plain,
    ( spl0_1166
    | ~ spl0_372
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4494,f4227,f3802,f25919]) ).

fof(f25919,plain,
    ( spl0_1166
  <=> ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f4494,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_372
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4453]) ).

fof(f4453,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_372
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f3803]) ).

fof(f25917,plain,
    ( spl0_1165
    | ~ spl0_313
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4492,f4227,f3137,f25915]) ).

fof(f25915,plain,
    ( spl0_1165
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f4492,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4455]) ).

fof(f4455,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f3138]) ).

fof(f25913,plain,
    ( spl0_1164
    | ~ spl0_352
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f3956,f3777,f3529,f25911]) ).

fof(f25911,plain,
    ( spl0_1164
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f3956,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0)) )
    | ~ spl0_352
    | ~ spl0_366 ),
    inference(duplicate_literal_removal,[],[f3927]) ).

fof(f3927,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0))
        | null_class = intersection(X1,complement(X0)) )
    | ~ spl0_352
    | ~ spl0_366 ),
    inference(resolution,[],[f3778,f3530]) ).

fof(f25909,plain,
    ( spl0_1163
    | ~ spl0_351
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3890,f3769,f3525,f25907]) ).

fof(f25907,plain,
    ( spl0_1163
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f3890,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_351
    | ~ spl0_364 ),
    inference(duplicate_literal_removal,[],[f3859]) ).

fof(f3859,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_351
    | ~ spl0_364 ),
    inference(resolution,[],[f3770,f3526]) ).

fof(f25905,plain,
    ( spl0_1162
    | ~ spl0_6
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f3742,f3614,f228,f25903]) ).

fof(f228,plain,
    ( spl0_6
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f3742,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_6
    | ~ spl0_358 ),
    inference(resolution,[],[f3615,f229]) ).

fof(f229,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f228]) ).

fof(f25901,plain,
    ( spl0_1161
    | ~ spl0_4
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f3548,f3498,f219,f25899]) ).

fof(f25899,plain,
    ( spl0_1161
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f3548,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) )
    | ~ spl0_4
    | ~ spl0_345 ),
    inference(resolution,[],[f3499,f220]) ).

fof(f25897,plain,
    ( spl0_1160
    | ~ spl0_130
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3293,f3149,f1012,f25895]) ).

fof(f25895,plain,
    ( spl0_1160
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f3293,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_130
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f3272]) ).

fof(f3272,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2)
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f1013]) ).

fof(f25893,plain,
    ( spl0_1159
    | ~ spl0_302
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3290,f3149,f2940,f25891]) ).

fof(f25891,plain,
    ( spl0_1159
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f3290,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f3278]) ).

fof(f3278,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f2941]) ).

fof(f25889,plain,
    ( spl0_1158
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_1128 ),
    inference(avatar_split_clause,[],[f25388,f24382,f2310,f393,f25886]) ).

fof(f24382,plain,
    ( spl0_1128
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f25388,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_1128 ),
    inference(forward_demodulation,[],[f25381,f2312]) ).

fof(f25381,plain,
    ( subclass(identity_relation,intersection(identity_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_1128 ),
    inference(superposition,[],[f24383,f395]) ).

fof(f24383,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
    | ~ spl0_1128 ),
    inference(avatar_component_clause,[],[f24382]) ).

fof(f25884,plain,
    ( spl0_1157
    | ~ spl0_310
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3288,f3149,f3092,f25882]) ).

fof(f25882,plain,
    ( spl0_1157
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f3288,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f3287]) ).

fof(f3287,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f3093]) ).

fof(f25880,plain,
    ( spl0_1156
    | ~ spl0_235
    | ~ spl0_283
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3047,f2818,f2723,f2310,f25878]) ).

fof(f25878,plain,
    ( spl0_1156
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f3047,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(subset_relation)) )
    | ~ spl0_235
    | ~ spl0_283
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f2987,f2312]) ).

fof(f2987,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_283
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f2982]) ).

fof(f2982,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(subset_relation))
        | null_class = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_283
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f2724]) ).

fof(f25876,plain,
    ( spl0_1155
    | ~ spl0_116
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2990,f2818,f919,f25874]) ).

fof(f25874,plain,
    ( spl0_1155
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f2990,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_116
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f2966]) ).

fof(f2966,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f920]) ).

fof(f25872,plain,
    ( spl0_1154
    | ~ spl0_285
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2988,f2818,f2731,f25870]) ).

fof(f25870,plain,
    ( spl0_1154
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f2988,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_285
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f2973]) ).

fof(f2973,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | null_class = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_285
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f2732]) ).

fof(f25868,plain,
    ( spl0_1153
    | ~ spl0_124
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2871,f2310,f955,f25866]) ).

fof(f2871,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_124
    | ~ spl0_235 ),
    inference(superposition,[],[f956,f2312]) ).

fof(f25859,plain,
    ( spl0_1152
    | spl0_1150
    | ~ spl0_97
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2807,f2739,f731,f25838,f25856]) ).

fof(f25856,plain,
    ( spl0_1152
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f25838,plain,
    ( spl0_1150
  <=> subclass(universal_class,complement(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f2807,plain,
    ( subclass(universal_class,complement(singleton_relation))
    | member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation)
    | ~ spl0_97
    | ~ spl0_287 ),
    inference(resolution,[],[f2740,f732]) ).

fof(f25846,plain,
    ( spl0_1151
    | ~ spl0_235
    | ~ spl0_1148 ),
    inference(avatar_split_clause,[],[f25836,f25827,f2310,f25843]) ).

fof(f25843,plain,
    ( spl0_1151
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f25827,plain,
    ( spl0_1148
  <=> member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f25836,plain,
    ( member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation)
    | ~ spl0_235
    | ~ spl0_1148 ),
    inference(forward_demodulation,[],[f25829,f2312]) ).

fof(f25829,plain,
    ( member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
    | ~ spl0_1148 ),
    inference(avatar_component_clause,[],[f25827]) ).

fof(f25841,plain,
    ( ~ spl0_1150
    | ~ spl0_235
    | spl0_1149 ),
    inference(avatar_split_clause,[],[f25835,f25831,f2310,f25838]) ).

fof(f25831,plain,
    ( spl0_1149
  <=> subclass(universal_class,complement(identity_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f25835,plain,
    ( ~ subclass(universal_class,complement(singleton_relation))
    | ~ spl0_235
    | spl0_1149 ),
    inference(forward_demodulation,[],[f25832,f2312]) ).

fof(f25832,plain,
    ( ~ subclass(universal_class,complement(identity_relation))
    | spl0_1149 ),
    inference(avatar_component_clause,[],[f25831]) ).

fof(f25834,plain,
    ( spl0_1148
    | spl0_1149
    | ~ spl0_103
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2805,f2739,f761,f25831,f25827]) ).

fof(f2805,plain,
    ( subclass(universal_class,complement(identity_relation))
    | member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
    | ~ spl0_103
    | ~ spl0_287 ),
    inference(resolution,[],[f2740,f762]) ).

fof(f25825,plain,
    ( spl0_1147
    | ~ spl0_38
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f2721,f2698,f372,f25823]) ).

fof(f25823,plain,
    ( spl0_1147
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f2721,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_280 ),
    inference(resolution,[],[f2700,f373]) ).

fof(f25818,plain,
    ( spl0_652
    | spl0_1146
    | ~ spl0_165
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2561,f2499,f1369,f25816,f9912]) ).

fof(f25816,plain,
    ( spl0_1146
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(domain_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f2561,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class) )
    | ~ spl0_165
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f1370]) ).

fof(f25814,plain,
    ( spl0_1145
    | ~ spl0_39
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2243,f2227,f376,f25812]) ).

fof(f376,plain,
    ( spl0_39
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f2243,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 )
    | ~ spl0_39
    | ~ spl0_224 ),
    inference(resolution,[],[f2228,f377]) ).

fof(f377,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f25810,plain,
    ( spl0_1144
    | ~ spl0_39
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2232,f2223,f376,f25808]) ).

fof(f2232,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 )
    | ~ spl0_39
    | ~ spl0_223 ),
    inference(resolution,[],[f2224,f377]) ).

fof(f25770,plain,
    ( spl0_1143
    | ~ spl0_41
    | ~ spl0_1128 ),
    inference(avatar_split_clause,[],[f25374,f24382,f384,f25767]) ).

fof(f25374,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,element_relation))
    | ~ spl0_41
    | ~ spl0_1128 ),
    inference(superposition,[],[f24383,f386]) ).

fof(f24447,plain,
    ( ~ spl0_1141
    | spl0_1142
    | ~ spl0_13
    | ~ spl0_1029 ),
    inference(avatar_split_clause,[],[f22153,f21929,f258,f24444,f24440]) ).

fof(f24440,plain,
    ( spl0_1141
  <=> inductive(complement(omega)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f21929,plain,
    ( spl0_1029
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f22153,plain,
    ( null_class = omega
    | ~ inductive(complement(omega))
    | ~ spl0_13
    | ~ spl0_1029 ),
    inference(resolution,[],[f21930,f259]) ).

fof(f21930,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(X0))
        | null_class = X0 )
    | ~ spl0_1029 ),
    inference(avatar_component_clause,[],[f21929]) ).

fof(f24434,plain,
    ( spl0_1140
    | ~ spl0_9
    | ~ spl0_735 ),
    inference(avatar_split_clause,[],[f12803,f12598,f240,f24431]) ).

fof(f24431,plain,
    ( spl0_1140
  <=> member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f12803,plain,
    ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),universal_class)
    | ~ spl0_9
    | ~ spl0_735 ),
    inference(superposition,[],[f241,f12600]) ).

fof(f24429,plain,
    ( spl0_1139
    | ~ spl0_9
    | ~ spl0_734 ),
    inference(avatar_split_clause,[],[f12725,f12593,f240,f24426]) ).

fof(f24426,plain,
    ( spl0_1139
  <=> member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f12725,plain,
    ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),universal_class)
    | ~ spl0_9
    | ~ spl0_734 ),
    inference(superposition,[],[f241,f12595]) ).

fof(f24424,plain,
    ( spl0_1138
    | ~ spl0_67
    | ~ spl0_681 ),
    inference(avatar_split_clause,[],[f10697,f10598,f556,f24422]) ).

fof(f24422,plain,
    ( spl0_1138
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(cross_product(X0,X1)))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f10697,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(cross_product(X0,X1)))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_681 ),
    inference(resolution,[],[f10599,f557]) ).

fof(f24420,plain,
    ( spl0_1137
    | ~ spl0_67
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10612,f10594,f556,f24418]) ).

fof(f24418,plain,
    ( spl0_1137
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f10612,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_680 ),
    inference(resolution,[],[f10595,f557]) ).

fof(f24416,plain,
    ( spl0_1136
    | ~ spl0_134
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5364,f4849,f1083,f24414]) ).

fof(f24414,plain,
    ( spl0_1136
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f5364,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_134
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5343]) ).

fof(f5343,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_134
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f1084]) ).

fof(f24412,plain,
    ( spl0_1135
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5362,f4849,f1087,f24410]) ).

fof(f24410,plain,
    ( spl0_1135
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f5362,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5345]) ).

fof(f5345,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(resolution,[],[f4850,f1088]) ).

fof(f24408,plain,
    ( spl0_1134
    | ~ spl0_134
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5340,f4845,f1083,f24406]) ).

fof(f24406,plain,
    ( spl0_1134
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f5340,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_134
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5319]) ).

fof(f5319,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_134
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f1084]) ).

fof(f24404,plain,
    ( spl0_1133
    | ~ spl0_135
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5338,f4845,f1087,f24402]) ).

fof(f24402,plain,
    ( spl0_1133
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f5338,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_135
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5321]) ).

fof(f5321,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_135
    | ~ spl0_418 ),
    inference(resolution,[],[f4846,f1088]) ).

fof(f24400,plain,
    ( spl0_1132
    | ~ spl0_27
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5304,f4832,f319,f24398]) ).

fof(f24398,plain,
    ( spl0_1132
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f5304,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
    | ~ spl0_27
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5251]) ).

fof(f5251,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
        | subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) )
    | ~ spl0_27
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f320]) ).

fof(f24396,plain,
    ( spl0_1131
    | ~ spl0_407
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5302,f4832,f4790,f24394]) ).

fof(f5302,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
    | ~ spl0_407
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5253]) ).

fof(f5253,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) )
    | ~ spl0_407
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4791]) ).

fof(f24392,plain,
    ( spl0_1130
    | ~ spl0_406
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5297,f4832,f4786,f24390]) ).

fof(f5297,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
    | ~ spl0_406
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5258]) ).

fof(f5258,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) )
    | ~ spl0_406
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f4787]) ).

fof(f24388,plain,
    ( spl0_1129
    | ~ spl0_405
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5240,f4828,f4782,f24386]) ).

fof(f5240,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
    | ~ spl0_405
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5185]) ).

fof(f5185,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) )
    | ~ spl0_405
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4783]) ).

fof(f24384,plain,
    ( spl0_1128
    | ~ spl0_27
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5239,f4828,f319,f24382]) ).

fof(f5239,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
    | ~ spl0_27
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5186]) ).

fof(f5186,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
        | subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) )
    | ~ spl0_27
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f320]) ).

fof(f24380,plain,
    ( spl0_1127
    | ~ spl0_404
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5236,f4828,f4778,f24378]) ).

fof(f5236,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
    | ~ spl0_404
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5189]) ).

fof(f5189,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) )
    | ~ spl0_404
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f4779]) ).

fof(f24376,plain,
    ( spl0_1126
    | ~ spl0_313
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5075,f4790,f3137,f24374]) ).

fof(f24374,plain,
    ( spl0_1126
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f5075,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
    | ~ spl0_313
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5035]) ).

fof(f5035,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_407 ),
    inference(resolution,[],[f4791,f3138]) ).

fof(f24372,plain,
    ( spl0_1125
    | ~ spl0_313
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5017,f4786,f3137,f24370]) ).

fof(f24370,plain,
    ( spl0_1125
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f5017,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_313
    | ~ spl0_406 ),
    inference(duplicate_literal_removal,[],[f4977]) ).

fof(f4977,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_406 ),
    inference(resolution,[],[f4787,f3138]) ).

fof(f24368,plain,
    ( spl0_1124
    | ~ spl0_313
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4958,f4782,f3137,f24366]) ).

fof(f24366,plain,
    ( spl0_1124
  <=> ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f4958,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
    | ~ spl0_313
    | ~ spl0_405 ),
    inference(duplicate_literal_removal,[],[f4918]) ).

fof(f4918,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_405 ),
    inference(resolution,[],[f4783,f3138]) ).

fof(f24364,plain,
    ( spl0_1123
    | ~ spl0_313
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f4900,f4778,f3137,f24362]) ).

fof(f24362,plain,
    ( spl0_1123
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f4900,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
    | ~ spl0_313
    | ~ spl0_404 ),
    inference(duplicate_literal_removal,[],[f4860]) ).

fof(f4860,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_404 ),
    inference(resolution,[],[f4779,f3138]) ).

fof(f24359,plain,
    ( spl0_1122
    | ~ spl0_372
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4633,f4239,f3802,f24357]) ).

fof(f24357,plain,
    ( spl0_1122
  <=> ! [X0,X1] :
        ( subclass(intersection(complement(X0),null_class),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f4633,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(X0),null_class),X1)
        | null_class = X0 )
    | ~ spl0_372
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4599]) ).

fof(f4599,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(X0),null_class),X1)
        | null_class = X0
        | subclass(intersection(complement(X0),null_class),X1) )
    | ~ spl0_372
    | ~ spl0_391 ),
    inference(resolution,[],[f4240,f3803]) ).

fof(f24355,plain,
    ( spl0_1121
    | ~ spl0_372
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4590,f4235,f3802,f24353]) ).

fof(f24353,plain,
    ( spl0_1121
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f4590,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2) )
    | ~ spl0_372
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4549]) ).

fof(f4549,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2)
        | subclass(intersection(complement(X1),X0),X2) )
    | ~ spl0_372
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f3803]) ).

fof(f24350,plain,
    ( spl0_1120
    | ~ spl0_373
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f4540,f4231,f3806,f24348]) ).

fof(f24348,plain,
    ( spl0_1120
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,complement(X0)),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f4540,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,complement(X0)),X1)
        | null_class = X0 )
    | ~ spl0_373
    | ~ spl0_389 ),
    inference(duplicate_literal_removal,[],[f4506]) ).

fof(f4506,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,complement(X0)),X1)
        | null_class = X0
        | subclass(intersection(null_class,complement(X0)),X1) )
    | ~ spl0_373
    | ~ spl0_389 ),
    inference(resolution,[],[f4232,f3807]) ).

fof(f24346,plain,
    ( spl0_1119
    | ~ spl0_373
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4493,f4227,f3806,f24344]) ).

fof(f24344,plain,
    ( spl0_1119
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f4493,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_373
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4454]) ).

fof(f4454,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_373
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f3807]) ).

fof(f24342,plain,
    ( spl0_1118
    | ~ spl0_351
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f3957,f3777,f3525,f24340]) ).

fof(f24340,plain,
    ( spl0_1118
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f3957,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_351
    | ~ spl0_366 ),
    inference(duplicate_literal_removal,[],[f3926]) ).

fof(f3926,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_351
    | ~ spl0_366 ),
    inference(resolution,[],[f3778,f3526]) ).

fof(f24338,plain,
    ( spl0_1117
    | ~ spl0_352
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f3889,f3769,f3529,f24336]) ).

fof(f24336,plain,
    ( spl0_1117
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f3889,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_352
    | ~ spl0_364 ),
    inference(duplicate_literal_removal,[],[f3860]) ).

fof(f3860,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1))
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_352
    | ~ spl0_364 ),
    inference(resolution,[],[f3770,f3530]) ).

fof(f24333,plain,
    ( spl0_1116
    | ~ spl0_134
    | ~ spl0_347 ),
    inference(avatar_split_clause,[],[f3592,f3506,f1083,f24331]) ).

fof(f24331,plain,
    ( spl0_1116
  <=> ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(null_class,X1),regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f3592,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(null_class,X1),regular(X0)) )
    | ~ spl0_134
    | ~ spl0_347 ),
    inference(duplicate_literal_removal,[],[f3583]) ).

fof(f3583,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(null_class,X1),regular(X0))
        | subclass(intersection(null_class,X1),regular(X0)) )
    | ~ spl0_134
    | ~ spl0_347 ),
    inference(resolution,[],[f3507,f1084]) ).

fof(f24328,plain,
    ( spl0_1115
    | ~ spl0_135
    | ~ spl0_347 ),
    inference(avatar_split_clause,[],[f3591,f3506,f1087,f24326]) ).

fof(f24326,plain,
    ( spl0_1115
  <=> ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(X1,null_class),regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f3591,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(X1,null_class),regular(X0)) )
    | ~ spl0_135
    | ~ spl0_347 ),
    inference(duplicate_literal_removal,[],[f3584]) ).

fof(f3584,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(X1,null_class),regular(X0))
        | subclass(intersection(X1,null_class),regular(X0)) )
    | ~ spl0_135
    | ~ spl0_347 ),
    inference(resolution,[],[f3507,f1088]) ).

fof(f24324,plain,
    ( spl0_1114
    | ~ spl0_327
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3448,f3332,f3210,f24322]) ).

fof(f24322,plain,
    ( spl0_1114
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f3448,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
    | ~ spl0_327
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3443]) ).

fof(f3443,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) )
    | ~ spl0_327
    | ~ spl0_335 ),
    inference(resolution,[],[f3333,f3211]) ).

fof(f24320,plain,
    ( spl0_1113
    | ~ spl0_327
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3434,f3328,f3210,f24317]) ).

fof(f24317,plain,
    ( spl0_1113
  <=> subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f3434,plain,
    ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | ~ spl0_327
    | ~ spl0_334 ),
    inference(duplicate_literal_removal,[],[f3429]) ).

fof(f3429,plain,
    ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | ~ spl0_327
    | ~ spl0_334 ),
    inference(resolution,[],[f3329,f3211]) ).

fof(f24315,plain,
    ( spl0_1112
    | ~ spl0_327
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f3422,f3324,f3210,f24312]) ).

fof(f24312,plain,
    ( spl0_1112
  <=> subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f3422,plain,
    ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | ~ spl0_327
    | ~ spl0_333 ),
    inference(duplicate_literal_removal,[],[f3417]) ).

fof(f3417,plain,
    ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | ~ spl0_327
    | ~ spl0_333 ),
    inference(resolution,[],[f3325,f3211]) ).

fof(f24310,plain,
    ( ~ spl0_1110
    | spl0_1111
    | ~ spl0_1011
    | ~ spl0_1094 ),
    inference(avatar_split_clause,[],[f24239,f23219,f21316,f24307,f24303]) ).

fof(f24303,plain,
    ( spl0_1110
  <=> subclass(x,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f24307,plain,
    ( spl0_1111
  <=> subclass(x,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f23219,plain,
    ( spl0_1094
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f24239,plain,
    ( subclass(x,null_class)
    | ~ subclass(x,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ spl0_1011
    | ~ spl0_1094 ),
    inference(superposition,[],[f23220,f21318]) ).

fof(f23220,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_1094 ),
    inference(avatar_component_clause,[],[f23219]) ).

fof(f24301,plain,
    ( spl0_1109
    | ~ spl0_327
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3409,f3310,f3210,f24299]) ).

fof(f24299,plain,
    ( spl0_1109
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f3409,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
    | ~ spl0_327
    | ~ spl0_332 ),
    inference(duplicate_literal_removal,[],[f3404]) ).

fof(f3404,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) )
    | ~ spl0_327
    | ~ spl0_332 ),
    inference(resolution,[],[f3311,f3211]) ).

fof(f24297,plain,
    ( spl0_1108
    | ~ spl0_134
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3379,f3210,f1083,f24295]) ).

fof(f24295,plain,
    ( spl0_1108
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f3379,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
    | ~ spl0_134
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3346]) ).

fof(f3346,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
        | subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) )
    | ~ spl0_134
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f1084]) ).

fof(f24293,plain,
    ( spl0_1107
    | ~ spl0_135
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3378,f3210,f1087,f24291]) ).

fof(f24291,plain,
    ( spl0_1107
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f3378,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
    | ~ spl0_135
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3347]) ).

fof(f3347,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
        | subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) )
    | ~ spl0_135
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f1088]) ).

fof(f24289,plain,
    ( spl0_1106
    | ~ spl0_320
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3373,f3210,f3172,f24287]) ).

fof(f24287,plain,
    ( spl0_1106
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f3373,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
    | ~ spl0_320
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3353]) ).

fof(f3353,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) )
    | ~ spl0_320
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f3173]) ).

fof(f24285,plain,
    ( spl0_1105
    | ~ spl0_324
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3372,f3210,f3193,f24283]) ).

fof(f24283,plain,
    ( spl0_1105
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f3372,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
    | ~ spl0_324
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3354]) ).

fof(f3354,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) )
    | ~ spl0_324
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f3194]) ).

fof(f24281,plain,
    ( ~ spl0_1104
    | spl0_274
    | ~ spl0_275
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2970,f2818,f2539,f2535,f24278]) ).

fof(f24278,plain,
    ( spl0_1104
  <=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f2970,plain,
    ( null_class = subset_relation
    | ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
    | ~ spl0_275
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f2541]) ).

fof(f2541,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2539]) ).

fof(f24276,plain,
    ( spl0_1103
    | ~ spl0_235
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f2881,f2529,f2310,f24274]) ).

fof(f24274,plain,
    ( spl0_1103
  <=> ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f2881,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_273 ),
    inference(superposition,[],[f2530,f2312]) ).

fof(f24272,plain,
    ( spl0_1102
    | ~ spl0_41
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2865,f2310,f384,f24269]) ).

fof(f24269,plain,
    ( spl0_1102
  <=> singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f2865,plain,
    ( singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation)
    | ~ spl0_41
    | ~ spl0_235 ),
    inference(superposition,[],[f386,f2312]) ).

fof(f24267,plain,
    ( spl0_1101
    | ~ spl0_38
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2717,f2539,f372,f24265]) ).

fof(f24265,plain,
    ( spl0_1101
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f2717,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) )
    | ~ spl0_38
    | ~ spl0_275 ),
    inference(resolution,[],[f2541,f373]) ).

fof(f24263,plain,
    ( spl0_1100
    | ~ spl0_110
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2245,f2227,f819,f24261]) ).

fof(f24261,plain,
    ( spl0_1100
  <=> ! [X0] :
        ( omega = intersection(X0,omega)
        | ~ inductive(intersection(X0,omega)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f819,plain,
    ( spl0_110
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f2245,plain,
    ( ! [X0] :
        ( omega = intersection(X0,omega)
        | ~ inductive(intersection(X0,omega)) )
    | ~ spl0_110
    | ~ spl0_224 ),
    inference(resolution,[],[f2228,f820]) ).

fof(f820,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f819]) ).

fof(f24259,plain,
    ( spl0_1099
    | ~ spl0_110
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2234,f2223,f819,f24257]) ).

fof(f24257,plain,
    ( spl0_1099
  <=> ! [X0] :
        ( omega = intersection(omega,X0)
        | ~ inductive(intersection(omega,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f2234,plain,
    ( ! [X0] :
        ( omega = intersection(omega,X0)
        | ~ inductive(intersection(omega,X0)) )
    | ~ spl0_110
    | ~ spl0_223 ),
    inference(resolution,[],[f2224,f820]) ).

fof(f23893,plain,
    ( ~ spl0_1098
    | spl0_813
    | ~ spl0_1080 ),
    inference(avatar_split_clause,[],[f23310,f23151,f15280,f23890]) ).

fof(f23890,plain,
    ( spl0_1098
  <=> subclass(composition_function,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f15280,plain,
    ( spl0_813
  <=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f23151,plain,
    ( spl0_1080
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f23310,plain,
    ( ~ subclass(composition_function,subset_relation)
    | spl0_813
    | ~ spl0_1080 ),
    inference(resolution,[],[f23152,f15282]) ).

fof(f15282,plain,
    ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
    | spl0_813 ),
    inference(avatar_component_clause,[],[f15280]) ).

fof(f23152,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_1080 ),
    inference(avatar_component_clause,[],[f23151]) ).

fof(f23233,plain,
    ( spl0_1097
    | ~ spl0_268
    | ~ spl0_681 ),
    inference(avatar_split_clause,[],[f10728,f10598,f2499,f23231]) ).

fof(f23231,plain,
    ( spl0_1097
  <=> ! [X0] :
        ( ~ subclass(universal_class,flip(X0))
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f10728,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(X0))
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_681 ),
    inference(resolution,[],[f10599,f2500]) ).

fof(f23229,plain,
    ( spl0_1096
    | ~ spl0_268
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10643,f10594,f2499,f23227]) ).

fof(f23227,plain,
    ( spl0_1096
  <=> ! [X0] :
        ( ~ subclass(universal_class,rotate(X0))
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f10643,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(X0))
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_268
    | ~ spl0_680 ),
    inference(resolution,[],[f10595,f2500]) ).

fof(f23225,plain,
    ( spl0_1095
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4731,f4270,f2364,f2310,f23223]) ).

fof(f23223,plain,
    ( spl0_1095
  <=> ! [X0] :
        ( ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(subset_relation,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f4731,plain,
    ( ! [X0] :
        ( ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(subset_relation,X0)) )
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_397 ),
    inference(forward_demodulation,[],[f4730,f2312]) ).

fof(f4730,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0) )
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_397 ),
    inference(forward_demodulation,[],[f4710,f2312]) ).

fof(f4710,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0) )
    | ~ spl0_244
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4697]) ).

fof(f4697,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0)
        | subclass(identity_relation,intersection(subset_relation,X0)) )
    | ~ spl0_244
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f2365]) ).

fof(f23221,plain,
    ( spl0_1094
    | ~ spl0_27
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4725,f4270,f319,f23219]) ).

fof(f4725,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4673]) ).

fof(f4673,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X0,X1)) )
    | ~ spl0_27
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f320]) ).

fof(f23217,plain,
    ( spl0_1093
    | ~ spl0_243
    | ~ spl0_397 ),
    inference(avatar_split_clause,[],[f4716,f4270,f2360,f23215]) ).

fof(f23215,plain,
    ( spl0_1093
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f4716,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_243
    | ~ spl0_397 ),
    inference(duplicate_literal_removal,[],[f4683]) ).

fof(f4683,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(element_relation,X0)) )
    | ~ spl0_243
    | ~ spl0_397 ),
    inference(resolution,[],[f4271,f2361]) ).

fof(f23212,plain,
    ( spl0_1092
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4635,f4239,f323,f23210]) ).

fof(f23210,plain,
    ( spl0_1092
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f323,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f4635,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X1 )
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4597]) ).

fof(f4597,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X1
        | subclass(intersection(X0,null_class),X1) )
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(resolution,[],[f4240,f324]) ).

fof(f324,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f323]) ).

fof(f23208,plain,
    ( spl0_1091
    | ~ spl0_28
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4592,f4235,f323,f23206]) ).

fof(f23206,plain,
    ( spl0_1091
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f4592,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1) )
    | ~ spl0_28
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4547]) ).

fof(f4547,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1)
        | subclass(intersection(X2,X0),X1) )
    | ~ spl0_28
    | ~ spl0_390 ),
    inference(resolution,[],[f4236,f324]) ).

fof(f23203,plain,
    ( spl0_1090
    | ~ spl0_28
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f4542,f4231,f323,f23201]) ).

fof(f23201,plain,
    ( spl0_1090
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f4542,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X1 )
    | ~ spl0_28
    | ~ spl0_389 ),
    inference(duplicate_literal_removal,[],[f4504]) ).

fof(f4504,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X1
        | subclass(intersection(null_class,X0),X1) )
    | ~ spl0_28
    | ~ spl0_389 ),
    inference(resolution,[],[f4232,f324]) ).

fof(f23199,plain,
    ( spl0_1089
    | ~ spl0_28
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4496,f4227,f323,f23197]) ).

fof(f23197,plain,
    ( spl0_1089
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f4496,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1) )
    | ~ spl0_28
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4451]) ).

fof(f4451,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1)
        | subclass(intersection(X0,X2),X1) )
    | ~ spl0_28
    | ~ spl0_388 ),
    inference(resolution,[],[f4228,f324]) ).

fof(f23195,plain,
    ( spl0_1088
    | ~ spl0_351
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4439,f4223,f3525,f23193]) ).

fof(f23193,plain,
    ( spl0_1088
  <=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f4439,plain,
    ( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_351
    | ~ spl0_387 ),
    inference(duplicate_literal_removal,[],[f4409]) ).

fof(f4409,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),intersection(X0,X1))
        | null_class = intersection(complement(X0),intersection(X0,X1)) )
    | ~ spl0_351
    | ~ spl0_387 ),
    inference(resolution,[],[f4224,f3526]) ).

fof(f23181,plain,
    ( spl0_1087
    | ~ spl0_351
    | ~ spl0_386 ),
    inference(avatar_split_clause,[],[f4398,f4219,f3525,f23179]) ).

fof(f23179,plain,
    ( spl0_1087
  <=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f4398,plain,
    ( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_351
    | ~ spl0_386 ),
    inference(duplicate_literal_removal,[],[f4368]) ).

fof(f4368,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),intersection(X1,X0))
        | null_class = intersection(complement(X0),intersection(X1,X0)) )
    | ~ spl0_351
    | ~ spl0_386 ),
    inference(resolution,[],[f4220,f3526]) ).

fof(f23177,plain,
    ( spl0_1086
    | ~ spl0_352
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f4351,f4215,f3529,f23175]) ).

fof(f23175,plain,
    ( spl0_1086
  <=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f4351,plain,
    ( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_352
    | ~ spl0_385 ),
    inference(duplicate_literal_removal,[],[f4321]) ).

fof(f4321,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,X1),complement(X0))
        | null_class = intersection(intersection(X0,X1),complement(X0)) )
    | ~ spl0_352
    | ~ spl0_385 ),
    inference(resolution,[],[f4216,f3530]) ).

fof(f23173,plain,
    ( spl0_1085
    | ~ spl0_352
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f4312,f4211,f3529,f23171]) ).

fof(f23171,plain,
    ( spl0_1085
  <=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f4312,plain,
    ( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_352
    | ~ spl0_384 ),
    inference(duplicate_literal_removal,[],[f4282]) ).

fof(f4282,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,X1),complement(X1))
        | null_class = intersection(intersection(X0,X1),complement(X1)) )
    | ~ spl0_352
    | ~ spl0_384 ),
    inference(resolution,[],[f4212,f3530]) ).

fof(f23169,plain,
    ( spl0_1084
    | ~ spl0_130
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3377,f3210,f1012,f23167]) ).

fof(f23167,plain,
    ( spl0_1084
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f3377,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3348]) ).

fof(f3348,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_130
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f1013]) ).

fof(f23165,plain,
    ( spl0_1083
    | ~ spl0_302
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3374,f3210,f2940,f23163]) ).

fof(f23163,plain,
    ( spl0_1083
  <=> ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f3374,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3352]) ).

fof(f3352,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_302
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f2941]) ).

fof(f23161,plain,
    ( spl0_1082
    | ~ spl0_310
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3370,f3210,f3092,f23159]) ).

fof(f23159,plain,
    ( spl0_1082
  <=> ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f3370,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3363]) ).

fof(f3363,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f3093]) ).

fof(f23157,plain,
    ( spl0_1081
    | ~ spl0_310
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3235,f3137,f3092,f23155]) ).

fof(f23155,plain,
    ( spl0_1081
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f3235,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3226]) ).

fof(f3226,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_310
    | ~ spl0_313 ),
    inference(resolution,[],[f3138,f3093]) ).

fof(f23153,plain,
    ( spl0_1080
    | ~ spl0_130
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3231,f3137,f1012,f23151]) ).

fof(f3231,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_130
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3230]) ).

fof(f3230,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_130
    | ~ spl0_313 ),
    inference(resolution,[],[f3138,f1013]) ).

fof(f23140,plain,
    ( ~ spl0_350
    | spl0_1079
    | ~ spl0_144
    | ~ spl0_235
    | ~ spl0_309 ),
    inference(avatar_split_clause,[],[f3084,f3070,f2310,f1167,f23137,f3520]) ).

fof(f3520,plain,
    ( spl0_350
  <=> member(regular(singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f23137,plain,
    ( spl0_1079
  <=> member(regular(singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f1167,plain,
    ( spl0_144
  <=> ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f3084,plain,
    ( member(regular(singleton_relation),singleton_relation)
    | ~ member(regular(singleton_relation),subset_relation)
    | ~ spl0_144
    | ~ spl0_235
    | ~ spl0_309 ),
    inference(forward_demodulation,[],[f3080,f2312]) ).

fof(f3080,plain,
    ( ~ member(regular(singleton_relation),subset_relation)
    | member(regular(singleton_relation),identity_relation)
    | ~ spl0_144
    | ~ spl0_309 ),
    inference(resolution,[],[f3072,f1168]) ).

fof(f1168,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1167]) ).

fof(f23135,plain,
    ( spl0_1078
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_1051 ),
    inference(avatar_split_clause,[],[f22712,f22026,f2310,f393,f23132]) ).

fof(f23132,plain,
    ( spl0_1078
  <=> subclass(singleton_relation,intersection(subset_relation,subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f22026,plain,
    ( spl0_1051
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f22712,plain,
    ( subclass(singleton_relation,intersection(subset_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_235
    | ~ spl0_1051 ),
    inference(forward_demodulation,[],[f22705,f2312]) ).

fof(f22705,plain,
    ( subclass(identity_relation,intersection(subset_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_1051 ),
    inference(superposition,[],[f22027,f395]) ).

fof(f22027,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
    | ~ spl0_1051 ),
    inference(avatar_component_clause,[],[f22026]) ).

fof(f23130,plain,
    ( spl0_1077
    | ~ spl0_37
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2921,f2503,f359,f23128]) ).

fof(f23128,plain,
    ( spl0_1077
  <=> ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f2503,plain,
    ( spl0_269
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f2921,plain,
    ( ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_37
    | ~ spl0_269 ),
    inference(resolution,[],[f2504,f360]) ).

fof(f2504,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f2503]) ).

fof(f23126,plain,
    ( spl0_1076
    | ~ spl0_235
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2877,f2364,f2310,f23124]) ).

fof(f23124,plain,
    ( spl0_1076
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),subset_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f2877,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),subset_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_244 ),
    inference(superposition,[],[f2365,f2312]) ).

fof(f23122,plain,
    ( ~ spl0_1074
    | spl0_1075
    | ~ spl0_112
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2779,f2731,f884,f23119,f23115]) ).

fof(f23115,plain,
    ( spl0_1074
  <=> subclass(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f23119,plain,
    ( spl0_1075
  <=> null_class = complement(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f884,plain,
    ( spl0_112
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2779,plain,
    ( null_class = complement(element_relation)
    | ~ subclass(complement(element_relation),singleton_relation)
    | ~ spl0_112
    | ~ spl0_285 ),
    inference(duplicate_literal_removal,[],[f2771]) ).

fof(f2771,plain,
    ( null_class = complement(element_relation)
    | ~ subclass(complement(element_relation),singleton_relation)
    | null_class = complement(element_relation)
    | ~ spl0_112
    | ~ spl0_285 ),
    inference(resolution,[],[f2732,f885]) ).

fof(f885,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f884]) ).

fof(f23113,plain,
    ( ~ spl0_1073
    | ~ spl0_235
    | spl0_1071 ),
    inference(avatar_split_clause,[],[f23108,f23100,f2310,f23110]) ).

fof(f23110,plain,
    ( spl0_1073
  <=> subclass(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f23100,plain,
    ( spl0_1071
  <=> subclass(complement(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f23108,plain,
    ( ~ subclass(complement(subset_relation),singleton_relation)
    | ~ spl0_235
    | spl0_1071 ),
    inference(forward_demodulation,[],[f23102,f2312]) ).

fof(f23102,plain,
    ( ~ subclass(complement(subset_relation),identity_relation)
    | spl0_1071 ),
    inference(avatar_component_clause,[],[f23100]) ).

fof(f23107,plain,
    ( ~ spl0_1071
    | spl0_1072
    | ~ spl0_112
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2770,f2723,f884,f23104,f23100]) ).

fof(f23104,plain,
    ( spl0_1072
  <=> null_class = complement(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f2770,plain,
    ( null_class = complement(subset_relation)
    | ~ subclass(complement(subset_relation),identity_relation)
    | ~ spl0_112
    | ~ spl0_283 ),
    inference(duplicate_literal_removal,[],[f2762]) ).

fof(f2762,plain,
    ( null_class = complement(subset_relation)
    | ~ subclass(complement(subset_relation),identity_relation)
    | null_class = complement(subset_relation)
    | ~ spl0_112
    | ~ spl0_283 ),
    inference(resolution,[],[f2724,f885]) ).

fof(f22986,plain,
    ( ~ spl0_275
    | ~ spl0_1070 ),
    inference(avatar_contradiction_clause,[],[f22970]) ).

fof(f22970,plain,
    ( $false
    | ~ spl0_275
    | ~ spl0_1070 ),
    inference(resolution,[],[f22962,f2541]) ).

fof(f22962,plain,
    ( ! [X0] : ~ member(regular(subset_relation),X0)
    | ~ spl0_1070 ),
    inference(avatar_component_clause,[],[f22961]) ).

fof(f22961,plain,
    ( spl0_1070
  <=> ! [X0] : ~ member(regular(subset_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f22985,plain,
    ( ~ spl0_470
    | ~ spl0_1070 ),
    inference(avatar_contradiction_clause,[],[f22973]) ).

fof(f22973,plain,
    ( $false
    | ~ spl0_470
    | ~ spl0_1070 ),
    inference(resolution,[],[f22962,f6193]) ).

fof(f22963,plain,
    ( spl0_1069
    | spl0_1070
    | ~ spl0_275
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f2715,f2558,f2539,f22961,f22957]) ).

fof(f22957,plain,
    ( spl0_1069
  <=> member(regular(subset_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f2715,plain,
    ( ! [X0] :
        ( ~ member(regular(subset_relation),X0)
        | member(regular(subset_relation),universal_class) )
    | ~ spl0_275
    | ~ spl0_276 ),
    inference(resolution,[],[f2541,f2559]) ).

fof(f22954,plain,
    ( spl0_1067
    | spl0_1068
    | ~ spl0_234
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f2671,f2558,f2304,f22952,f22948]) ).

fof(f22948,plain,
    ( spl0_1067
  <=> member(regular(identity_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f22952,plain,
    ( spl0_1068
  <=> ! [X0] : ~ member(regular(identity_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f2671,plain,
    ( ! [X0] :
        ( ~ member(regular(identity_relation),X0)
        | member(regular(identity_relation),universal_class) )
    | ~ spl0_234
    | ~ spl0_276 ),
    inference(resolution,[],[f2559,f2306]) ).

fof(f22755,plain,
    ( spl0_1066
    | ~ spl0_41
    | ~ spl0_1051 ),
    inference(avatar_split_clause,[],[f22700,f22026,f384,f22752]) ).

fof(f22752,plain,
    ( spl0_1066
  <=> subclass(singleton_relation,intersection(element_relation,element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f22700,plain,
    ( subclass(singleton_relation,intersection(element_relation,element_relation))
    | ~ spl0_41
    | ~ spl0_1051 ),
    inference(superposition,[],[f22027,f386]) ).

fof(f22164,plain,
    ( ~ spl0_1065
    | ~ spl0_926
    | ~ spl0_1024 ),
    inference(avatar_split_clause,[],[f22116,f21906,f18166,f22161]) ).

fof(f22161,plain,
    ( spl0_1065
  <=> subclass(element_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f21906,plain,
    ( spl0_1024
  <=> ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f22116,plain,
    ( ~ subclass(element_relation,null_class)
    | ~ spl0_926
    | ~ spl0_1024 ),
    inference(resolution,[],[f21907,f18167]) ).

fof(f21907,plain,
    ( ! [X0] :
        ( member(regular(singleton_relation),X0)
        | ~ subclass(element_relation,X0) )
    | ~ spl0_1024 ),
    inference(avatar_component_clause,[],[f21906]) ).

fof(f22086,plain,
    ( spl0_1064
    | ~ spl0_50
    | ~ spl0_786 ),
    inference(avatar_split_clause,[],[f14743,f14704,f452,f22084]) ).

fof(f22084,plain,
    ( spl0_1064
  <=> ! [X0] : intersection(null_class,X0) = intersection(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f14743,plain,
    ( ! [X0] : intersection(null_class,X0) = intersection(X0,null_class)
    | ~ spl0_50
    | ~ spl0_786 ),
    inference(superposition,[],[f453,f14706]) ).

fof(f22082,plain,
    ( spl0_1063
    | ~ spl0_9
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f10977,f10793,f240,f22079]) ).

fof(f22079,plain,
    ( spl0_1063
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f10977,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class)
    | ~ spl0_9
    | ~ spl0_686 ),
    inference(superposition,[],[f241,f10795]) ).

fof(f22077,plain,
    ( spl0_1062
    | ~ spl0_9
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10903,f10783,f240,f22074]) ).

fof(f22074,plain,
    ( spl0_1062
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f10903,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class)
    | ~ spl0_9
    | ~ spl0_684 ),
    inference(superposition,[],[f241,f10785]) ).

fof(f22072,plain,
    ( spl0_1061
    | ~ spl0_9
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f10829,f10778,f240,f22069]) ).

fof(f22069,plain,
    ( spl0_1061
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f10829,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class)
    | ~ spl0_9
    | ~ spl0_683 ),
    inference(superposition,[],[f241,f10780]) ).

fof(f22067,plain,
    ( spl0_642
    | ~ spl0_1060
    | ~ spl0_361
    | ~ spl0_681 ),
    inference(avatar_split_clause,[],[f10709,f10598,f3757,f22064,f9715]) ).

fof(f9715,plain,
    ( spl0_642
  <=> ! [X0] : member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f22064,plain,
    ( spl0_1060
  <=> subclass(universal_class,flip(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f10709,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(subset_relation))
        | member(X0,universal_class) )
    | ~ spl0_361
    | ~ spl0_681 ),
    inference(resolution,[],[f10599,f3758]) ).

fof(f22062,plain,
    ( spl0_642
    | ~ spl0_1059
    | ~ spl0_361
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10624,f10594,f3757,f22059,f9715]) ).

fof(f22059,plain,
    ( spl0_1059
  <=> subclass(universal_class,rotate(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f10624,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(subset_relation))
        | member(X0,universal_class) )
    | ~ spl0_361
    | ~ spl0_680 ),
    inference(resolution,[],[f10595,f3758]) ).

fof(f22057,plain,
    ( ~ spl0_1058
    | spl0_652
    | ~ spl0_66
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6764,f6441,f552,f9912,f22054]) ).

fof(f22054,plain,
    ( spl0_1058
  <=> subclass(domain_relation,complement(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f552,plain,
    ( spl0_66
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f6764,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(domain_relation)) )
    | ~ spl0_66
    | ~ spl0_489 ),
    inference(duplicate_literal_removal,[],[f6763]) ).

fof(f6763,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(domain_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_66
    | ~ spl0_489 ),
    inference(resolution,[],[f6442,f553]) ).

fof(f553,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f552]) ).

fof(f22052,plain,
    ( spl0_1057
    | ~ spl0_134
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5306,f4832,f1083,f22050]) ).

fof(f22050,plain,
    ( spl0_1057
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f5306,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0))
    | ~ spl0_134
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5249]) ).

fof(f5249,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X0))
        | subclass(intersection(X0,X1),intersection(X0,X0)) )
    | ~ spl0_134
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f1084]) ).

fof(f22048,plain,
    ( spl0_1056
    | ~ spl0_135
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5303,f4832,f1087,f22046]) ).

fof(f22046,plain,
    ( spl0_1056
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f5303,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0))
    | ~ spl0_135
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5252]) ).

fof(f5252,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X0))
        | subclass(intersection(X0,X1),intersection(X1,X0)) )
    | ~ spl0_135
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f1088]) ).

fof(f22044,plain,
    ( spl0_1055
    | ~ spl0_320
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5294,f4832,f3172,f22042]) ).

fof(f22042,plain,
    ( spl0_1055
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f5294,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
    | ~ spl0_320
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5262]) ).

fof(f5262,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) )
    | ~ spl0_320
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f3173]) ).

fof(f22040,plain,
    ( spl0_1054
    | ~ spl0_324
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5293,f4832,f3193,f22038]) ).

fof(f5293,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
    | ~ spl0_324
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5263]) ).

fof(f5263,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) )
    | ~ spl0_324
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f3194]) ).

fof(f22036,plain,
    ( spl0_1053
    | ~ spl0_332
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5291,f4832,f3310,f22034]) ).

fof(f22034,plain,
    ( spl0_1053
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f5291,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
    | ~ spl0_332
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5274]) ).

fof(f5274,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) )
    | ~ spl0_332
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f3311]) ).

fof(f22032,plain,
    ( spl0_1052
    | ~ spl0_335
    | ~ spl0_417 ),
    inference(avatar_split_clause,[],[f5290,f4832,f3332,f22030]) ).

fof(f5290,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
    | ~ spl0_335
    | ~ spl0_417 ),
    inference(duplicate_literal_removal,[],[f5275]) ).

fof(f5275,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) )
    | ~ spl0_335
    | ~ spl0_417 ),
    inference(resolution,[],[f4833,f3333]) ).

fof(f22028,plain,
    ( spl0_1051
    | ~ spl0_135
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5238,f4828,f1087,f22026]) ).

fof(f5238,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
    | ~ spl0_135
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5187]) ).

fof(f5187,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X1))
        | subclass(intersection(X0,X1),intersection(X1,X1)) )
    | ~ spl0_135
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f1088]) ).

fof(f22024,plain,
    ( spl0_1050
    | ~ spl0_49
    | ~ spl0_1011 ),
    inference(avatar_split_clause,[],[f21741,f21316,f448,f22022]) ).

fof(f22022,plain,
    ( spl0_1050
  <=> ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
        | ~ member(X0,x) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f21741,plain,
    ( ! [X0] :
        ( member(X0,null_class)
        | ~ member(X0,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
        | ~ member(X0,x) )
    | ~ spl0_49
    | ~ spl0_1011 ),
    inference(superposition,[],[f449,f21318]) ).

fof(f22020,plain,
    ( spl0_1049
    | ~ spl0_320
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5229,f4828,f3172,f22018]) ).

fof(f22018,plain,
    ( spl0_1049
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f5229,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
    | ~ spl0_320
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5197]) ).

fof(f5197,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) )
    | ~ spl0_320
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f3173]) ).

fof(f22016,plain,
    ( spl0_1048
    | ~ spl0_324
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5228,f4828,f3193,f22014]) ).

fof(f22014,plain,
    ( spl0_1048
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f5228,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
    | ~ spl0_324
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5198]) ).

fof(f5198,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) )
    | ~ spl0_324
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f3194]) ).

fof(f22012,plain,
    ( spl0_1047
    | ~ spl0_332
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5226,f4828,f3310,f22010]) ).

fof(f22010,plain,
    ( spl0_1047
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f5226,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
    | ~ spl0_332
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5209]) ).

fof(f5209,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) )
    | ~ spl0_332
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f3311]) ).

fof(f22008,plain,
    ( spl0_1046
    | ~ spl0_335
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f5225,f4828,f3332,f22006]) ).

fof(f22006,plain,
    ( spl0_1046
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f5225,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
    | ~ spl0_335
    | ~ spl0_416 ),
    inference(duplicate_literal_removal,[],[f5210]) ).

fof(f5210,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) )
    | ~ spl0_335
    | ~ spl0_416 ),
    inference(resolution,[],[f4829,f3333]) ).

fof(f22004,plain,
    ( spl0_1045
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5078,f4790,f323,f22002]) ).

fof(f22002,plain,
    ( spl0_1045
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f5078,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1)
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5032]) ).

fof(f5032,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X1)
        | subclass(intersection(X0,intersection(X1,X2)),X1) )
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(resolution,[],[f4791,f324]) ).

fof(f22000,plain,
    ( spl0_1044
    | ~ spl0_28
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5020,f4786,f323,f21998]) ).

fof(f21998,plain,
    ( spl0_1044
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f5020,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2)
    | ~ spl0_28
    | ~ spl0_406 ),
    inference(duplicate_literal_removal,[],[f4974]) ).

fof(f4974,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X2)
        | subclass(intersection(X0,intersection(X1,X2)),X2) )
    | ~ spl0_28
    | ~ spl0_406 ),
    inference(resolution,[],[f4787,f324]) ).

fof(f21996,plain,
    ( spl0_1043
    | ~ spl0_28
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4961,f4782,f323,f21994]) ).

fof(f21994,plain,
    ( spl0_1043
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f4961,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0)
    | ~ spl0_28
    | ~ spl0_405 ),
    inference(duplicate_literal_removal,[],[f4915]) ).

fof(f4915,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X0)
        | subclass(intersection(intersection(X0,X1),X2),X0) )
    | ~ spl0_28
    | ~ spl0_405 ),
    inference(resolution,[],[f4783,f324]) ).

fof(f21992,plain,
    ( spl0_1042
    | ~ spl0_28
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f4903,f4778,f323,f21990]) ).

fof(f21990,plain,
    ( spl0_1042
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f4903,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1)
    | ~ spl0_28
    | ~ spl0_404 ),
    inference(duplicate_literal_removal,[],[f4857]) ).

fof(f4857,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X1)
        | subclass(intersection(intersection(X0,X1),X2),X1) )
    | ~ spl0_28
    | ~ spl0_404 ),
    inference(resolution,[],[f4779,f324]) ).

fof(f21988,plain,
    ( spl0_1041
    | ~ spl0_313
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3450,f3332,f3137,f21986]) ).

fof(f21986,plain,
    ( spl0_1041
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f3450,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
    | ~ spl0_313
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3441]) ).

fof(f3441,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_335 ),
    inference(resolution,[],[f3333,f3138]) ).

fof(f21984,plain,
    ( spl0_1040
    | ~ spl0_28
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3437,f3328,f323,f21981]) ).

fof(f21981,plain,
    ( spl0_1040
  <=> subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f3437,plain,
    ( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_28
    | ~ spl0_334 ),
    inference(duplicate_literal_removal,[],[f3426]) ).

fof(f3426,plain,
    ( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_28
    | ~ spl0_334 ),
    inference(resolution,[],[f3329,f324]) ).

fof(f21976,plain,
    ( spl0_1039
    | ~ spl0_28
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f3425,f3324,f323,f21973]) ).

fof(f21973,plain,
    ( spl0_1039
  <=> subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f3425,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_28
    | ~ spl0_333 ),
    inference(duplicate_literal_removal,[],[f3414]) ).

fof(f3414,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_28
    | ~ spl0_333 ),
    inference(resolution,[],[f3325,f324]) ).

fof(f21971,plain,
    ( spl0_1038
    | ~ spl0_313
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3411,f3310,f3137,f21969]) ).

fof(f21969,plain,
    ( spl0_1038
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f3411,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
    | ~ spl0_313
    | ~ spl0_332 ),
    inference(duplicate_literal_removal,[],[f3402]) ).

fof(f3402,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
        | subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_313
    | ~ spl0_332 ),
    inference(resolution,[],[f3311,f3138]) ).

fof(f21967,plain,
    ( spl0_1037
    | ~ spl0_14
    | ~ spl0_328 ),
    inference(avatar_split_clause,[],[f3390,f3214,f262,f21965]) ).

fof(f21965,plain,
    ( spl0_1037
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f3214,plain,
    ( spl0_328
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f3390,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(X0),universal_class) )
    | ~ spl0_14
    | ~ spl0_328 ),
    inference(resolution,[],[f3215,f264]) ).

fof(f3215,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_328 ),
    inference(avatar_component_clause,[],[f3214]) ).

fof(f21963,plain,
    ( spl0_1036
    | ~ spl0_50
    | ~ spl0_286
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3381,f3210,f2735,f452,f21960]) ).

fof(f21960,plain,
    ( spl0_1036
  <=> subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f3381,plain,
    ( subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class)))
    | ~ spl0_50
    | ~ spl0_286
    | ~ spl0_327 ),
    inference(forward_demodulation,[],[f3376,f453]) ).

fof(f3376,plain,
    ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | ~ spl0_286
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3349]) ).

fof(f3349,plain,
    ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | ~ spl0_286
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f2736]) ).

fof(f21958,plain,
    ( spl0_1035
    | ~ spl0_27
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3297,f3149,f319,f21956]) ).

fof(f21956,plain,
    ( spl0_1035
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f3297,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f3268]) ).

fof(f3268,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0))
        | subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_316 ),
    inference(resolution,[],[f3150,f320]) ).

fof(f21954,plain,
    ( spl0_1034
    | ~ spl0_134
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3233,f3137,f1083,f21952]) ).

fof(f21952,plain,
    ( spl0_1034
  <=> ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f3233,plain,
    ( ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
    | ~ spl0_134
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3228]) ).

fof(f3228,plain,
    ( ! [X0] :
        ( subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_134
    | ~ spl0_313 ),
    inference(resolution,[],[f3138,f1084]) ).

fof(f21950,plain,
    ( spl0_1033
    | ~ spl0_135
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3232,f3137,f1087,f21948]) ).

fof(f21948,plain,
    ( spl0_1033
  <=> ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f3232,plain,
    ( ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_135
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3229]) ).

fof(f3229,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) )
    | ~ spl0_135
    | ~ spl0_313 ),
    inference(resolution,[],[f3138,f1088]) ).

fof(f21946,plain,
    ( ~ spl0_1032
    | ~ spl0_20
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f3075,f3065,f287,f21943]) ).

fof(f21943,plain,
    ( spl0_1032
  <=> member(regular(singleton_relation),compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f3075,plain,
    ( ~ member(regular(singleton_relation),compose(element_relation,complement(singleton_relation)))
    | ~ spl0_20
    | ~ spl0_308 ),
    inference(resolution,[],[f3067,f288]) ).

fof(f21941,plain,
    ( spl0_231
    | ~ spl0_1031
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3048,f2818,f2310,f2304,f21938,f2282]) ).

fof(f21938,plain,
    ( spl0_1031
  <=> subclass(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f3048,plain,
    ( ~ subclass(singleton_relation,complement(subset_relation))
    | null_class = singleton_relation
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f3014,f2312]) ).

fof(f3014,plain,
    ( null_class = singleton_relation
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f2981,f2312]) ).

fof(f2981,plain,
    ( null_class = identity_relation
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_234
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f2306]) ).

fof(f21936,plain,
    ( ~ spl0_1030
    | ~ spl0_145
    | ~ spl0_1011 ),
    inference(avatar_split_clause,[],[f21800,f21316,f1171,f21933]) ).

fof(f21933,plain,
    ( spl0_1030
  <=> member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f21800,plain,
    ( ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(x))
    | ~ spl0_145
    | ~ spl0_1011 ),
    inference(trivial_inequality_removal,[],[f21715]) ).

fof(f21715,plain,
    ( null_class != null_class
    | ~ member(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),domain_of(x))
    | ~ spl0_145
    | ~ spl0_1011 ),
    inference(superposition,[],[f1172,f21318]) ).

fof(f21931,plain,
    ( spl0_1029
    | ~ spl0_23
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2992,f2818,f299,f21929]) ).

fof(f2992,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_23
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f2964]) ).

fof(f2964,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0))
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f300]) ).

fof(f21927,plain,
    ( ~ spl0_1028
    | spl0_231
    | ~ spl0_232
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2972,f2818,f2286,f2282,f21924]) ).

fof(f21924,plain,
    ( spl0_1028
  <=> subclass(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f2972,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(element_relation))
    | ~ spl0_232
    | ~ spl0_292 ),
    inference(resolution,[],[f2819,f2288]) ).

fof(f21922,plain,
    ( spl0_652
    | ~ spl0_1027
    | ~ spl0_66
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2584,f2499,f552,f21919,f9912]) ).

fof(f21919,plain,
    ( spl0_1027
  <=> subclass(universal_class,complement(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f2584,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(domain_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_66
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f553]) ).

fof(f21917,plain,
    ( spl0_1026
    | ~ spl0_106
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2562,f2499,f802,f21915]) ).

fof(f21915,plain,
    ( spl0_1026
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f2562,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(universal_class,X0) )
    | ~ spl0_106
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f803]) ).

fof(f21912,plain,
    ( spl0_1025
    | ~ spl0_38
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2437,f2304,f372,f21910]) ).

fof(f21910,plain,
    ( spl0_1025
  <=> ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f2437,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) )
    | ~ spl0_38
    | ~ spl0_234 ),
    inference(resolution,[],[f2306,f373]) ).

fof(f21908,plain,
    ( spl0_1024
    | ~ spl0_38
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f2327,f2286,f372,f21906]) ).

fof(f2327,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_38
    | ~ spl0_232 ),
    inference(resolution,[],[f2288,f373]) ).

fof(f21903,plain,
    ( spl0_1023
    | ~ spl0_43
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2240,f2223,f393,f21900]) ).

fof(f21900,plain,
    ( spl0_1023
  <=> subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f2240,plain,
    ( subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_43
    | ~ spl0_223 ),
    inference(superposition,[],[f2224,f395]) ).

fof(f21897,plain,
    ( spl0_1022
    | ~ spl0_41
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2239,f2223,f384,f21894]) ).

fof(f21894,plain,
    ( spl0_1022
  <=> subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f2239,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_41
    | ~ spl0_223 ),
    inference(superposition,[],[f2224,f386]) ).

fof(f21622,plain,
    ( spl0_1021
    | ~ spl0_90
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1842,f1812,f686,f21620]) ).

fof(f21620,plain,
    ( spl0_1021
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f686,plain,
    ( spl0_90
  <=> ! [X9,X11,X10] :
        ( ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f1812,plain,
    ( spl0_204
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f1842,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_90
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f687]) ).

fof(f687,plain,
    ( ! [X10,X11,X9] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | ~ operation(X10) )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f686]) ).

fof(f1813,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_204 ),
    inference(avatar_component_clause,[],[f1812]) ).

fof(f21618,plain,
    ( spl0_1020
    | ~ spl0_90
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1816,f1803,f686,f21616]) ).

fof(f21616,plain,
    ( spl0_1020
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f1803,plain,
    ( spl0_202
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f1816,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_90
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f687]) ).

fof(f1804,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f1803]) ).

fof(f21553,plain,
    ( spl0_1019
    | ~ spl0_111
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2128,f2124,f823,f21551]) ).

fof(f21551,plain,
    ( spl0_1019
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f2124,plain,
    ( spl0_221
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f2128,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_221 ),
    inference(resolution,[],[f2125,f824]) ).

fof(f2125,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f2124]) ).

fof(f21520,plain,
    ( spl0_1018
    | ~ spl0_101
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1879,f1868,f750,f21518]) ).

fof(f21518,plain,
    ( spl0_1018
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(composition_function,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ homomorphism(X3,X0,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))))),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)))))))),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(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))))))),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)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(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(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))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(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(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))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f750,plain,
    ( spl0_101
  <=> ! [X10,X11,X0,X9,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
        | ~ homomorphism(X9,X10,X11)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1868,plain,
    ( spl0_205
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f1879,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ homomorphism(X3,X0,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))))),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)))))))),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(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))))))),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)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(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(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))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(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(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))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f751]) ).

fof(f751,plain,
    ( ! [X10,X0,X11,X1,X9] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
        | ~ homomorphism(X9,X10,X11)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f750]) ).

fof(f1869,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
        | ~ subclass(composition_function,X2)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_205 ),
    inference(avatar_component_clause,[],[f1868]) ).

fof(f21490,plain,
    ( spl0_1017
    | ~ spl0_197
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2016,f1994,f1704,f21488]) ).

fof(f21488,plain,
    ( spl0_1017
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f1704,plain,
    ( spl0_197
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f1994,plain,
    ( spl0_211
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f2016,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_197
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1705]) ).

fof(f1705,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f1704]) ).

fof(f1995,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_211 ),
    inference(avatar_component_clause,[],[f1994]) ).

fof(f21486,plain,
    ( ~ spl0_4
    | spl0_1010 ),
    inference(avatar_contradiction_clause,[],[f21485]) ).

fof(f21485,plain,
    ( $false
    | ~ spl0_4
    | spl0_1010 ),
    inference(resolution,[],[f21314,f220]) ).

fof(f21314,plain,
    ( ~ subclass(domain_of(intersection(x,y)),universal_class)
    | spl0_1010 ),
    inference(avatar_component_clause,[],[f21312]) ).

fof(f21312,plain,
    ( spl0_1010
  <=> subclass(domain_of(intersection(x,y)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f21421,plain,
    ( spl0_1016
    | ~ spl0_77
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2127,f2124,f613,f21419]) ).

fof(f21419,plain,
    ( spl0_1016
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f2127,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_221 ),
    inference(resolution,[],[f2125,f614]) ).

fof(f21407,plain,
    ( spl0_1015
    | ~ spl0_40
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2131,f2124,f380,f21405]) ).

fof(f21405,plain,
    ( spl0_1015
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f2131,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_221 ),
    inference(superposition,[],[f2125,f381]) ).

fof(f21377,plain,
    ( spl0_1014
    | ~ spl0_205
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2002,f1994,f1868,f21375]) ).

fof(f21375,plain,
    ( spl0_1014
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,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))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f2002,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,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))),cross_product(universal_class,universal_class)) )
    | ~ spl0_205
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1869]) ).

fof(f21347,plain,
    ( spl0_1013
    | ~ spl0_92
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2021,f1994,f696,f21345]) ).

fof(f21345,plain,
    ( spl0_1013
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f696,plain,
    ( spl0_92
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f2021,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_92
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f697]) ).

fof(f697,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f696]) ).

fof(f21330,plain,
    ( spl0_1012
    | ~ spl0_101
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1752,f1745,f750,f21328]) ).

fof(f21328,plain,
    ( spl0_1012
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(X3))
        | ~ operation(X2)
        | ~ homomorphism(X4,X3,X5)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f1745,plain,
    ( spl0_199
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f1752,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(X3))
        | ~ operation(X2)
        | ~ homomorphism(X4,X3,X5)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f751]) ).

fof(f1746,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | ~ operation(X0) )
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f1745]) ).

fof(f21319,plain,
    ( ~ spl0_1010
    | spl0_1011
    | spl0_1
    | ~ spl0_515 ),
    inference(avatar_split_clause,[],[f7305,f7035,f204,f21316,f21312]) ).

fof(f7035,plain,
    ( spl0_515
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f7305,plain,
    ( null_class = intersection(x,cross_product(unordered_pair(not_subclass_element(domain_of(intersection(x,y)),domain_of(x)),not_subclass_element(domain_of(intersection(x,y)),domain_of(x))),universal_class))
    | ~ subclass(domain_of(intersection(x,y)),universal_class)
    | spl0_1
    | ~ spl0_515 ),
    inference(resolution,[],[f7036,f206]) ).

fof(f206,plain,
    ( ~ subclass(domain_of(intersection(x,y)),domain_of(x))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f7036,plain,
    ( ! [X0,X1] :
        ( subclass(X1,domain_of(X0))
        | 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,universal_class) )
    | ~ spl0_515 ),
    inference(avatar_component_clause,[],[f7035]) ).

fof(f21310,plain,
    ( spl0_1009
    | ~ spl0_198
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2118,f2110,f1711,f21308]) ).

fof(f21308,plain,
    ( spl0_1009
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f2110,plain,
    ( spl0_219
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f2118,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(regular(cross_product(X0,X1)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_219 ),
    inference(superposition,[],[f2111,f1712]) ).

fof(f2111,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2110]) ).

fof(f21292,plain,
    ( spl0_1008
    | ~ spl0_101
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1731,f1711,f750,f21290]) ).

fof(f21290,plain,
    ( spl0_1008
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
        | ~ homomorphism(X3,X2,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f1731,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
        | ~ homomorphism(X3,X2,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_101
    | ~ spl0_198 ),
    inference(superposition,[],[f751,f1712]) ).

fof(f21007,plain,
    ( spl0_1007
    | ~ spl0_195
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1855,f1812,f1656,f21005]) ).

fof(f21005,plain,
    ( spl0_1007
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f1656,plain,
    ( spl0_195
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f1855,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) )
    | ~ spl0_195
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1657]) ).

fof(f1657,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class) )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f1656]) ).

fof(f20988,plain,
    ( spl0_1006
    | ~ spl0_196
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1847,f1812,f1660,f20986]) ).

fof(f20986,plain,
    ( spl0_1006
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f1660,plain,
    ( spl0_196
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f1847,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) )
    | ~ spl0_196
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1661]) ).

fof(f1661,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class) )
    | ~ spl0_196 ),
    inference(avatar_component_clause,[],[f1660]) ).

fof(f20984,plain,
    ( spl0_1005
    | ~ spl0_195
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1829,f1803,f1656,f20982]) ).

fof(f20982,plain,
    ( spl0_1005
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f1829,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) )
    | ~ spl0_195
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1657]) ).

fof(f20980,plain,
    ( spl0_1004
    | ~ spl0_196
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1821,f1803,f1660,f20978]) ).

fof(f20978,plain,
    ( spl0_1004
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f1821,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) )
    | ~ spl0_196
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1661]) ).

fof(f20976,plain,
    ( spl0_1003
    | ~ spl0_93
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1692,f1660,f702,f20974]) ).

fof(f20974,plain,
    ( spl0_1003
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f702,plain,
    ( spl0_93
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f1692,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f703]) ).

fof(f703,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f702]) ).

fof(f20972,plain,
    ( spl0_1002
    | ~ spl0_93
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1672,f1656,f702,f20970]) ).

fof(f20970,plain,
    ( spl0_1002
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f1672,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f703]) ).

fof(f20968,plain,
    ( spl0_1001
    | ~ spl0_9
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2113,f2110,f240,f20966]) ).

fof(f20966,plain,
    ( spl0_1001
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f2113,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) )
    | ~ spl0_9
    | ~ spl0_219 ),
    inference(resolution,[],[f2111,f241]) ).

fof(f20964,plain,
    ( spl0_1000
    | ~ spl0_101
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1413,f1369,f750,f20962]) ).

fof(f20962,plain,
    ( spl0_1000
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(domain_relation,domain_of(X0))
        | ~ member(X1,universal_class)
        | ~ homomorphism(X2,X0,X3)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))),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(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))))),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(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(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f1413,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(domain_relation,domain_of(X0))
        | ~ member(X1,universal_class)
        | ~ homomorphism(X2,X0,X3)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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))))),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(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))))),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(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(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f751]) ).

fof(f20933,plain,
    ( spl0_999
    | ~ spl0_23
    | ~ spl0_130
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17187,f17014,f1012,f299,f20931]) ).

fof(f20931,plain,
    ( spl0_999
  <=> ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f17014,plain,
    ( spl0_888
  <=> ! [X0] : ~ member(X0,domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f17187,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1) )
    | ~ spl0_23
    | ~ spl0_130
    | ~ spl0_888 ),
    inference(forward_demodulation,[],[f17132,f17111]) ).

fof(f17111,plain,
    ( null_class = domain_of(null_class)
    | ~ spl0_23
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f300]) ).

fof(f17015,plain,
    ( ! [X0] : ~ member(X0,domain_of(null_class))
    | ~ spl0_888 ),
    inference(avatar_component_clause,[],[f17014]) ).

fof(f17132,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,domain_of(null_class))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f1013]) ).

fof(f20929,plain,
    ( spl0_998
    | ~ spl0_235
    | ~ spl0_997 ),
    inference(avatar_split_clause,[],[f20925,f20922,f2310,f20927]) ).

fof(f20927,plain,
    ( spl0_998
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),singleton_relation)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f20922,plain,
    ( spl0_997
  <=> ! [X0,X3,X2,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f20925,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),singleton_relation)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
    | ~ spl0_235
    | ~ spl0_997 ),
    inference(forward_demodulation,[],[f20923,f2312]) ).

fof(f20923,plain,
    ( ! [X2,X3,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
    | ~ spl0_997 ),
    inference(avatar_component_clause,[],[f20922]) ).

fof(f20924,plain,
    ( spl0_997
    | ~ spl0_50
    | ~ spl0_101
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1002,f959,f750,f452,f20922]) ).

fof(f1002,plain,
    ( ! [X2,X3,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
    | ~ spl0_50
    | ~ spl0_101
    | ~ spl0_125 ),
    inference(forward_demodulation,[],[f1000,f453]) ).

fof(f1000,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_125 ),
    inference(resolution,[],[f960,f751]) ).

fof(f20852,plain,
    ( spl0_996
    | ~ spl0_84
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1846,f1812,f654,f20850]) ).

fof(f20850,plain,
    ( spl0_996
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f654,plain,
    ( spl0_84
  <=> ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f1846,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_84
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f655]) ).

fof(f655,plain,
    ( ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f654]) ).

fof(f20848,plain,
    ( spl0_995
    | ~ spl0_84
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1820,f1803,f654,f20846]) ).

fof(f20846,plain,
    ( spl0_995
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f1820,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_84
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f655]) ).

fof(f20798,plain,
    ( spl0_994
    | ~ spl0_111
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2101,f2097,f823,f20796]) ).

fof(f20796,plain,
    ( spl0_994
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f2097,plain,
    ( spl0_218
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f2101,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_218 ),
    inference(resolution,[],[f2098,f824]) ).

fof(f2098,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f2097]) ).

fof(f20794,plain,
    ( spl0_993
    | ~ spl0_101
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f830,f802,f750,f20792]) ).

fof(f20792,plain,
    ( spl0_993
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(X0))
        | ~ homomorphism(X1,X0,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f830,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(X0))
        | ~ homomorphism(X1,X0,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f751]) ).

fof(f20789,plain,
    ( spl0_992
    | ~ spl0_23
    | ~ spl0_376
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17160,f17014,f3818,f299,f20787]) ).

fof(f20787,plain,
    ( spl0_992
  <=> ! [X0] : subclass(intersection(universal_class,X0),complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f17160,plain,
    ( ! [X0] : subclass(intersection(universal_class,X0),complement(null_class))
    | ~ spl0_23
    | ~ spl0_376
    | ~ spl0_888 ),
    inference(forward_demodulation,[],[f17117,f17111]) ).

fof(f17117,plain,
    ( ! [X0] : subclass(intersection(universal_class,X0),complement(domain_of(null_class)))
    | ~ spl0_376
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f3819]) ).

fof(f20785,plain,
    ( ~ spl0_990
    | spl0_991
    | ~ spl0_40
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2134,f2124,f380,f20783,f20779]) ).

fof(f20783,plain,
    ( spl0_991
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ operation(X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f2134,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ operation(X3)
        | ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(null_class,universal_class))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_221 ),
    inference(superposition,[],[f2125,f381]) ).

fof(f20771,plain,
    ( spl0_989
    | ~ spl0_40
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2104,f2097,f380,f20769]) ).

fof(f20769,plain,
    ( spl0_989
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f2104,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_218 ),
    inference(superposition,[],[f2098,f381]) ).

fof(f20625,plain,
    ( spl0_988
    | ~ spl0_95
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1884,f1868,f723,f20623]) ).

fof(f20623,plain,
    ( spl0_988
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,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))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f723,plain,
    ( spl0_95
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f1884,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,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))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) )
    | ~ spl0_95
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f724]) ).

fof(f724,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f723]) ).

fof(f20573,plain,
    ( spl0_987
    | ~ spl0_77
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2100,f2097,f613,f20571]) ).

fof(f20571,plain,
    ( spl0_987
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f2100,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_218 ),
    inference(resolution,[],[f2098,f614]) ).

fof(f20569,plain,
    ( spl0_985
    | ~ spl0_986
    | ~ spl0_99
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1886,f1868,f739,f20566,f20563]) ).

fof(f20563,plain,
    ( spl0_985
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(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(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),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(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f20566,plain,
    ( spl0_986
  <=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f739,plain,
    ( spl0_99
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1886,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,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))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),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(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3) )
    | ~ spl0_99
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f740]) ).

fof(f740,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f739]) ).

fof(f20534,plain,
    ( spl0_984
    | ~ spl0_23
    | ~ spl0_375
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17156,f17014,f3814,f299,f20532]) ).

fof(f20532,plain,
    ( spl0_984
  <=> ! [X0] : subclass(intersection(X0,universal_class),complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f17156,plain,
    ( ! [X0] : subclass(intersection(X0,universal_class),complement(null_class))
    | ~ spl0_23
    | ~ spl0_375
    | ~ spl0_888 ),
    inference(forward_demodulation,[],[f17115,f17111]) ).

fof(f17115,plain,
    ( ! [X0] : subclass(intersection(X0,universal_class),complement(domain_of(null_class)))
    | ~ spl0_375
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f3815]) ).

fof(f20530,plain,
    ( spl0_983
    | ~ spl0_186
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2020,f1994,f1578,f20528]) ).

fof(f20528,plain,
    ( spl0_983
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),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_983])]) ).

fof(f2020,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_186
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1579]) ).

fof(f20508,plain,
    ( spl0_982
    | ~ spl0_204
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1899,f1868,f1812,f20506]) ).

fof(f20506,plain,
    ( spl0_982
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,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)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f1899,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,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)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_204
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1813]) ).

fof(f20504,plain,
    ( spl0_981
    | ~ spl0_202
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1898,f1868,f1803,f20502]) ).

fof(f20502,plain,
    ( spl0_981
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f1898,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_202
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1804]) ).

fof(f20500,plain,
    ( spl0_980
    | ~ spl0_93
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1897,f1868,f702,f20498]) ).

fof(f20498,plain,
    ( spl0_980
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(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(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,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(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),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(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f1897,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(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(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,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(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),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(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f703]) ).

fof(f20478,plain,
    ( spl0_979
    | ~ spl0_100
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1730,f1711,f745,f20476]) ).

fof(f20476,plain,
    ( spl0_979
  <=> ! [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))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(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(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))))))),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)))))))))),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(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))))))),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))))))))))))),application_function)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f745,plain,
    ( spl0_100
  <=> ! [X4,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1730,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))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(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(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))))))),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)))))))))),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(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))))))),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))))))))))))),application_function)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_100
    | ~ spl0_198 ),
    inference(superposition,[],[f746,f1712]) ).

fof(f746,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f745]) ).

fof(f20427,plain,
    ( spl0_978
    | ~ spl0_134
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17104,f17014,f1083,f20425]) ).

fof(f20425,plain,
    ( spl0_978
  <=> ! [X0,X1] : subclass(intersection(domain_of(null_class),X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f17104,plain,
    ( ! [X0,X1] : subclass(intersection(domain_of(null_class),X0),X1)
    | ~ spl0_134
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f1084]) ).

fof(f20423,plain,
    ( spl0_977
    | ~ spl0_205
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2025,f1998,f1868,f20421]) ).

fof(f20421,plain,
    ( spl0_977
  <=> ! [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(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,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))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f1998,plain,
    ( spl0_212
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f2025,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(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,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))),cross_product(universal_class,universal_class)) )
    | ~ spl0_205
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1869]) ).

fof(f1999,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_212 ),
    inference(avatar_component_clause,[],[f1998]) ).

fof(f20379,plain,
    ( spl0_976
    | ~ spl0_165
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2001,f1994,f1369,f20377]) ).

fof(f20377,plain,
    ( spl0_976
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f2001,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_165
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1370]) ).

fof(f20375,plain,
    ( spl0_975
    | ~ spl0_79
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1685,f1660,f628,f20373]) ).

fof(f20373,plain,
    ( spl0_975
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f1685,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f629]) ).

fof(f20371,plain,
    ( spl0_974
    | ~ spl0_79
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1665,f1656,f628,f20369]) ).

fof(f20369,plain,
    ( spl0_974
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f1665,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f629]) ).

fof(f20322,plain,
    ( spl0_973
    | ~ spl0_92
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2044,f1998,f696,f20320]) ).

fof(f20320,plain,
    ( spl0_973
  <=> ! [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(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f2044,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_92
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f697]) ).

fof(f20299,plain,
    ( spl0_972
    | ~ spl0_287
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17106,f17014,f2739,f20296]) ).

fof(f20296,plain,
    ( spl0_972
  <=> subclass(universal_class,complement(domain_of(null_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).

fof(f17106,plain,
    ( subclass(universal_class,complement(domain_of(null_class)))
    | ~ spl0_287
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f2740]) ).

fof(f20268,plain,
    ( spl0_971
    | ~ spl0_198
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2065,f2051,f1711,f20266]) ).

fof(f20266,plain,
    ( spl0_971
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(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(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))))))),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)))))))))),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(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))))))),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))))))))))))),application_function)
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | ~ member(X2,universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f2051,plain,
    ( spl0_213
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f2065,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(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(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))))))),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)))))))))),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(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))))))),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))))))))))))),application_function)
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | ~ member(X2,universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_213 ),
    inference(superposition,[],[f2052,f1712]) ).

fof(f2052,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(X0,domain_of(X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f2051]) ).

fof(f20264,plain,
    ( spl0_970
    | ~ spl0_66
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2022,f1994,f552,f20262]) ).

fof(f20262,plain,
    ( spl0_970
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f2022,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_66
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f553]) ).

fof(f20086,plain,
    ( spl0_969
    | ~ spl0_199
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2064,f2051,f1745,f20084]) ).

fof(f20084,plain,
    ( spl0_969
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,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(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),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(X1,X2,X3),not_homomorphism1(X1,X2,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(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).

fof(f2064,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,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(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),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(X1,X2,X3),not_homomorphism1(X1,X2,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(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
        | ~ operation(X3) )
    | ~ spl0_199
    | ~ spl0_213 ),
    inference(resolution,[],[f2052,f1746]) ).

fof(f20082,plain,
    ( spl0_968
    | ~ spl0_209
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2041,f1998,f1935,f20080]) ).

fof(f20080,plain,
    ( spl0_968
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).

fof(f1935,plain,
    ( spl0_209
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f2041,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_209
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1936]) ).

fof(f1936,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f1935]) ).

fof(f19751,plain,
    ( spl0_967
    | ~ spl0_70
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2037,f1998,f568,f19749]) ).

fof(f19749,plain,
    ( spl0_967
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f568,plain,
    ( spl0_70
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,domain_of(X0))
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f2037,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
    | ~ spl0_70
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f569]) ).

fof(f569,plain,
    ( ! [X0,X4] :
        ( member(X4,domain_of(X0))
        | ~ member(X4,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f568]) ).

fof(f19747,plain,
    ( spl0_966
    | ~ spl0_209
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2018,f1994,f1935,f19745]) ).

fof(f19745,plain,
    ( spl0_966
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f2018,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_209
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1936]) ).

fof(f19743,plain,
    ( spl0_965
    | ~ spl0_70
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2014,f1994,f568,f19741]) ).

fof(f19741,plain,
    ( spl0_965
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f2014,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
    | ~ spl0_70
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f569]) ).

fof(f19717,plain,
    ( spl0_964
    | ~ spl0_198
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2046,f1998,f1711,f19715]) ).

fof(f19715,plain,
    ( spl0_964
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f2046,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_212 ),
    inference(superposition,[],[f1999,f1712]) ).

fof(f19713,plain,
    ( spl0_963
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1901,f1868,f1294,f19711]) ).

fof(f19711,plain,
    ( spl0_963
  <=> ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f1294,plain,
    ( spl0_158
  <=> ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1901,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1295]) ).

fof(f1295,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1294]) ).

fof(f19668,plain,
    ( spl0_962
    | ~ spl0_197
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2048,f1998,f1704,f19666]) ).

fof(f19666,plain,
    ( spl0_962
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f2048,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_197
    | ~ spl0_212 ),
    inference(duplicate_literal_removal,[],[f2039]) ).

fof(f2039,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_197
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1705]) ).

fof(f19605,plain,
    ( spl0_961
    | ~ spl0_199
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1861,f1812,f1745,f19603]) ).

fof(f19603,plain,
    ( spl0_961
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f1861,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_199
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1746]) ).

fof(f19601,plain,
    ( spl0_960
    | ~ spl0_199
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1835,f1803,f1745,f19599]) ).

fof(f19599,plain,
    ( spl0_960
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f1835,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_199
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1746]) ).

fof(f19597,plain,
    ( spl0_959
    | ~ spl0_93
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1766,f1745,f702,f19595]) ).

fof(f19595,plain,
    ( spl0_959
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f1766,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f703]) ).

fof(f19547,plain,
    ( spl0_958
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_957 ),
    inference(avatar_split_clause,[],[f19543,f19539,f16537,f14704,f19545]) ).

fof(f19545,plain,
    ( spl0_958
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f16537,plain,
    ( spl0_869
  <=> ! [X0] : null_class = intersection(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f19539,plain,
    ( spl0_957
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f19543,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_957 ),
    inference(forward_demodulation,[],[f19542,f16538]) ).

fof(f16538,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_869 ),
    inference(avatar_component_clause,[],[f16537]) ).

fof(f19542,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(null_class,X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_786
    | ~ spl0_957 ),
    inference(forward_demodulation,[],[f19540,f14706]) ).

fof(f19540,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_957 ),
    inference(avatar_component_clause,[],[f19539]) ).

fof(f19541,plain,
    ( spl0_957
    | ~ spl0_206
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2040,f1998,f1906,f19539]) ).

fof(f1906,plain,
    ( spl0_206
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(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))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_206
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1907]) ).

fof(f1907,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_206 ),
    inference(avatar_component_clause,[],[f1906]) ).

fof(f19491,plain,
    ( spl0_956
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_954 ),
    inference(avatar_split_clause,[],[f19482,f19478,f16537,f14704,f19489]) ).

fof(f19489,plain,
    ( spl0_956
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f19478,plain,
    ( spl0_954
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f19482,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_954 ),
    inference(forward_demodulation,[],[f19481,f16538]) ).

fof(f19481,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_786
    | ~ spl0_954 ),
    inference(forward_demodulation,[],[f19479,f14706]) ).

fof(f19479,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_954 ),
    inference(avatar_component_clause,[],[f19478]) ).

fof(f19487,plain,
    ( spl0_955
    | ~ spl0_55
    | ~ spl0_938 ),
    inference(avatar_split_clause,[],[f18954,f18828,f477,f19484]) ).

fof(f19484,plain,
    ( spl0_955
  <=> universal_class = complement(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f477,plain,
    ( spl0_55
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f18828,plain,
    ( spl0_938
  <=> subclass(universal_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f18954,plain,
    ( universal_class = complement(null_class)
    | ~ spl0_55
    | ~ spl0_938 ),
    inference(resolution,[],[f18830,f478]) ).

fof(f478,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f477]) ).

fof(f18830,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_938 ),
    inference(avatar_component_clause,[],[f18828]) ).

fof(f19480,plain,
    ( spl0_954
    | ~ spl0_206
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2017,f1994,f1906,f19478]) ).

fof(f2017,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_206
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1907]) ).

fof(f19270,plain,
    ( spl0_953
    | ~ spl0_135
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1850,f1812,f1087,f19268]) ).

fof(f19268,plain,
    ( spl0_953
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f1850,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
    | ~ spl0_135
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1088]) ).

fof(f19266,plain,
    ( spl0_952
    | ~ spl0_134
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1844,f1812,f1083,f19264]) ).

fof(f19264,plain,
    ( spl0_952
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f1844,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
    | ~ spl0_134
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1084]) ).

fof(f19262,plain,
    ( spl0_951
    | ~ spl0_135
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1824,f1803,f1087,f19260]) ).

fof(f19260,plain,
    ( spl0_951
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f1824,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
    | ~ spl0_135
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1088]) ).

fof(f19257,plain,
    ( spl0_950
    | ~ spl0_228
    | ~ spl0_938 ),
    inference(avatar_split_clause,[],[f18953,f18828,f2265,f19254]) ).

fof(f19254,plain,
    ( spl0_950
  <=> member(null_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f2265,plain,
    ( spl0_228
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f18953,plain,
    ( member(null_class,complement(null_class))
    | ~ spl0_228
    | ~ spl0_938 ),
    inference(resolution,[],[f18830,f2266]) ).

fof(f2266,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_228 ),
    inference(avatar_component_clause,[],[f2265]) ).

fof(f19252,plain,
    ( spl0_949
    | ~ spl0_134
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1818,f1803,f1083,f19250]) ).

fof(f19250,plain,
    ( spl0_949
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f1818,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
    | ~ spl0_134
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1084]) ).

fof(f19248,plain,
    ( spl0_948
    | ~ spl0_93
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1137,f1087,f702,f19246]) ).

fof(f19246,plain,
    ( spl0_948
  <=> ! [X4,X0,X3,X2,X1] :
        ( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f1137,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f703]) ).

fof(f19244,plain,
    ( spl0_947
    | ~ spl0_93
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1119,f1083,f702,f19242]) ).

fof(f19242,plain,
    ( spl0_947
  <=> ! [X4,X0,X3,X2,X1] :
        ( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f1119,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f703]) ).

fof(f19164,plain,
    ( spl0_946
    | ~ spl0_99
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1729,f1711,f739,f19162]) ).

fof(f19162,plain,
    ( spl0_946
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f1729,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_99
    | ~ spl0_198 ),
    inference(superposition,[],[f740,f1712]) ).

fof(f18919,plain,
    ( spl0_945
    | ~ spl0_129
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1857,f1812,f1008,f18917]) ).

fof(f18917,plain,
    ( spl0_945
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f1857,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_129
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1009]) ).

fof(f18915,plain,
    ( spl0_944
    | ~ spl0_128
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1849,f1812,f1004,f18913]) ).

fof(f18913,plain,
    ( spl0_944
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f1849,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_128
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1005]) ).

fof(f18911,plain,
    ( spl0_943
    | ~ spl0_129
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1831,f1803,f1008,f18909]) ).

fof(f18909,plain,
    ( spl0_943
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f1831,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_129
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1009]) ).

fof(f18907,plain,
    ( spl0_942
    | ~ spl0_128
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1823,f1803,f1004,f18905]) ).

fof(f18905,plain,
    ( spl0_942
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f1823,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_128
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1005]) ).

fof(f18903,plain,
    ( spl0_941
    | ~ spl0_93
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1050,f1008,f702,f18901]) ).

fof(f18901,plain,
    ( spl0_941
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f1050,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f703]) ).

fof(f18899,plain,
    ( spl0_940
    | ~ spl0_93
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1034,f1004,f702,f18897]) ).

fof(f18897,plain,
    ( spl0_940
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f1034,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f703]) ).

fof(f18835,plain,
    ( spl0_939
    | ~ spl0_27
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1843,f1812,f319,f18833]) ).

fof(f18833,plain,
    ( spl0_939
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f1843,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f320]) ).

fof(f18831,plain,
    ( spl0_938
    | ~ spl0_287
    | ~ spl0_926 ),
    inference(avatar_split_clause,[],[f18460,f18166,f2739,f18828]) ).

fof(f18460,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_287
    | ~ spl0_926 ),
    inference(resolution,[],[f18167,f2740]) ).

fof(f18826,plain,
    ( spl0_937
    | ~ spl0_27
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1817,f1803,f319,f18824]) ).

fof(f18824,plain,
    ( spl0_937
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f1817,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f320]) ).

fof(f18782,plain,
    ( spl0_936
    | ~ spl0_111
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2084,f2080,f823,f18780]) ).

fof(f18780,plain,
    ( spl0_936
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f2080,plain,
    ( spl0_216
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2084,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_216 ),
    inference(resolution,[],[f2081,f824]) ).

fof(f2081,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2080]) ).

fof(f18720,plain,
    ( spl0_935
    | ~ spl0_23
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1848,f1812,f299,f18718]) ).

fof(f18718,plain,
    ( spl0_935
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f1848,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f300]) ).

fof(f18716,plain,
    ( spl0_934
    | ~ spl0_23
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1822,f1803,f299,f18714]) ).

fof(f18714,plain,
    ( spl0_934
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f1822,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f300]) ).

fof(f18577,plain,
    ( spl0_933
    | ~ spl0_96
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1885,f1868,f727,f18575]) ).

fof(f18575,plain,
    ( spl0_933
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f727,plain,
    ( spl0_96
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1885,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) )
    | ~ spl0_96
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f728]) ).

fof(f728,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f727]) ).

fof(f18456,plain,
    ( spl0_932
    | ~ spl0_111
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2071,f2067,f823,f18454]) ).

fof(f18454,plain,
    ( spl0_932
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f2067,plain,
    ( spl0_215
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f2071,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_215 ),
    inference(resolution,[],[f2068,f824]) ).

fof(f2068,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f2067]) ).

fof(f18406,plain,
    ( spl0_931
    | ~ spl0_98
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1728,f1711,f735,f18404]) ).

fof(f18404,plain,
    ( spl0_931
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f735,plain,
    ( spl0_98
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1728,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_98
    | ~ spl0_198 ),
    inference(superposition,[],[f736,f1712]) ).

fof(f736,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f735]) ).

fof(f18402,plain,
    ( spl0_929
    | ~ spl0_930
    | ~ spl0_99
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1420,f1369,f739,f18399,f18396]) ).

fof(f18396,plain,
    ( spl0_929
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f18399,plain,
    ( spl0_930
  <=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f1420,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2) )
    | ~ spl0_99
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f740]) ).

fof(f18204,plain,
    ( spl0_928
    | ~ spl0_49
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2033,f1998,f448,f18202]) ).

fof(f18202,plain,
    ( spl0_928
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f2033,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_49
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f449]) ).

fof(f18200,plain,
    ( spl0_927
    | ~ spl0_49
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2010,f1994,f448,f18198]) ).

fof(f18198,plain,
    ( spl0_927
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f2010,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
    | ~ spl0_49
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f449]) ).

fof(f18168,plain,
    ( spl0_926
    | ~ spl0_888
    | ~ spl0_915 ),
    inference(avatar_split_clause,[],[f17878,f17701,f17014,f18166]) ).

fof(f17878,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_888
    | ~ spl0_915 ),
    inference(superposition,[],[f17015,f17703]) ).

fof(f18113,plain,
    ( spl0_925
    | ~ spl0_44
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2035,f1998,f424,f18111]) ).

fof(f18111,plain,
    ( spl0_925
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f2035,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_44
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f425]) ).

fof(f18109,plain,
    ( spl0_924
    | ~ spl0_44
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2012,f1994,f424,f18107]) ).

fof(f18107,plain,
    ( spl0_924
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f2012,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_44
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f425]) ).

fof(f18105,plain,
    ( spl0_923
    | ~ spl0_79
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1625,f1620,f628,f18103]) ).

fof(f18103,plain,
    ( spl0_923
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f1620,plain,
    ( spl0_193
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f1625,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f629]) ).

fof(f1621,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f1620]) ).

fof(f17742,plain,
    ( spl0_922
    | ~ spl0_30
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2029,f1998,f331,f17740]) ).

fof(f17740,plain,
    ( spl0_922
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f2029,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_30
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f332]) ).

fof(f17738,plain,
    ( spl0_921
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2028,f1998,f327,f17736]) ).

fof(f17736,plain,
    ( spl0_921
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f2028,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f328]) ).

fof(f17734,plain,
    ( spl0_920
    | ~ spl0_198
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2023,f1994,f1711,f17732]) ).

fof(f17732,plain,
    ( spl0_920
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f2023,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_211 ),
    inference(superposition,[],[f1995,f1712]) ).

fof(f17730,plain,
    ( spl0_919
    | ~ spl0_30
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2006,f1994,f331,f17728]) ).

fof(f17728,plain,
    ( spl0_919
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f2006,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_30
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f332]) ).

fof(f17726,plain,
    ( spl0_918
    | ~ spl0_29
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2005,f1994,f327,f17724]) ).

fof(f17724,plain,
    ( spl0_918
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f2005,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_29
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f328]) ).

fof(f17722,plain,
    ( spl0_917
    | ~ spl0_158
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1768,f1745,f1294,f17720]) ).

fof(f17720,plain,
    ( spl0_917
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
        | ~ operation(X2)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f1768,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
        | ~ operation(X2)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f1295]) ).

fof(f17718,plain,
    ( spl0_916
    | ~ spl0_96
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1727,f1711,f727,f17716]) ).

fof(f17716,plain,
    ( spl0_916
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f1727,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_96
    | ~ spl0_198 ),
    inference(superposition,[],[f728,f1712]) ).

fof(f17704,plain,
    ( spl0_915
    | ~ spl0_23
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17111,f17014,f299,f17701]) ).

fof(f17671,plain,
    ( spl0_914
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_913 ),
    inference(avatar_split_clause,[],[f17667,f17659,f16537,f14704,f17669]) ).

fof(f17669,plain,
    ( spl0_914
  <=> ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f17659,plain,
    ( spl0_913
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f17667,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f17666,f16538]) ).

fof(f17666,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f17665,f14706]) ).

fof(f17665,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f17664,f16538]) ).

fof(f17664,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f17663,f14706]) ).

fof(f17663,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f17662,f16538]) ).

fof(f17662,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_913 ),
    inference(forward_demodulation,[],[f17660,f14706]) ).

fof(f17660,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_913 ),
    inference(avatar_component_clause,[],[f17659]) ).

fof(f17661,plain,
    ( spl0_913
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2087,f2080,f380,f17659]) ).

fof(f2087,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(superposition,[],[f2081,f381]) ).

fof(f17657,plain,
    ( spl0_912
    | ~ spl0_193
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1854,f1812,f1620,f17655]) ).

fof(f17655,plain,
    ( spl0_912
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f1854,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_193
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1621]) ).

fof(f17653,plain,
    ( spl0_911
    | ~ spl0_193
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1828,f1803,f1620,f17651]) ).

fof(f17651,plain,
    ( spl0_911
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(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_911])]) ).

fof(f1828,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_193
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1621]) ).

fof(f17649,plain,
    ( spl0_910
    | ~ spl0_93
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1632,f1620,f702,f17647]) ).

fof(f17647,plain,
    ( spl0_910
  <=> ! [X0,X3,X2,X1] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f1632,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f703]) ).

fof(f17637,plain,
    ( spl0_909
    | spl0_853
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_907 ),
    inference(avatar_split_clause,[],[f17628,f17620,f16537,f14704,f16041,f17635]) ).

fof(f17635,plain,
    ( spl0_909
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f16041,plain,
    ( spl0_853
  <=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f17620,plain,
    ( spl0_907
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f17628,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17627,f16538]) ).

fof(f17627,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17626,f14706]) ).

fof(f17626,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17625,f16538]) ).

fof(f17625,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17624,f14706]) ).

fof(f17624,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_869
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17623,f16538]) ).

fof(f17623,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_786
    | ~ spl0_907 ),
    inference(forward_demodulation,[],[f17621,f14706]) ).

fof(f17621,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_907 ),
    inference(avatar_component_clause,[],[f17620]) ).

fof(f17632,plain,
    ( spl0_908
    | ~ spl0_27
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17103,f17014,f319,f17630]) ).

fof(f17630,plain,
    ( spl0_908
  <=> ! [X0] : subclass(domain_of(null_class),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f17103,plain,
    ( ! [X0] : subclass(domain_of(null_class),X0)
    | ~ spl0_27
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f320]) ).

fof(f17622,plain,
    ( spl0_907
    | ~ spl0_40
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2074,f2067,f380,f17620]) ).

fof(f2074,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_215 ),
    inference(superposition,[],[f2068,f381]) ).

fof(f17605,plain,
    ( spl0_906
    | ~ spl0_24
    | ~ spl0_100
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1874,f1868,f745,f303,f17603]) ).

fof(f17603,plain,
    ( spl0_906
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).

fof(f1874,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_100
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f746]) ).

fof(f17577,plain,
    ( spl0_905
    | ~ spl0_111
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2060,f2051,f823,f17575]) ).

fof(f17575,plain,
    ( spl0_905
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f2060,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_213 ),
    inference(resolution,[],[f2052,f824]) ).

fof(f17534,plain,
    ( spl0_904
    | ~ spl0_77
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2083,f2080,f613,f17532]) ).

fof(f17532,plain,
    ( spl0_904
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f2083,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_216 ),
    inference(resolution,[],[f2081,f614]) ).

fof(f17393,plain,
    ( spl0_903
    | ~ spl0_77
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2070,f2067,f613,f17391]) ).

fof(f17391,plain,
    ( spl0_903
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f2070,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_215 ),
    inference(resolution,[],[f2068,f614]) ).

fof(f17388,plain,
    ( ~ spl0_902
    | ~ spl0_12
    | ~ spl0_888 ),
    inference(avatar_split_clause,[],[f17107,f17014,f254,f17385]) ).

fof(f17385,plain,
    ( spl0_902
  <=> inductive(domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f254,plain,
    ( spl0_12
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f17107,plain,
    ( ~ inductive(domain_of(null_class))
    | ~ spl0_12
    | ~ spl0_888 ),
    inference(resolution,[],[f17015,f255]) ).

fof(f255,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f17383,plain,
    ( spl0_901
    | ~ spl0_95
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1726,f1711,f723,f17381]) ).

fof(f17381,plain,
    ( spl0_901
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f1726,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_95
    | ~ spl0_198 ),
    inference(superposition,[],[f724,f1712]) ).

fof(f17236,plain,
    ( spl0_652
    | spl0_900
    | ~ spl0_77
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2059,f2051,f613,f17234,f9912]) ).

fof(f2059,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_77
    | ~ spl0_213 ),
    inference(resolution,[],[f2052,f614]) ).

fof(f17232,plain,
    ( spl0_899
    | ~ spl0_95
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1418,f1369,f723,f17230]) ).

fof(f17230,plain,
    ( spl0_899
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,rotate(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f1418,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,rotate(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) )
    | ~ spl0_95
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f724]) ).

fof(f17228,plain,
    ( ~ spl0_897
    | spl0_898
    | ~ spl0_90
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1205,f1167,f686,f17226,f17222]) ).

fof(f17222,plain,
    ( spl0_897
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f17226,plain,
    ( spl0_898
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
        | homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | ~ operation(X1)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f1205,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation)
        | ~ operation(X1)
        | ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
        | ~ operation(flip(cross_product(subset_relation,universal_class))) )
    | ~ spl0_90
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f687]) ).

fof(f17220,plain,
    ( spl0_895
    | ~ spl0_896
    | ~ spl0_100
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f838,f802,f745,f17217,f17214]) ).

fof(f17214,plain,
    ( spl0_895
  <=> ! [X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f17217,plain,
    ( spl0_896
  <=> subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f838,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) )
    | ~ spl0_100
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f746]) ).

fof(f17100,plain,
    ( spl0_893
    | ~ spl0_894
    | ~ spl0_185
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1893,f1868,f1556,f17097,f17094]) ).

fof(f17094,plain,
    ( spl0_893
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f17097,plain,
    ( spl0_894
  <=> subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).

fof(f1893,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_185
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1557]) ).

fof(f17047,plain,
    ( spl0_892
    | ~ spl0_162
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2034,f1998,f1351,f17045]) ).

fof(f17045,plain,
    ( spl0_892
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).

fof(f1351,plain,
    ( spl0_162
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f2034,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_162
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1352]) ).

fof(f1352,plain,
    ( ! [X0] :
        ( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1351]) ).

fof(f17043,plain,
    ( spl0_891
    | ~ spl0_162
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2011,f1994,f1351,f17041]) ).

fof(f17041,plain,
    ( spl0_891
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f2011,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_162
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1352]) ).

fof(f17024,plain,
    ( spl0_890
    | ~ spl0_171
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1852,f1812,f1456,f17022]) ).

fof(f17022,plain,
    ( spl0_890
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).

fof(f1456,plain,
    ( spl0_171
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f1852,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_171
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1457]) ).

fof(f1457,plain,
    ( ! [X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1456]) ).

fof(f17020,plain,
    ( spl0_889
    | ~ spl0_171
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1826,f1803,f1456,f17018]) ).

fof(f17018,plain,
    ( spl0_889
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f1826,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_171
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1457]) ).

fof(f17016,plain,
    ( spl0_888
    | ~ spl0_145
    | ~ spl0_869 ),
    inference(avatar_split_clause,[],[f16860,f16537,f1171,f17014]) ).

fof(f16860,plain,
    ( ! [X0] : ~ member(X0,domain_of(null_class))
    | ~ spl0_145
    | ~ spl0_869 ),
    inference(trivial_inequality_removal,[],[f16812]) ).

fof(f16812,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(null_class)) )
    | ~ spl0_145
    | ~ spl0_869 ),
    inference(superposition,[],[f1172,f16538]) ).

fof(f17012,plain,
    ( spl0_887
    | ~ spl0_93
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1506,f1456,f702,f17010]) ).

fof(f17010,plain,
    ( spl0_887
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f1506,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f703]) ).

fof(f16971,plain,
    ( spl0_886
    | ~ spl0_186
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2047,f1998,f1578,f16969]) ).

fof(f16969,plain,
    ( spl0_886
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f2047,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_186
    | ~ spl0_212 ),
    inference(duplicate_literal_removal,[],[f2043]) ).

fof(f2043,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_186
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1579]) ).

fof(f16926,plain,
    ( spl0_885
    | ~ spl0_165
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2024,f1998,f1369,f16924]) ).

fof(f16924,plain,
    ( spl0_885
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
        | ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f2024,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
        | ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_165
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1370]) ).

fof(f16737,plain,
    ( spl0_884
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2090,f2080,f380,f16735]) ).

fof(f16735,plain,
    ( spl0_884
  <=> ! [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_884])]) ).

fof(f2090,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(superposition,[],[f2081,f381]) ).

fof(f16733,plain,
    ( spl0_883
    | ~ spl0_199
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1931,f1923,f1745,f16731]) ).

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

fof(f1923,plain,
    ( spl0_208
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f1931,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2) )
    | ~ spl0_199
    | ~ spl0_208 ),
    inference(resolution,[],[f1924,f1746]) ).

fof(f1924,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_208 ),
    inference(avatar_component_clause,[],[f1923]) ).

fof(f16729,plain,
    ( spl0_882
    | ~ spl0_165
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1851,f1812,f1369,f16727]) ).

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

fof(f1851,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_165
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1370]) ).

fof(f16725,plain,
    ( spl0_881
    | ~ spl0_165
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1825,f1803,f1369,f16723]) ).

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

fof(f1825,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_165
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1370]) ).

fof(f16721,plain,
    ( spl0_880
    | ~ spl0_93
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1430,f1369,f702,f16719]) ).

fof(f16719,plain,
    ( spl0_880
  <=> ! [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_880])]) ).

fof(f1430,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f703]) ).

fof(f16603,plain,
    ( spl0_879
    | ~ spl0_224
    | ~ spl0_836 ),
    inference(avatar_split_clause,[],[f16388,f15771,f2227,f16601]) ).

fof(f16388,plain,
    ( ! [X0] : null_class = intersection(X0,null_class)
    | ~ spl0_224
    | ~ spl0_836 ),
    inference(resolution,[],[f15772,f2228]) ).

fof(f16599,plain,
    ( spl0_878
    | ~ spl0_235
    | ~ spl0_873 ),
    inference(avatar_split_clause,[],[f16558,f16555,f2310,f16597]) ).

fof(f16597,plain,
    ( spl0_878
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f16555,plain,
    ( spl0_873
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f16558,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_235
    | ~ spl0_873 ),
    inference(forward_demodulation,[],[f16556,f2312]) ).

fof(f16556,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
    | ~ spl0_873 ),
    inference(avatar_component_clause,[],[f16555]) ).

fof(f16595,plain,
    ( spl0_877
    | ~ spl0_235
    | ~ spl0_872 ),
    inference(avatar_split_clause,[],[f16553,f16550,f2310,f16593]) ).

fof(f16593,plain,
    ( spl0_877
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f16550,plain,
    ( spl0_872
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f16553,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_872 ),
    inference(forward_demodulation,[],[f16551,f2312]) ).

fof(f16551,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
    | ~ spl0_872 ),
    inference(avatar_component_clause,[],[f16550]) ).

fof(f16570,plain,
    ( spl0_876
    | ~ spl0_235
    | ~ spl0_870 ),
    inference(avatar_split_clause,[],[f16544,f16541,f2310,f16568]) ).

fof(f16568,plain,
    ( spl0_876
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f16541,plain,
    ( spl0_870
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f16544,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_235
    | ~ spl0_870 ),
    inference(forward_demodulation,[],[f16542,f2312]) ).

fof(f16542,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
    | ~ spl0_870 ),
    inference(avatar_component_clause,[],[f16541]) ).

fof(f16566,plain,
    ( spl0_875
    | ~ spl0_235
    | ~ spl0_868 ),
    inference(avatar_split_clause,[],[f16535,f16532,f2310,f16564]) ).

fof(f16564,plain,
    ( spl0_875
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f16532,plain,
    ( spl0_868
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f16535,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_868 ),
    inference(forward_demodulation,[],[f16533,f2312]) ).

fof(f16533,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
    | ~ spl0_868 ),
    inference(avatar_component_clause,[],[f16532]) ).

fof(f16562,plain,
    ( spl0_874
    | ~ spl0_123
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2042,f1998,f951,f16560]) ).

fof(f16560,plain,
    ( spl0_874
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f951,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f2042,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 )
    | ~ spl0_123
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f952]) ).

fof(f952,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,null_class)
        | null_class = X0 )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f951]) ).

fof(f16557,plain,
    ( spl0_873
    | ~ spl0_125
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2038,f1998,f959,f16555]) ).

fof(f2038,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
    | ~ spl0_125
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f960]) ).

fof(f16552,plain,
    ( spl0_872
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2036,f1998,f955,f16550]) ).

fof(f2036,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f956]) ).

fof(f16548,plain,
    ( spl0_871
    | ~ spl0_123
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2019,f1994,f951,f16546]) ).

fof(f16546,plain,
    ( spl0_871
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).

fof(f2019,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 )
    | ~ spl0_123
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f952]) ).

fof(f16543,plain,
    ( spl0_870
    | ~ spl0_125
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2015,f1994,f959,f16541]) ).

fof(f2015,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
    | ~ spl0_125
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f960]) ).

fof(f16539,plain,
    ( spl0_869
    | ~ spl0_223
    | ~ spl0_836 ),
    inference(avatar_split_clause,[],[f16387,f15771,f2223,f16537]) ).

fof(f16387,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_223
    | ~ spl0_836 ),
    inference(resolution,[],[f15772,f2224]) ).

fof(f16534,plain,
    ( spl0_868
    | ~ spl0_124
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2013,f1994,f955,f16532]) ).

fof(f2013,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f956]) ).

fof(f16413,plain,
    ( spl0_867
    | ~ spl0_66
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2045,f1998,f552,f16411]) ).

fof(f16411,plain,
    ( spl0_867
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
        | ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f2045,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
        | ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_66
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f553]) ).

fof(f16409,plain,
    ( spl0_866
    | ~ spl0_142
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1903,f1868,f1159,f16407]) ).

fof(f16407,plain,
    ( spl0_866
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,regular(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f1159,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1903,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,regular(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1160]) ).

fof(f1160,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,null_class)
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1159]) ).

fof(f16404,plain,
    ( spl0_864
    | ~ spl0_865
    | ~ spl0_144
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1900,f1868,f1167,f16401,f16398]) ).

fof(f16398,plain,
    ( spl0_864
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f16401,plain,
    ( spl0_865
  <=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f1900,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1168]) ).

fof(f16383,plain,
    ( ~ spl0_863
    | ~ spl0_235
    | spl0_862 ),
    inference(avatar_split_clause,[],[f16378,f16374,f2310,f16380]) ).

fof(f16380,plain,
    ( spl0_863
  <=> subclass(composition_function,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f16374,plain,
    ( spl0_862
  <=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f16378,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_862 ),
    inference(forward_demodulation,[],[f16376,f2312]) ).

fof(f16376,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
    | spl0_862 ),
    inference(avatar_component_clause,[],[f16374]) ).

fof(f16377,plain,
    ( spl0_861
    | ~ spl0_862
    | ~ spl0_143
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1895,f1868,f1163,f16374,f16371]) ).

fof(f16371,plain,
    ( spl0_861
  <=> ! [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_861])]) ).

fof(f1895,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f1164]) ).

fof(f16369,plain,
    ( spl0_860
    | ~ spl0_170
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1860,f1812,f1452,f16367]) ).

fof(f16367,plain,
    ( spl0_860
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f1452,plain,
    ( spl0_170
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f1860,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_170
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1453]) ).

fof(f1453,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_170 ),
    inference(avatar_component_clause,[],[f1452]) ).

fof(f16365,plain,
    ( spl0_859
    | ~ spl0_170
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1834,f1803,f1452,f16363]) ).

fof(f16363,plain,
    ( spl0_859
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f1834,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_170
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1453]) ).

fof(f16302,plain,
    ( spl0_858
    | spl0_631
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1500,f1456,f628,f9582,f16300]) ).

fof(f16300,plain,
    ( spl0_858
  <=> ! [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_858])]) ).

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

fof(f1500,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) )
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f629]) ).

fof(f16298,plain,
    ( spl0_857
    | ~ spl0_93
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1488,f1452,f702,f16296]) ).

fof(f16296,plain,
    ( spl0_857
  <=> ! [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_857])]) ).

fof(f1488,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f703]) ).

fof(f16281,plain,
    ( ~ spl0_80
    | spl0_179
    | ~ spl0_853 ),
    inference(avatar_split_clause,[],[f16051,f16041,f1522,f636]) ).

fof(f1522,plain,
    ( spl0_179
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f16051,plain,
    ( ~ member(null_class,universal_class)
    | spl0_179
    | ~ spl0_853 ),
    inference(superposition,[],[f1523,f16043]) ).

fof(f16043,plain,
    ( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
    | ~ spl0_853 ),
    inference(avatar_component_clause,[],[f16041]) ).

fof(f1523,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | spl0_179 ),
    inference(avatar_component_clause,[],[f1522]) ).

fof(f16235,plain,
    ( spl0_856
    | ~ spl0_111
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2031,f1998,f823,f16233]) ).

fof(f16233,plain,
    ( spl0_856
  <=> ! [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_856])]) ).

fof(f2031,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f824]) ).

fof(f16231,plain,
    ( spl0_855
    | ~ spl0_111
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2008,f1994,f823,f16229]) ).

fof(f16229,plain,
    ( spl0_855
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_855])]) ).

fof(f2008,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f824]) ).

fof(f16047,plain,
    ( spl0_853
    | spl0_854
    | ~ spl0_40
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2077,f2067,f380,f16045,f16041]) ).

fof(f16045,plain,
    ( spl0_854
  <=> ! [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_854])]) ).

fof(f2077,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_215 ),
    inference(superposition,[],[f2068,f381]) ).

fof(f16039,plain,
    ( spl0_852
    | ~ spl0_48
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1889,f1868,f444,f16037]) ).

fof(f16037,plain,
    ( spl0_852
  <=> ! [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_852])]) ).

fof(f444,plain,
    ( spl0_48
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1889,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,unordered_pair(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f445]) ).

fof(f445,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f16018,plain,
    ( spl0_851
    | ~ spl0_158
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1634,f1620,f1294,f16016]) ).

fof(f16016,plain,
    ( spl0_851
  <=> ! [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_851])]) ).

fof(f1634,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f1295]) ).

fof(f16014,plain,
    ( spl0_850
    | ~ spl0_32
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f11994,f9140,f339,f16012]) ).

fof(f16012,plain,
    ( spl0_850
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f11994,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0) )
    | ~ spl0_32
    | ~ spl0_603 ),
    inference(superposition,[],[f340,f9141]) ).

fof(f15998,plain,
    ( spl0_849
    | ~ spl0_185
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1762,f1745,f1556,f15996]) ).

fof(f15996,plain,
    ( spl0_849
  <=> ! [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_849])]) ).

fof(f1762,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_185
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f1557]) ).

fof(f15994,plain,
    ( spl0_848
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1654,f1639,f568,f452,f15992]) ).

fof(f15992,plain,
    ( spl0_848
  <=> ! [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_848])]) ).

fof(f1639,plain,
    ( spl0_194
  <=> ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f1654,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_194 ),
    inference(forward_demodulation,[],[f1650,f453]) ).

fof(f1650,plain,
    ( ! [X0] :
        ( null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class),X0) )
    | ~ spl0_70
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f569]) ).

fof(f1640,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
        | complement(X0) = null_class
        | ~ member(complement(X0),universal_class) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f1639]) ).

fof(f15898,plain,
    ( spl0_847
    | ~ spl0_235
    | ~ spl0_842 ),
    inference(avatar_split_clause,[],[f15878,f15875,f2310,f15896]) ).

fof(f15896,plain,
    ( spl0_847
  <=> ! [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_847])]) ).

fof(f15875,plain,
    ( spl0_842
  <=> ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f15878,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_842 ),
    inference(forward_demodulation,[],[f15876,f2312]) ).

fof(f15876,plain,
    ( ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_842 ),
    inference(avatar_component_clause,[],[f15875]) ).

fof(f15894,plain,
    ( spl0_846
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(avatar_split_clause,[],[f15873,f15867,f2310,f15892]) ).

fof(f15892,plain,
    ( spl0_846
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(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_846])]) ).

fof(f15867,plain,
    ( spl0_841
  <=> ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f15873,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15872,f2312]) ).

fof(f15872,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15871,f2312]) ).

fof(f15871,plain,
    ( ! [X0] :
        ( ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15870,f2312]) ).

fof(f15870,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_841 ),
    inference(forward_demodulation,[],[f15868,f2312]) ).

fof(f15868,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_841 ),
    inference(avatar_component_clause,[],[f15867]) ).

fof(f15890,plain,
    ( spl0_845
    | ~ spl0_20
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f3598,f3477,f287,f15888]) ).

fof(f15888,plain,
    ( spl0_845
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f3477,plain,
    ( spl0_341
  <=> null_class = complement(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f3598,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_20
    | ~ spl0_341 ),
    inference(superposition,[],[f288,f3479]) ).

fof(f3479,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f3477]) ).

fof(f15886,plain,
    ( spl0_844
    | ~ spl0_235
    | ~ spl0_840 ),
    inference(avatar_split_clause,[],[f15865,f15862,f2310,f15884]) ).

fof(f15884,plain,
    ( spl0_844
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f15862,plain,
    ( spl0_840
  <=> ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f15865,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_840 ),
    inference(forward_demodulation,[],[f15863,f2312]) ).

fof(f15863,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_840 ),
    inference(avatar_component_clause,[],[f15862]) ).

fof(f15882,plain,
    ( spl0_843
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(avatar_split_clause,[],[f15860,f15854,f2310,f15880]) ).

fof(f15880,plain,
    ( spl0_843
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f15854,plain,
    ( spl0_839
  <=> ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f15860,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15859,f2312]) ).

fof(f15859,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15858,f2312]) ).

fof(f15858,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15857,f2312]) ).

fof(f15857,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_839 ),
    inference(forward_demodulation,[],[f15855,f2312]) ).

fof(f15855,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_839 ),
    inference(avatar_component_clause,[],[f15854]) ).

fof(f15877,plain,
    ( spl0_842
    | ~ spl0_144
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1693,f1660,f1167,f15875]) ).

fof(f1693,plain,
    ( ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f1168]) ).

fof(f15869,plain,
    ( spl0_841
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1690,f1660,f1163,f15867]) ).

fof(f1690,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f1164]) ).

fof(f15864,plain,
    ( spl0_840
    | ~ spl0_144
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1673,f1656,f1167,f15862]) ).

fof(f1673,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f1168]) ).

fof(f15856,plain,
    ( spl0_839
    | ~ spl0_143
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1670,f1656,f1163,f15854]) ).

fof(f1670,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f1164]) ).

fof(f15793,plain,
    ( spl0_631
    | spl0_838
    | ~ spl0_79
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1482,f1452,f628,f15791,f9582]) ).

fof(f15791,plain,
    ( spl0_838
  <=> ! [X0,X3] :
        ( ~ function(X0)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))))))
        | ~ member(X3,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f1482,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,cross_product(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))))) )
    | ~ spl0_79
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f629]) ).

fof(f15777,plain,
    ( spl0_837
    | ~ spl0_198
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1940,f1935,f1711,f15775]) ).

fof(f15775,plain,
    ( spl0_837
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f1940,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_209 ),
    inference(superposition,[],[f1936,f1712]) ).

fof(f15773,plain,
    ( spl0_836
    | ~ spl0_39
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f3157,f2727,f376,f15771]) ).

fof(f2727,plain,
    ( spl0_284
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f3157,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 )
    | ~ spl0_39
    | ~ spl0_284 ),
    inference(resolution,[],[f2728,f377]) ).

fof(f2728,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f2727]) ).

fof(f15769,plain,
    ( spl0_834
    | ~ spl0_835
    | ~ spl0_99
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f843,f802,f739,f15766,f15763]) ).

fof(f15763,plain,
    ( spl0_834
  <=> ! [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_834])]) ).

fof(f15766,plain,
    ( spl0_835
  <=> subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f843,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_99
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f740]) ).

fof(f15735,plain,
    ( spl0_833
    | ~ spl0_176
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2009,f1994,f1477,f15733]) ).

fof(f15733,plain,
    ( spl0_833
  <=> ! [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_833])]) ).

fof(f1477,plain,
    ( spl0_176
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f2009,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_176
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f1478]) ).

fof(f1478,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f1477]) ).

fof(f15728,plain,
    ( ~ spl0_831
    | ~ spl0_832
    | spl0_633
    | ~ spl0_162
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1647,f1639,f1351,f9660,f15725,f15721]) ).

fof(f15721,plain,
    ( spl0_831
  <=> 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_831])]) ).

fof(f15725,plain,
    ( spl0_832
  <=> 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_832])]) ).

fof(f9660,plain,
    ( spl0_633
  <=> null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f1647,plain,
    ( null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_162
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f1352]) ).

fof(f15669,plain,
    ( spl0_830
    | ~ spl0_176
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2049,f1998,f1477,f15667]) ).

fof(f15667,plain,
    ( spl0_830
  <=> ! [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_830])]) ).

fof(f2049,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_176
    | ~ spl0_212 ),
    inference(duplicate_literal_removal,[],[f2032]) ).

fof(f2032,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_176
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f1478]) ).

fof(f15665,plain,
    ( spl0_829
    | ~ spl0_89
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1938,f1935,f682,f15663]) ).

fof(f15663,plain,
    ( spl0_829
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f682,plain,
    ( spl0_89
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f1938,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_209 ),
    inference(resolution,[],[f1936,f683]) ).

fof(f683,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f682]) ).

fof(f15583,plain,
    ( spl0_828
    | ~ spl0_235
    | ~ spl0_822 ),
    inference(avatar_split_clause,[],[f15552,f15549,f2310,f15581]) ).

fof(f15581,plain,
    ( spl0_828
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f15549,plain,
    ( spl0_822
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f15552,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_822 ),
    inference(forward_demodulation,[],[f15550,f2312]) ).

fof(f15550,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
    | ~ spl0_822 ),
    inference(avatar_component_clause,[],[f15549]) ).

fof(f15579,plain,
    ( spl0_827
    | ~ spl0_235
    | ~ spl0_821 ),
    inference(avatar_split_clause,[],[f15547,f15544,f2310,f15577]) ).

fof(f15577,plain,
    ( spl0_827
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f15544,plain,
    ( spl0_821
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f15547,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_821 ),
    inference(forward_demodulation,[],[f15545,f2312]) ).

fof(f15545,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
    | ~ spl0_821 ),
    inference(avatar_component_clause,[],[f15544]) ).

fof(f15568,plain,
    ( spl0_826
    | ~ spl0_198
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1932,f1923,f1711,f15566]) ).

fof(f15566,plain,
    ( spl0_826
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),compose(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f1932,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),compose(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_208 ),
    inference(superposition,[],[f1924,f1712]) ).

fof(f15564,plain,
    ( spl0_825
    | ~ spl0_152
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1853,f1812,f1247,f15562]) ).

fof(f15562,plain,
    ( spl0_825
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f1247,plain,
    ( spl0_152
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1853,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_152
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1248]) ).

fof(f1248,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1247]) ).

fof(f15560,plain,
    ( spl0_824
    | ~ spl0_152
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1827,f1803,f1247,f15558]) ).

fof(f15558,plain,
    ( spl0_824
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f1827,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_152
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1248]) ).

fof(f15556,plain,
    ( spl0_823
    | ~ spl0_142
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1770,f1745,f1159,f15554]) ).

fof(f15554,plain,
    ( spl0_823
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),regular(X3))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f1770,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),regular(X3))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
        | null_class = X3 )
    | ~ spl0_142
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f1160]) ).

fof(f15551,plain,
    ( spl0_822
    | ~ spl0_144
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1767,f1745,f1167,f15549]) ).

fof(f1767,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f1168]) ).

fof(f15546,plain,
    ( spl0_821
    | ~ spl0_143
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1764,f1745,f1163,f15544]) ).

fof(f1764,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f1164]) ).

fof(f15542,plain,
    ( spl0_820
    | ~ spl0_93
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1267,f1247,f702,f15540]) ).

fof(f15540,plain,
    ( spl0_820
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f1267,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f703]) ).

fof(f15513,plain,
    ( spl0_819
    | ~ spl0_786
    | ~ spl0_817 ),
    inference(avatar_split_clause,[],[f15504,f15501,f14704,f15511]) ).

fof(f15511,plain,
    ( spl0_819
  <=> ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(null_class,X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f15501,plain,
    ( spl0_817
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f15504,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_786
    | ~ spl0_817 ),
    inference(forward_demodulation,[],[f15502,f14706]) ).

fof(f15502,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_817 ),
    inference(avatar_component_clause,[],[f15501]) ).

fof(f15509,plain,
    ( ~ spl0_818
    | ~ spl0_22
    | spl0_813 ),
    inference(avatar_split_clause,[],[f15284,f15280,f295,f15506]) ).

fof(f15506,plain,
    ( spl0_818
  <=> function(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f15284,plain,
    ( ~ function(composition_function)
    | ~ spl0_22
    | spl0_813 ),
    inference(resolution,[],[f15282,f296]) ).

fof(f15503,plain,
    ( spl0_817
    | ~ spl0_198
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1911,f1906,f1711,f15501]) ).

fof(f1911,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_198
    | ~ spl0_206 ),
    inference(superposition,[],[f1907,f1712]) ).

fof(f15499,plain,
    ( spl0_816
    | ~ spl0_48
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1758,f1745,f444,f15497]) ).

fof(f15497,plain,
    ( spl0_816
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),unordered_pair(X3,X4))
        | ~ operation(X2)
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f1758,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),unordered_pair(X3,X4))
        | ~ operation(X2)
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 )
    | ~ spl0_48
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f445]) ).

fof(f15292,plain,
    ( spl0_815
    | ~ spl0_77
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2030,f1998,f613,f15290]) ).

fof(f15290,plain,
    ( spl0_815
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f2030,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_77
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f614]) ).

fof(f15288,plain,
    ( spl0_814
    | ~ spl0_77
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2007,f1994,f613,f15286]) ).

fof(f15286,plain,
    ( spl0_814
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f2007,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
    | ~ spl0_77
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f614]) ).

fof(f15283,plain,
    ( spl0_812
    | ~ spl0_813
    | ~ spl0_85
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1877,f1868,f664,f15280,f15277]) ).

fof(f15277,plain,
    ( spl0_812
  <=> ! [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_812])]) ).

fof(f1877,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_85
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f665]) ).

fof(f15275,plain,
    ( spl0_811
    | ~ spl0_48
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1684,f1660,f444,f15273]) ).

fof(f15273,plain,
    ( spl0_811
  <=> ! [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_811])]) ).

fof(f1684,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f445]) ).

fof(f15271,plain,
    ( spl0_810
    | ~ spl0_48
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1664,f1656,f444,f15269]) ).

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

fof(f1664,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 )
    | ~ spl0_48
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f445]) ).

fof(f15267,plain,
    ( spl0_809
    | ~ spl0_96
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1419,f1369,f727,f15265]) ).

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

fof(f1419,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,flip(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) )
    | ~ spl0_96
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f728]) ).

fof(f15261,plain,
    ( ~ spl0_808
    | ~ spl0_235
    | spl0_806 ),
    inference(avatar_split_clause,[],[f15253,f15245,f2310,f15258]) ).

fof(f15258,plain,
    ( spl0_808
  <=> 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_808])]) ).

fof(f15245,plain,
    ( spl0_806
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f15253,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_806 ),
    inference(forward_demodulation,[],[f15246,f2312]) ).

fof(f15246,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_806 ),
    inference(avatar_component_clause,[],[f15245]) ).

fof(f15252,plain,
    ( spl0_527
    | ~ spl0_805
    | spl0_806
    | ~ spl0_807
    | ~ spl0_84
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1209,f1167,f654,f15249,f15245,f15241,f7414]) ).

fof(f15241,plain,
    ( spl0_805
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f15249,plain,
    ( spl0_807
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f1209,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
    | ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_84
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f655]) ).

fof(f15237,plain,
    ( ~ spl0_804
    | ~ spl0_235
    | spl0_788 ),
    inference(avatar_split_clause,[],[f14810,f14801,f2310,f15234]) ).

fof(f15234,plain,
    ( spl0_804
  <=> subset_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f14801,plain,
    ( spl0_788
  <=> identity_relation = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f14810,plain,
    ( subset_relation != singleton_relation
    | ~ spl0_235
    | spl0_788 ),
    inference(forward_demodulation,[],[f14802,f2312]) ).

fof(f14802,plain,
    ( identity_relation != subset_relation
    | spl0_788 ),
    inference(avatar_component_clause,[],[f14801]) ).

fof(f15229,plain,
    ( ~ spl0_803
    | ~ spl0_235
    | spl0_799 ),
    inference(avatar_split_clause,[],[f15213,f15204,f2310,f15226]) ).

fof(f15226,plain,
    ( spl0_803
  <=> 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_803])]) ).

fof(f15204,plain,
    ( spl0_799
  <=> 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_799])]) ).

fof(f15213,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_799 ),
    inference(forward_demodulation,[],[f15205,f2312]) ).

fof(f15205,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_799 ),
    inference(avatar_component_clause,[],[f15204]) ).

fof(f15224,plain,
    ( ~ spl0_802
    | ~ spl0_235
    | spl0_800 ),
    inference(avatar_split_clause,[],[f15212,f15208,f2310,f15221]) ).

fof(f15221,plain,
    ( spl0_802
  <=> 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_802])]) ).

fof(f15208,plain,
    ( spl0_800
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f15212,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation)
    | ~ spl0_235
    | spl0_800 ),
    inference(forward_demodulation,[],[f15210,f2312]) ).

fof(f15210,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_800 ),
    inference(avatar_component_clause,[],[f15208]) ).

fof(f15219,plain,
    ( ~ spl0_801
    | ~ spl0_235
    | spl0_798 ),
    inference(avatar_split_clause,[],[f15214,f15200,f2310,f15216]) ).

fof(f15216,plain,
    ( spl0_801
  <=> member(complement(compose(element_relation,complement(singleton_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f15200,plain,
    ( spl0_798
  <=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f15214,plain,
    ( ~ member(complement(compose(element_relation,complement(singleton_relation))),universal_class)
    | ~ spl0_235
    | spl0_798 ),
    inference(forward_demodulation,[],[f15202,f2312]) ).

fof(f15202,plain,
    ( ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | spl0_798 ),
    inference(avatar_component_clause,[],[f15200]) ).

fof(f15211,plain,
    ( spl0_521
    | ~ spl0_798
    | spl0_799
    | ~ spl0_800
    | ~ spl0_84
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1195,f1163,f654,f15208,f15204,f15200,f7372]) ).

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

fof(f1195,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_84
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f655]) ).

fof(f15188,plain,
    ( spl0_797
    | ~ spl0_38
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1939,f1935,f372,f15186]) ).

fof(f15186,plain,
    ( spl0_797
  <=> ! [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_797])]) ).

fof(f1939,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_38
    | ~ spl0_209 ),
    inference(resolution,[],[f1936,f373]) ).

fof(f15004,plain,
    ( ~ spl0_796
    | ~ spl0_235
    | spl0_789 ),
    inference(avatar_split_clause,[],[f14809,f14805,f2310,f15001]) ).

fof(f14805,plain,
    ( spl0_789
  <=> subclass(subset_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f14809,plain,
    ( ~ subclass(subset_relation,singleton_relation)
    | ~ spl0_235
    | spl0_789 ),
    inference(forward_demodulation,[],[f14807,f2312]) ).

fof(f14807,plain,
    ( ~ subclass(subset_relation,identity_relation)
    | spl0_789 ),
    inference(avatar_component_clause,[],[f14805]) ).

fof(f14999,plain,
    ( spl0_795
    | ~ spl0_154
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1785,f1773,f1277,f14997]) ).

fof(f14997,plain,
    ( spl0_795
  <=> ! [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_795])]) ).

fof(f1277,plain,
    ( spl0_154
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1773,plain,
    ( spl0_200
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f1785,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_154
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1278]) ).

fof(f1278,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1277]) ).

fof(f1774,plain,
    ( ! [X2,X0,X1] :
        ( subclass(cross_product(X0,X1),X2)
        | not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))))) )
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f1773]) ).

fof(f14995,plain,
    ( spl0_794
    | ~ spl0_153
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1784,f1773,f1273,f14993]) ).

fof(f14993,plain,
    ( spl0_794
  <=> ! [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_794])]) ).

fof(f1273,plain,
    ( spl0_153
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f1784,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_153
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1274]) ).

fof(f1274,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1273]) ).

fof(f14856,plain,
    ( spl0_793
    | ~ spl0_786
    | ~ spl0_792 ),
    inference(avatar_split_clause,[],[f14852,f14849,f14704,f14854]) ).

fof(f14854,plain,
    ( spl0_793
  <=> ! [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_793])]) ).

fof(f14849,plain,
    ( spl0_792
  <=> ! [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_792])]) ).

fof(f14852,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_786
    | ~ spl0_792 ),
    inference(forward_demodulation,[],[f14850,f14706]) ).

fof(f14850,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_792 ),
    inference(avatar_component_clause,[],[f14849]) ).

fof(f14851,plain,
    ( spl0_792
    | ~ spl0_89
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1909,f1906,f682,f14849]) ).

fof(f1909,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_206 ),
    inference(resolution,[],[f1907,f683]) ).

fof(f14847,plain,
    ( spl0_791
    | ~ spl0_142
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1695,f1660,f1159,f14845]) ).

fof(f14845,plain,
    ( spl0_791
  <=> ! [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_791])]) ).

fof(f1695,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(regular(X0),X1)
        | ~ member(intersection(regular(X0),X1),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f1160]) ).

fof(f14843,plain,
    ( spl0_790
    | ~ spl0_142
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1675,f1656,f1159,f14841]) ).

fof(f14841,plain,
    ( spl0_790
  <=> ! [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_790])]) ).

fof(f1675,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,regular(X1))
        | ~ member(intersection(X0,regular(X1)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_142
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f1160]) ).

fof(f14808,plain,
    ( spl0_788
    | ~ spl0_789
    | ~ spl0_39
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2693,f2466,f376,f14805,f14801]) ).

fof(f2466,plain,
    ( spl0_264
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2693,plain,
    ( ~ subclass(subset_relation,identity_relation)
    | identity_relation = subset_relation
    | ~ spl0_39
    | ~ spl0_264 ),
    inference(resolution,[],[f2468,f377]) ).

fof(f2468,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f2466]) ).

fof(f14710,plain,
    ( spl0_786
    | spl0_787
    | ~ spl0_40
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1942,f1935,f380,f14708,f14704]) ).

fof(f14708,plain,
    ( spl0_787
  <=> ! [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_787])]) ).

fof(f1942,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_209 ),
    inference(superposition,[],[f1936,f381]) ).

fof(f14702,plain,
    ( spl0_785
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1839,f1803,f380,f14700]) ).

fof(f14700,plain,
    ( spl0_785
  <=> ! [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_785])]) ).

fof(f1839,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(superposition,[],[f1804,f381]) ).

fof(f14695,plain,
    ( spl0_783
    | ~ spl0_784
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1800,f1793,f380,f14692,f14689]) ).

fof(f14689,plain,
    ( spl0_783
  <=> ! [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_783])]) ).

fof(f1793,plain,
    ( spl0_201
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1800,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(superposition,[],[f1794,f381]) ).

fof(f1794,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2)) )
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f1793]) ).

fof(f14687,plain,
    ( spl0_782
    | ~ spl0_158
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1508,f1456,f1294,f14685]) ).

fof(f14685,plain,
    ( spl0_782
  <=> ! [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_782])]) ).

fof(f1508,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f1295]) ).

fof(f14634,plain,
    ( spl0_781
    | ~ spl0_49
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1646,f1639,f448,f14632]) ).

fof(f14632,plain,
    ( spl0_781
  <=> ! [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_781])]) ).

fof(f1646,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(complement(intersection(X0,X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) )
    | ~ spl0_49
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f449]) ).

fof(f14604,plain,
    ( spl0_780
    | ~ spl0_185
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1628,f1620,f1556,f14602]) ).

fof(f14602,plain,
    ( spl0_780
  <=> ! [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_780])]) ).

fof(f1628,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_185
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f1557]) ).

fof(f14520,plain,
    ( spl0_779
    | ~ spl0_130
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1859,f1812,f1012,f14518]) ).

fof(f14518,plain,
    ( spl0_779
  <=> ! [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_779])]) ).

fof(f1859,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | subclass(X1,X2) )
    | ~ spl0_130
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f1013]) ).

fof(f14516,plain,
    ( spl0_778
    | ~ spl0_130
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1833,f1803,f1012,f14514]) ).

fof(f14514,plain,
    ( spl0_778
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(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_778])]) ).

fof(f1833,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X1,X2) )
    | ~ spl0_130
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f1013]) ).

fof(f14512,plain,
    ( spl0_777
    | ~ spl0_114
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1789,f1773,f892,f14510]) ).

fof(f14510,plain,
    ( spl0_777
  <=> ! [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_777])]) ).

fof(f1789,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
        | function(cross_product(X0,X1))
        | ~ single_valued_class(cross_product(X0,X1)) )
    | ~ spl0_114
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f893]) ).

fof(f14508,plain,
    ( spl0_776
    | ~ spl0_93
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1068,f1012,f702,f14506]) ).

fof(f14506,plain,
    ( spl0_776
  <=> ! [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_776])]) ).

fof(f1068,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f703]) ).

fof(f14336,plain,
    ( spl0_775
    | ~ spl0_146
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1779,f1773,f1221,f14334]) ).

fof(f14334,plain,
    ( spl0_775
  <=> ! [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_775])]) ).

fof(f1221,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1779,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_146
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1222]) ).

fof(f1222,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1221]) ).

fof(f14332,plain,
    ( spl0_774
    | ~ spl0_158
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1432,f1369,f1294,f14330]) ).

fof(f14330,plain,
    ( spl0_774
  <=> ! [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_774])]) ).

fof(f1432,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f1295]) ).

fof(f14328,plain,
    ( spl0_773
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1132,f1087,f628,f14326]) ).

fof(f14326,plain,
    ( spl0_773
  <=> ! [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_773])]) ).

fof(f1132,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,cross_product(X1,X2)),X3)
        | not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) )
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f629]) ).

fof(f14324,plain,
    ( spl0_772
    | ~ spl0_79
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1114,f1083,f628,f14322]) ).

fof(f14322,plain,
    ( spl0_772
  <=> ! [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_772])]) ).

fof(f1114,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(cross_product(X0,X1),X2),X3)
        | not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) )
    | ~ spl0_79
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f629]) ).

fof(f14266,plain,
    ( spl0_771
    | ~ spl0_38
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1910,f1906,f372,f14264]) ).

fof(f14264,plain,
    ( spl0_771
  <=> ! [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_771])]) ).

fof(f1910,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
    | ~ spl0_38
    | ~ spl0_206 ),
    inference(resolution,[],[f1907,f373]) ).

fof(f14251,plain,
    ( spl0_769
    | ~ spl0_770
    | ~ spl0_39
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f2533,f2393,f376,f14248,f14244]) ).

fof(f14244,plain,
    ( spl0_769
  <=> element_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f2393,plain,
    ( spl0_251
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f2533,plain,
    ( ~ subclass(element_relation,singleton_relation)
    | element_relation = singleton_relation
    | ~ spl0_39
    | ~ spl0_251 ),
    inference(resolution,[],[f2395,f377]) ).

fof(f2395,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f2393]) ).

fof(f14028,plain,
    ( spl0_768
    | ~ spl0_106
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1858,f1812,f802,f14026]) ).

fof(f14026,plain,
    ( spl0_768
  <=> ! [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_768])]) ).

fof(f1858,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_106
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f803]) ).

fof(f14024,plain,
    ( spl0_767
    | ~ spl0_70
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1841,f1812,f568,f14022]) ).

fof(f14022,plain,
    ( spl0_767
  <=> ! [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_767])]) ).

fof(f1841,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_70
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f569]) ).

fof(f14020,plain,
    ( spl0_766
    | ~ spl0_106
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1832,f1803,f802,f14018]) ).

fof(f14018,plain,
    ( spl0_766
  <=> ! [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_766])]) ).

fof(f1832,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_106
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f803]) ).

fof(f14016,plain,
    ( spl0_765
    | ~ spl0_70
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1815,f1803,f568,f14014]) ).

fof(f14014,plain,
    ( spl0_765
  <=> ! [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_765])]) ).

fof(f1815,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_70
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f569]) ).

fof(f13965,plain,
    ( spl0_764
    | ~ spl0_184
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1786,f1773,f1549,f13963]) ).

fof(f13963,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f1549,plain,
    ( spl0_184
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f1786,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ member(X3,X0)
        | ~ member(X4,X1)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) )
    | ~ spl0_184
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1550]) ).

fof(f1550,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(cross_product(X3,X1),X4)
        | ~ member(X2,X3)
        | ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_184 ),
    inference(avatar_component_clause,[],[f1549]) ).

fof(f13961,plain,
    ( spl0_763
    | ~ spl0_158
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1490,f1452,f1294,f13959]) ).

fof(f13959,plain,
    ( spl0_763
  <=> ! [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_763])]) ).

fof(f1490,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
        | ~ member(X1,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
    | ~ spl0_158
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f1295]) ).

fof(f13957,plain,
    ( spl0_762
    | ~ spl0_93
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f851,f802,f702,f13955]) ).

fof(f13955,plain,
    ( spl0_762
  <=> ! [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_762])]) ).

fof(f851,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f703]) ).

fof(f13863,plain,
    ( spl0_761
    | ~ spl0_116
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1856,f1812,f919,f13861]) ).

fof(f13861,plain,
    ( spl0_761
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(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_761])]) ).

fof(f1856,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | null_class = X1 )
    | ~ spl0_116
    | ~ spl0_204 ),
    inference(resolution,[],[f1813,f920]) ).

fof(f13859,plain,
    ( spl0_760
    | ~ spl0_116
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1830,f1803,f919,f13857]) ).

fof(f13857,plain,
    ( spl0_760
  <=> ! [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_760])]) ).

fof(f1830,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | null_class = X1 )
    | ~ spl0_116
    | ~ spl0_202 ),
    inference(resolution,[],[f1804,f920]) ).

fof(f13783,plain,
    ( spl0_759
    | ~ spl0_44
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1648,f1639,f424,f13781]) ).

fof(f13781,plain,
    ( spl0_759
  <=> ! [X0] :
        ( null_class = complement(complement(X0))
        | ~ member(complement(complement(X0)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f1648,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | ~ member(complement(complement(X0)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_44
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f425]) ).

fof(f13779,plain,
    ( spl0_758
    | ~ spl0_163
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1617,f1609,f1361,f13777]) ).

fof(f13777,plain,
    ( spl0_758
  <=> ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f1361,plain,
    ( spl0_163
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f1609,plain,
    ( spl0_191
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1617,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 )
    | ~ spl0_163
    | ~ spl0_191 ),
    inference(resolution,[],[f1610,f1362]) ).

fof(f1362,plain,
    ( ! [X2,X0,X1] :
        ( subclass(unordered_pair(X0,X1),X2)
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0 )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1361]) ).

fof(f1610,plain,
    ( ! [X0] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | ~ inductive(X0)
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f1609]) ).

fof(f13775,plain,
    ( spl0_757
    | ~ spl0_93
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f979,f919,f702,f13773]) ).

fof(f13773,plain,
    ( spl0_757
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f979,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f703]) ).

fof(f13643,plain,
    ( spl0_756
    | ~ spl0_106
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2026,f1998,f802,f13641]) ).

fof(f13641,plain,
    ( spl0_756
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f2026,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_106
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f803]) ).

fof(f13639,plain,
    ( spl0_755
    | ~ spl0_106
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2003,f1994,f802,f13637]) ).

fof(f13637,plain,
    ( spl0_755
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f2003,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_106
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f803]) ).

fof(f13572,plain,
    ( spl0_754
    | ~ spl0_111
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1927,f1923,f823,f13570]) ).

fof(f13570,plain,
    ( spl0_754
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f1927,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_208 ),
    inference(resolution,[],[f1924,f824]) ).

fof(f13568,plain,
    ( spl0_753
    | ~ spl0_40
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1863,f1812,f380,f13566]) ).

fof(f13566,plain,
    ( spl0_753
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f1863,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_204 ),
    inference(superposition,[],[f1813,f381]) ).

fof(f13564,plain,
    ( spl0_752
    | ~ spl0_162
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1392,f1365,f1351,f13562]) ).

fof(f13562,plain,
    ( spl0_752
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f1392,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_162
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f1352]) ).

fof(f13533,plain,
    ( spl0_751
    | ~ spl0_38
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1888,f1868,f372,f13531]) ).

fof(f13531,plain,
    ( spl0_751
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f1888,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) )
    | ~ spl0_38
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f373]) ).

fof(f13529,plain,
    ( spl0_750
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1797,f1793,f380,f13527]) ).

fof(f13527,plain,
    ( spl0_750
  <=> ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1797,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(superposition,[],[f1794,f381]) ).

fof(f13467,plain,
    ( spl0_749
    | spl0_631
    | ~ spl0_79
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1261,f1247,f628,f9582,f13465]) ).

fof(f13465,plain,
    ( spl0_749
  <=> ! [X2] :
        ( ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f1261,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) )
    | ~ spl0_79
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f629]) ).

fof(f13443,plain,
    ( spl0_748
    | ~ spl0_341
    | ~ spl0_616 ),
    inference(avatar_split_clause,[],[f13018,f9350,f3477,f13440]) ).

fof(f13440,plain,
    ( spl0_748
  <=> null_class = intersection(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f9350,plain,
    ( spl0_616
  <=> ! [X0] : null_class = intersection(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f13018,plain,
    ( null_class = intersection(universal_class,null_class)
    | ~ spl0_341
    | ~ spl0_616 ),
    inference(superposition,[],[f9351,f3479]) ).

fof(f9351,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_616 ),
    inference(avatar_component_clause,[],[f9350]) ).

fof(f13147,plain,
    ( spl0_747
    | ~ spl0_31
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1892,f1868,f335,f13145]) ).

fof(f13145,plain,
    ( spl0_747
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f1892,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) )
    | ~ spl0_31
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f336]) ).

fof(f13143,plain,
    ( spl0_746
    | ~ spl0_32
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1891,f1868,f339,f13141]) ).

fof(f13141,plain,
    ( spl0_746
  <=> ! [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_746])]) ).

fof(f1891,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) )
    | ~ spl0_32
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f340]) ).

fof(f13017,plain,
    ( spl0_745
    | ~ spl0_89
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1881,f1868,f682,f13015]) ).

fof(f13015,plain,
    ( spl0_745
  <=> ! [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_745])]) ).

fof(f1881,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,compose(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f683]) ).

fof(f13013,plain,
    ( spl0_744
    | ~ spl0_85
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1750,f1745,f664,f13011]) ).

fof(f13011,plain,
    ( spl0_744
  <=> ! [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_744])]) ).

fof(f1750,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_85
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f665]) ).

fof(f13009,plain,
    ( spl0_743
    | ~ spl0_163
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1743,f1711,f1361,f13007]) ).

fof(f13007,plain,
    ( spl0_743
  <=> ! [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_743])]) ).

fof(f1743,plain,
    ( ! [X2,X0,X1] :
        ( subclass(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_163
    | ~ spl0_198 ),
    inference(superposition,[],[f1362,f1712]) ).

fof(f13005,plain,
    ( spl0_742
    | ~ spl0_91
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1725,f1711,f691,f13003]) ).

fof(f13003,plain,
    ( spl0_742
  <=> ! [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_742])]) ).

fof(f691,plain,
    ( spl0_91
  <=> ! [X4,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1725,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_91
    | ~ spl0_198 ),
    inference(superposition,[],[f692,f1712]) ).

fof(f692,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4 )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f691]) ).

fof(f13001,plain,
    ( spl0_741
    | ~ spl0_84
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1181,f1159,f654,f12999]) ).

fof(f12999,plain,
    ( spl0_741
  <=> ! [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_741])]) ).

fof(f1181,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
        | null_class = X0
        | ~ member(regular(X0),universal_class)
        | null_class = regular(X0) )
    | ~ spl0_84
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f655]) ).

fof(f12997,plain,
    ( spl0_740
    | ~ spl0_79
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1045,f1008,f628,f12995]) ).

fof(f12995,plain,
    ( spl0_740
  <=> ! [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_740])]) ).

fof(f1045,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) )
    | ~ spl0_79
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f629]) ).

fof(f12993,plain,
    ( spl0_739
    | ~ spl0_79
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1029,f1004,f628,f12991]) ).

fof(f12991,plain,
    ( spl0_739
  <=> ! [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_739])]) ).

fof(f1029,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) )
    | ~ spl0_79
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f629]) ).

fof(f12613,plain,
    ( spl0_738
    | ~ spl0_9
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2027,f1998,f240,f12611]) ).

fof(f12611,plain,
    ( spl0_738
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f2027,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_9
    | ~ spl0_212 ),
    inference(resolution,[],[f1999,f241]) ).

fof(f12609,plain,
    ( spl0_737
    | ~ spl0_9
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2004,f1994,f240,f12607]) ).

fof(f12607,plain,
    ( spl0_737
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f2004,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_9
    | ~ spl0_211 ),
    inference(resolution,[],[f1995,f241]) ).

fof(f12605,plain,
    ( spl0_736
    | ~ spl0_20
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1894,f1868,f287,f12603]) ).

fof(f12603,plain,
    ( spl0_736
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,complement(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f1894,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,complement(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) )
    | ~ spl0_20
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f288]) ).

fof(f12601,plain,
    ( spl0_735
    | spl0_150
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1783,f1773,f1238,f12598]) ).

fof(f1238,plain,
    ( spl0_150
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1783,plain,
    ( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)))))
    | spl0_150
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1240]) ).

fof(f1240,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | spl0_150 ),
    inference(avatar_component_clause,[],[f1238]) ).

fof(f12596,plain,
    ( spl0_734
    | spl0_148
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1782,f1773,f1229,f12593]) ).

fof(f1229,plain,
    ( spl0_148
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1782,plain,
    ( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)))))
    | spl0_148
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1231]) ).

fof(f1231,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | spl0_148 ),
    inference(avatar_component_clause,[],[f1229]) ).

fof(f12591,plain,
    ( spl0_733
    | ~ spl0_137
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1780,f1773,f1095,f12589]) ).

fof(f1095,plain,
    ( spl0_137
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1780,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_137
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1096]) ).

fof(f1096,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1095]) ).

fof(f12197,plain,
    ( spl0_732
    | ~ spl0_235
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f12158,f12155,f2310,f12195]) ).

fof(f12195,plain,
    ( spl0_732
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
        | null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f12155,plain,
    ( spl0_723
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f12158,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
        | null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_723 ),
    inference(forward_demodulation,[],[f12156,f2312]) ).

fof(f12156,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_723 ),
    inference(avatar_component_clause,[],[f12155]) ).

fof(f12193,plain,
    ( spl0_731
    | ~ spl0_235
    | ~ spl0_722 ),
    inference(avatar_split_clause,[],[f12153,f12150,f2310,f12191]) ).

fof(f12191,plain,
    ( spl0_731
  <=> ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f12150,plain,
    ( spl0_722
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f12153,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_722 ),
    inference(forward_demodulation,[],[f12151,f2312]) ).

fof(f12151,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_722 ),
    inference(avatar_component_clause,[],[f12150]) ).

fof(f12189,plain,
    ( spl0_730
    | ~ spl0_9
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1916,f1913,f240,f12187]) ).

fof(f12187,plain,
    ( spl0_730
  <=> ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f1913,plain,
    ( spl0_207
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f1916,plain,
    ( ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_9
    | ~ spl0_207 ),
    inference(resolution,[],[f1914,f241]) ).

fof(f1914,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f1913]) ).

fof(f12185,plain,
    ( ~ spl0_729
    | ~ spl0_235
    | spl0_728 ),
    inference(avatar_split_clause,[],[f12180,f12176,f2310,f12182]) ).

fof(f12182,plain,
    ( spl0_729
  <=> subclass(composition_function,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f12176,plain,
    ( spl0_728
  <=> subclass(composition_function,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f12180,plain,
    ( ~ subclass(composition_function,singleton_relation)
    | ~ spl0_235
    | spl0_728 ),
    inference(forward_demodulation,[],[f12178,f2312]) ).

fof(f12178,plain,
    ( ~ subclass(composition_function,identity_relation)
    | spl0_728 ),
    inference(avatar_component_clause,[],[f12176]) ).

fof(f12179,plain,
    ( spl0_727
    | ~ spl0_728
    | ~ spl0_103
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1902,f1868,f761,f12176,f12173]) ).

fof(f12173,plain,
    ( spl0_727
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f1902,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,identity_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f762]) ).

fof(f12171,plain,
    ( spl0_726
    | ~ spl0_341
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f11988,f9140,f3477,f12168]) ).

fof(f12168,plain,
    ( spl0_726
  <=> null_class = intersection(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f11988,plain,
    ( null_class = intersection(null_class,universal_class)
    | ~ spl0_341
    | ~ spl0_603 ),
    inference(superposition,[],[f9141,f3479]) ).

fof(f12166,plain,
    ( spl0_725
    | ~ spl0_160
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1741,f1711,f1316,f12164]) ).

fof(f12164,plain,
    ( spl0_725
  <=> ! [X0,X1] :
        ( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
        | null_class = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f1316,plain,
    ( spl0_160
  <=> ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f1741,plain,
    ( ! [X0,X1] :
        ( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
        | null_class = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_160
    | ~ spl0_198 ),
    inference(superposition,[],[f1317,f1712]) ).

fof(f1317,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1316]) ).

fof(f12162,plain,
    ( spl0_724
    | ~ spl0_142
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1636,f1620,f1159,f12160]) ).

fof(f12160,plain,
    ( spl0_724
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f1636,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_142
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f1160]) ).

fof(f12157,plain,
    ( spl0_723
    | ~ spl0_144
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1633,f1620,f1167,f12155]) ).

fof(f1633,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f1168]) ).

fof(f12152,plain,
    ( spl0_722
    | ~ spl0_143
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1630,f1620,f1163,f12150]) ).

fof(f1630,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f1164]) ).

fof(f12110,plain,
    ( spl0_721
    | ~ spl0_39
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1788,f1773,f376,f12108]) ).

fof(f12108,plain,
    ( spl0_721
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ subclass(X2,cross_product(X0,X1))
        | cross_product(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f1788,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ subclass(X2,cross_product(X0,X1))
        | cross_product(X0,X1) = X2 )
    | ~ spl0_39
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f377]) ).

fof(f12106,plain,
    ( spl0_720
    | ~ spl0_89
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1754,f1745,f682,f12104]) ).

fof(f12104,plain,
    ( spl0_720
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f1754,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f683]) ).

fof(f12102,plain,
    ( spl0_719
    | ~ spl0_94
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f881,f823,f718,f12100]) ).

fof(f12100,plain,
    ( spl0_719
  <=> ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f718,plain,
    ( spl0_94
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f881,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_94
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f719]) ).

fof(f719,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f718]) ).

fof(f11903,plain,
    ( spl0_718
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1838,f1803,f452,f11901]) ).

fof(f11901,plain,
    ( spl0_718
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f1838,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(superposition,[],[f1804,f453]) ).

fof(f11899,plain,
    ( spl0_717
    | ~ spl0_132
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1740,f1711,f1020,f11897]) ).

fof(f11897,plain,
    ( spl0_717
  <=> ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f1020,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1740,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_132
    | ~ spl0_198 ),
    inference(superposition,[],[f1021,f1712]) ).

fof(f1021,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1020]) ).

fof(f11895,plain,
    ( spl0_716
    | ~ spl0_48
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1624,f1620,f444,f11893]) ).

fof(f11893,plain,
    ( spl0_716
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f1624,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 )
    | ~ spl0_48
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f445]) ).

fof(f11866,plain,
    ( spl0_715
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1799,f1793,f452,f11864]) ).

fof(f11864,plain,
    ( spl0_715
  <=> ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f1799,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(superposition,[],[f1794,f453]) ).

fof(f11790,plain,
    ( spl0_714
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1796,f1793,f452,f11788]) ).

fof(f11788,plain,
    ( spl0_714
  <=> ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f1796,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(superposition,[],[f1794,f453]) ).

fof(f11786,plain,
    ( spl0_713
    | ~ spl0_89
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1724,f1711,f682,f11784]) ).

fof(f11784,plain,
    ( spl0_713
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f1724,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_89
    | ~ spl0_198 ),
    inference(superposition,[],[f683,f1712]) ).

fof(f11758,plain,
    ( spl0_712
    | ~ spl0_77
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1933,f1923,f613,f11756]) ).

fof(f11756,plain,
    ( spl0_712
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f1933,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_208 ),
    inference(duplicate_literal_removal,[],[f1926]) ).

fof(f1926,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_208 ),
    inference(resolution,[],[f1924,f614]) ).

fof(f11754,plain,
    ( spl0_711
    | ~ spl0_136
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1776,f1773,f1091,f11752]) ).

fof(f11752,plain,
    ( spl0_711
  <=> ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f1091,plain,
    ( spl0_136
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1776,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_136
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f1092]) ).

fof(f1092,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1091]) ).

fof(f11740,plain,
    ( spl0_710
    | ~ spl0_30
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1735,f1711,f331,f11738]) ).

fof(f11738,plain,
    ( spl0_710
  <=> ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f1735,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_30
    | ~ spl0_198 ),
    inference(superposition,[],[f332,f1712]) ).

fof(f11736,plain,
    ( ~ spl0_708
    | spl0_709
    | ~ spl0_165
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1568,f1556,f1369,f11734,f11730]) ).

fof(f11730,plain,
    ( spl0_708
  <=> subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f11734,plain,
    ( spl0_709
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f1568,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class) )
    | ~ spl0_165
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f1370]) ).

fof(f11653,plain,
    ( spl0_707
    | ~ spl0_38
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1757,f1745,f372,f11651]) ).

fof(f11651,plain,
    ( spl0_707
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),X3)
        | ~ operation(X2)
        | ~ subclass(X3,X4)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f1757,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),X3)
        | ~ operation(X2)
        | ~ subclass(X3,X4)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
    | ~ spl0_38
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f373]) ).

fof(f11647,plain,
    ( ~ spl0_706
    | ~ spl0_235
    | spl0_704 ),
    inference(avatar_split_clause,[],[f11642,f11634,f2310,f11644]) ).

fof(f11644,plain,
    ( spl0_706
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f11634,plain,
    ( spl0_704
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f11642,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_704 ),
    inference(forward_demodulation,[],[f11636,f2312]) ).

fof(f11636,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
    | spl0_704 ),
    inference(avatar_component_clause,[],[f11634]) ).

fof(f11641,plain,
    ( ~ spl0_704
    | ~ spl0_705
    | spl0_430
    | ~ spl0_125
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1651,f1639,f959,f5490,f11638,f11634]) ).

fof(f11638,plain,
    ( spl0_705
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f5490,plain,
    ( spl0_430
  <=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f1651,plain,
    ( null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
    | ~ spl0_125
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f960]) ).

fof(f11630,plain,
    ( ~ spl0_703
    | ~ spl0_235
    | spl0_700 ),
    inference(avatar_split_clause,[],[f11610,f11601,f2310,f11627]) ).

fof(f11627,plain,
    ( spl0_703
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f11601,plain,
    ( spl0_700
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f11610,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_235
    | spl0_700 ),
    inference(forward_demodulation,[],[f11603,f2312]) ).

fof(f11603,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | spl0_700 ),
    inference(avatar_component_clause,[],[f11601]) ).

fof(f11625,plain,
    ( ~ spl0_702
    | ~ spl0_235
    | spl0_701 ),
    inference(avatar_split_clause,[],[f11609,f11605,f2310,f11622]) ).

fof(f11622,plain,
    ( spl0_702
  <=> member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f11605,plain,
    ( spl0_701
  <=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f11609,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class)
    | ~ spl0_235
    | spl0_701 ),
    inference(forward_demodulation,[],[f11607,f2312]) ).

fof(f11607,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | spl0_701 ),
    inference(avatar_component_clause,[],[f11605]) ).

fof(f11608,plain,
    ( ~ spl0_700
    | ~ spl0_701
    | spl0_425
    | ~ spl0_124
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1649,f1639,f955,f5463,f11605,f11601]) ).

fof(f5463,plain,
    ( spl0_425
  <=> null_class = complement(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f1649,plain,
    ( null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_124
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f956]) ).

fof(f11574,plain,
    ( spl0_699
    | ~ spl0_31
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1761,f1745,f335,f11572]) ).

fof(f11572,plain,
    ( spl0_699
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f1761,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
    | ~ spl0_31
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f336]) ).

fof(f11570,plain,
    ( spl0_698
    | ~ spl0_32
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1760,f1745,f339,f11568]) ).

fof(f11568,plain,
    ( spl0_698
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f1760,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
    | ~ spl0_32
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f340]) ).

fof(f11477,plain,
    ( spl0_697
    | ~ spl0_20
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1763,f1745,f287,f11475]) ).

fof(f11475,plain,
    ( spl0_697
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(X3))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f1763,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(X3))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
    | ~ spl0_20
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f288]) ).

fof(f11473,plain,
    ( spl0_696
    | ~ spl0_48
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1736,f1711,f444,f11471]) ).

fof(f11471,plain,
    ( spl0_696
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f1736,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
        | cross_product(X0,X1) = null_class )
    | ~ spl0_48
    | ~ spl0_198 ),
    inference(superposition,[],[f445,f1712]) ).

fof(f11454,plain,
    ( spl0_695
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1771,f1745,f731,f11452]) ).

fof(f11452,plain,
    ( spl0_695
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),singleton_relation)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f1771,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),singleton_relation)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation) )
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f732]) ).

fof(f11449,plain,
    ( spl0_694
    | ~ spl0_103
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1769,f1745,f761,f11447]) ).

fof(f11447,plain,
    ( spl0_694
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),identity_relation)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f1769,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),identity_relation)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f762]) ).

fof(f11445,plain,
    ( spl0_693
    | ~ spl0_126
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1738,f1711,f963,f11443]) ).

fof(f11443,plain,
    ( spl0_693
  <=> ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f963,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1738,plain,
    ( ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_126
    | ~ spl0_198 ),
    inference(superposition,[],[f964,f1712]) ).

fof(f964,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | null_class = X1
        | null_class = X0 )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f963]) ).

fof(f11042,plain,
    ( spl0_692
    | ~ spl0_38
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1709,f1704,f372,f11040]) ).

fof(f11040,plain,
    ( spl0_692
  <=> ! [X0,X1] :
        ( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(successor_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f1709,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(successor_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) )
    | ~ spl0_38
    | ~ spl0_197 ),
    inference(resolution,[],[f1705,f373]) ).

fof(f11038,plain,
    ( spl0_691
    | ~ spl0_31
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1687,f1660,f335,f11036]) ).

fof(f11036,plain,
    ( spl0_691
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f1687,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_31
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f336]) ).

fof(f11034,plain,
    ( spl0_690
    | ~ spl0_32
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1686,f1660,f339,f11032]) ).

fof(f11032,plain,
    ( spl0_690
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f1686,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_32
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f340]) ).

fof(f11030,plain,
    ( spl0_689
    | ~ spl0_31
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1667,f1656,f335,f11028]) ).

fof(f11028,plain,
    ( spl0_689
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f1667,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_31
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f336]) ).

fof(f11026,plain,
    ( spl0_688
    | ~ spl0_32
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1666,f1656,f339,f11024]) ).

fof(f11024,plain,
    ( spl0_688
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f1666,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
    | ~ spl0_32
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f340]) ).

fof(f11022,plain,
    ( spl0_687
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1408,f1365,f568,f452,f11020]) ).

fof(f11020,plain,
    ( spl0_687
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f1408,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(forward_demodulation,[],[f1395,f453]) ).

fof(f1395,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class),X2) )
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f569]) ).

fof(f10796,plain,
    ( spl0_686
    | spl0_122
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1781,f1773,f946,f10793]) ).

fof(f946,plain,
    ( spl0_122
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1781,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
    | spl0_122
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f948]) ).

fof(f948,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | spl0_122 ),
    inference(avatar_component_clause,[],[f946]) ).

fof(f10791,plain,
    ( spl0_685
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f10437,f8668,f2310,f2304,f10788]) ).

fof(f10788,plain,
    ( spl0_685
  <=> member(regular(singleton_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f8668,plain,
    ( spl0_569
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f10437,plain,
    ( member(regular(singleton_relation),universal_class)
    | ~ spl0_234
    | ~ spl0_235
    | ~ spl0_569 ),
    inference(forward_demodulation,[],[f10378,f2312]) ).

fof(f10378,plain,
    ( member(regular(identity_relation),universal_class)
    | ~ spl0_234
    | ~ spl0_569 ),
    inference(resolution,[],[f8669,f2306]) ).

fof(f8669,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_569 ),
    inference(avatar_component_clause,[],[f8668]) ).

fof(f10786,plain,
    ( spl0_684
    | spl0_120
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1778,f1773,f936,f10783]) ).

fof(f936,plain,
    ( spl0_120
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1778,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
    | spl0_120
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f938]) ).

fof(f938,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_120 ),
    inference(avatar_component_clause,[],[f936]) ).

fof(f10781,plain,
    ( spl0_683
    | spl0_118
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1777,f1773,f927,f10778]) ).

fof(f927,plain,
    ( spl0_118
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1777,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
    | spl0_118
    | ~ spl0_200 ),
    inference(resolution,[],[f1774,f929]) ).

fof(f929,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_118 ),
    inference(avatar_component_clause,[],[f927]) ).

fof(f10604,plain,
    ( spl0_682
    | ~ spl0_152
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1312,f1294,f1247,f10602]) ).

fof(f10602,plain,
    ( spl0_682
  <=> ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f1312,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_152
    | ~ spl0_158 ),
    inference(resolution,[],[f1295,f1248]) ).

fof(f10600,plain,
    ( spl0_681
    | ~ spl0_96
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f842,f802,f727,f10598]) ).

fof(f842,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
    | ~ spl0_96
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f728]) ).

fof(f10596,plain,
    ( spl0_680
    | ~ spl0_95
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f841,f802,f723,f10594]) ).

fof(f841,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
    | ~ spl0_95
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f724]) ).

fof(f10563,plain,
    ( spl0_678
    | ~ spl0_679
    | ~ spl0_78
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1880,f1868,f624,f10560,f10557]) ).

fof(f10557,plain,
    ( spl0_678
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f10560,plain,
    ( spl0_679
  <=> subclass(composition_function,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f624,plain,
    ( spl0_78
  <=> ! [X0,X1] :
        ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1880,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_78
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f625]) ).

fof(f625,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f624]) ).

fof(f10555,plain,
    ( spl0_677
    | ~ spl0_78
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1753,f1745,f624,f10553]) ).

fof(f10553,plain,
    ( spl0_677
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),successor_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f1753,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),successor_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) )
    | ~ spl0_78
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f625]) ).

fof(f10551,plain,
    ( spl0_676
    | ~ spl0_142
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1510,f1456,f1159,f10549]) ).

fof(f10549,plain,
    ( spl0_676
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f1510,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f1160]) ).

fof(f10547,plain,
    ( spl0_675
    | ~ spl0_435
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1504,f1456,f1163,f5514,f10545]) ).

fof(f10545,plain,
    ( spl0_675
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f5514,plain,
    ( spl0_435
  <=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1504,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f1164]) ).

fof(f10447,plain,
    ( spl0_674
    | ~ spl0_131
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1739,f1711,f1016,f10445]) ).

fof(f10445,plain,
    ( spl0_674
  <=> ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f1016,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f1739,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_131
    | ~ spl0_198 ),
    inference(superposition,[],[f1017,f1712]) ).

fof(f1017,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1016]) ).

fof(f10443,plain,
    ( spl0_673
    | ~ spl0_78
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1720,f1711,f624,f10441]) ).

fof(f10441,plain,
    ( spl0_673
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),successor_relation)
        | second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f1720,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),successor_relation)
        | second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_78
    | ~ spl0_198 ),
    inference(superposition,[],[f625,f1712]) ).

fof(f10374,plain,
    ( spl0_672
    | ~ spl0_20
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1689,f1660,f287,f10372]) ).

fof(f10372,plain,
    ( spl0_672
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f1689,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f288]) ).

fof(f10370,plain,
    ( spl0_671
    | ~ spl0_20
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1669,f1656,f287,f10368]) ).

fof(f10368,plain,
    ( spl0_671
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f1669,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_20
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f288]) ).

fof(f10363,plain,
    ( ~ spl0_669
    | ~ spl0_670
    | spl0_344
    | ~ spl0_111
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1645,f1639,f823,f3490,f10360,f10356]) ).

fof(f10356,plain,
    ( spl0_669
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f10360,plain,
    ( spl0_670
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f1645,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_111
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f824]) ).

fof(f9981,plain,
    ( spl0_668
    | ~ spl0_176
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1732,f1711,f1477,f9979]) ).

fof(f9979,plain,
    ( spl0_668
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f1732,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_176
    | ~ spl0_198 ),
    inference(superposition,[],[f1478,f1712]) ).

fof(f9977,plain,
    ( spl0_667
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1691,f1660,f888,f9975]) ).

fof(f9975,plain,
    ( spl0_667
  <=> ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f888,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1691,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f889]) ).

fof(f889,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f888]) ).

fof(f9973,plain,
    ( spl0_666
    | ~ spl0_38
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1683,f1660,f372,f9971]) ).

fof(f9971,plain,
    ( spl0_666
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f1683,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
    | ~ spl0_38
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f373]) ).

fof(f9969,plain,
    ( spl0_665
    | ~ spl0_113
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1671,f1656,f888,f9967]) ).

fof(f9967,plain,
    ( spl0_665
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f1671,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_113
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f889]) ).

fof(f9965,plain,
    ( spl0_664
    | ~ spl0_38
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1663,f1656,f372,f9963]) ).

fof(f9963,plain,
    ( spl0_664
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f1663,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
    | ~ spl0_38
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f373]) ).

fof(f9961,plain,
    ( spl0_663
    | ~ spl0_123
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1652,f1639,f951,f9959]) ).

fof(f9959,plain,
    ( spl0_663
  <=> ! [X0] :
        ( null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f1652,plain,
    ( ! [X0] :
        ( null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = X0 )
    | ~ spl0_123
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f952]) ).

fof(f9957,plain,
    ( spl0_662
    | ~ spl0_48
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1499,f1456,f444,f9955]) ).

fof(f9955,plain,
    ( spl0_662
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f1499,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
    | ~ spl0_48
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f445]) ).

fof(f9953,plain,
    ( spl0_661
    | ~ spl0_142
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1492,f1452,f1159,f9951]) ).

fof(f9951,plain,
    ( spl0_661
  <=> ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f1492,plain,
    ( ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | null_class = X1 )
    | ~ spl0_142
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f1160]) ).

fof(f9949,plain,
    ( ~ spl0_435
    | spl0_660
    | ~ spl0_143
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1486,f1452,f1163,f9947,f5514]) ).

fof(f9947,plain,
    ( spl0_660
  <=> ! [X0,X1] :
        ( ~ function(X0)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation)
        | ~ member(X1,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f1486,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f1164]) ).

fof(f9945,plain,
    ( spl0_659
    | ~ spl0_142
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1434,f1369,f1159,f9943]) ).

fof(f9943,plain,
    ( spl0_659
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,regular(X0))
        | ~ member(X1,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f1434,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,regular(X0))
        | ~ member(X1,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f1160]) ).

fof(f9940,plain,
    ( spl0_657
    | ~ spl0_658
    | ~ spl0_144
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1431,f1369,f1167,f9937,f9934]) ).

fof(f9934,plain,
    ( spl0_657
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f9937,plain,
    ( spl0_658
  <=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f1431,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation) )
    | ~ spl0_144
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f1168]) ).

fof(f9932,plain,
    ( ~ spl0_656
    | ~ spl0_235
    | spl0_655 ),
    inference(avatar_split_clause,[],[f9927,f9923,f2310,f9929]) ).

fof(f9929,plain,
    ( spl0_656
  <=> subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f9923,plain,
    ( spl0_655
  <=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f9927,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_655 ),
    inference(forward_demodulation,[],[f9925,f2312]) ).

fof(f9925,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
    | spl0_655 ),
    inference(avatar_component_clause,[],[f9923]) ).

fof(f9926,plain,
    ( spl0_654
    | ~ spl0_655
    | ~ spl0_143
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1428,f1369,f1163,f9923,f9920]) ).

fof(f9920,plain,
    ( spl0_654
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f1428,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f1164]) ).

fof(f9918,plain,
    ( spl0_652
    | ~ spl0_653
    | ~ spl0_9
    | ~ spl0_341
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6767,f6441,f3477,f240,f9915,f9912]) ).

fof(f9915,plain,
    ( spl0_653
  <=> subclass(domain_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f6767,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_9
    | ~ spl0_341
    | ~ spl0_489 ),
    inference(forward_demodulation,[],[f6744,f3479]) ).

fof(f6744,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(universal_class)) )
    | ~ spl0_9
    | ~ spl0_489 ),
    inference(resolution,[],[f6442,f241]) ).

fof(f9910,plain,
    ( spl0_651
    | ~ spl0_79
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1063,f1012,f628,f9908]) ).

fof(f9908,plain,
    ( spl0_651
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f1063,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) )
    | ~ spl0_79
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f629]) ).

fof(f9904,plain,
    ( spl0_650
    | ~ spl0_87
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1723,f1711,f673,f9902]) ).

fof(f9902,plain,
    ( spl0_650
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f673,plain,
    ( spl0_87
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f1723,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_87
    | ~ spl0_198 ),
    inference(superposition,[],[f674,f1712]) ).

fof(f674,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
        | compose(X0,X1) = X4 )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f673]) ).

fof(f9782,plain,
    ( spl0_649
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1882,f1868,f584,f9780]) ).

fof(f9780,plain,
    ( spl0_649
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f1882,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) )
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f585]) ).

fof(f9778,plain,
    ( spl0_648
    | ~ spl0_29
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1734,f1711,f327,f9776]) ).

fof(f9776,plain,
    ( spl0_648
  <=> ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f1734,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_29
    | ~ spl0_198 ),
    inference(superposition,[],[f328,f1712]) ).

fof(f9774,plain,
    ( spl0_647
    | ~ spl0_48
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1481,f1452,f444,f9772]) ).

fof(f9772,plain,
    ( spl0_647
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,unordered_pair(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f1481,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,unordered_pair(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 )
    | ~ spl0_48
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f445]) ).

fof(f9770,plain,
    ( spl0_646
    | ~ spl0_48
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1423,f1369,f444,f9768]) ).

fof(f9768,plain,
    ( spl0_646
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f1423,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 )
    | ~ spl0_48
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f445]) ).

fof(f9766,plain,
    ( spl0_645
    | ~ spl0_49
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1391,f1365,f448,f9764]) ).

fof(f9764,plain,
    ( spl0_645
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
        | subclass(X0,intersection(X1,intersection(X2,X3)))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f1391,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
        | subclass(X0,intersection(X1,intersection(X2,X3)))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) )
    | ~ spl0_49
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f449]) ).

fof(f9762,plain,
    ( spl0_644
    | ~ spl0_115
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1358,f1351,f915,f9760]) ).

fof(f9760,plain,
    ( spl0_644
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f915,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1358,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_115
    | ~ spl0_162 ),
    inference(resolution,[],[f1352,f916]) ).

fof(f916,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f915]) ).

fof(f9721,plain,
    ( spl0_643
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(avatar_split_clause,[],[f9688,f9683,f2310,f9719]) ).

fof(f9719,plain,
    ( spl0_643
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f9683,plain,
    ( spl0_637
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f9688,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f9687,f2312]) ).

fof(f9687,plain,
    ( ! [X0] :
        ( ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f9686,f2312]) ).

fof(f9686,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f9684,f2312]) ).

fof(f9684,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_637 ),
    inference(avatar_component_clause,[],[f9683]) ).

fof(f9717,plain,
    ( ~ spl0_641
    | spl0_642
    | ~ spl0_106
    | ~ spl0_360 ),
    inference(avatar_split_clause,[],[f3839,f3753,f802,f9715,f9711]) ).

fof(f9711,plain,
    ( spl0_641
  <=> subclass(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f3839,plain,
    ( ! [X0] :
        ( member(X0,universal_class)
        | ~ subclass(universal_class,subset_relation) )
    | ~ spl0_106
    | ~ spl0_360 ),
    inference(resolution,[],[f3754,f803]) ).

fof(f9700,plain,
    ( spl0_640
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(avatar_split_clause,[],[f9677,f9672,f2310,f9698]) ).

fof(f9698,plain,
    ( spl0_640
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f9672,plain,
    ( spl0_635
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f9677,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(forward_demodulation,[],[f9676,f2312]) ).

fof(f9676,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(forward_demodulation,[],[f9675,f2312]) ).

fof(f9675,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_635 ),
    inference(forward_demodulation,[],[f9673,f2312]) ).

fof(f9673,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_635 ),
    inference(avatar_component_clause,[],[f9672]) ).

fof(f9696,plain,
    ( spl0_639
    | ~ spl0_67
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1876,f1868,f556,f9694]) ).

fof(f9694,plain,
    ( spl0_639
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f1876,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) )
    | ~ spl0_67
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f557]) ).

fof(f9692,plain,
    ( spl0_638
    | ~ spl0_97
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1696,f1660,f731,f9690]) ).

fof(f9690,plain,
    ( spl0_638
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f1696,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_97
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f732]) ).

fof(f9685,plain,
    ( spl0_637
    | ~ spl0_103
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1694,f1660,f761,f9683]) ).

fof(f1694,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_196 ),
    inference(resolution,[],[f1661,f762]) ).

fof(f9681,plain,
    ( spl0_636
    | ~ spl0_97
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1676,f1656,f731,f9679]) ).

fof(f9679,plain,
    ( spl0_636
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f1676,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_97
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f732]) ).

fof(f9674,plain,
    ( spl0_635
    | ~ spl0_103
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1674,f1656,f761,f9672]) ).

fof(f1674,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_195 ),
    inference(resolution,[],[f1657,f762]) ).

fof(f9667,plain,
    ( spl0_633
    | ~ spl0_634
    | ~ spl0_112
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1359,f1351,f884,f9664,f9660]) ).

fof(f9664,plain,
    ( spl0_634
  <=> member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f1359,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_112
    | ~ spl0_162 ),
    inference(resolution,[],[f1352,f885]) ).

fof(f9658,plain,
    ( spl0_632
    | ~ spl0_4
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f3738,f3595,f219,f9656]) ).

fof(f9656,plain,
    ( spl0_632
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f3738,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_357 ),
    inference(resolution,[],[f3596,f220]) ).

fof(f9584,plain,
    ( spl0_630
    | spl0_631
    | ~ spl0_79
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f847,f802,f628,f9582,f9579]) ).

fof(f847,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) )
    | ~ spl0_79
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f629]) ).

fof(f9528,plain,
    ( spl0_628
    | ~ spl0_629
    | ~ spl0_64
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1883,f1868,f539,f9525,f9522]) ).

fof(f9522,plain,
    ( spl0_628
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f9525,plain,
    ( spl0_629
  <=> subclass(composition_function,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f1883,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_64
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f540]) ).

fof(f9520,plain,
    ( spl0_627
    | ~ spl0_89
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1415,f1369,f682,f9518]) ).

fof(f9518,plain,
    ( spl0_627
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,compose(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f1415,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,compose(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f683]) ).

fof(f9516,plain,
    ( spl0_626
    | ~ spl0_28
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1357,f1351,f323,f9514]) ).

fof(f1357,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_28
    | ~ spl0_162 ),
    inference(resolution,[],[f1352,f324]) ).

fof(f9458,plain,
    ( spl0_625
    | ~ spl0_235
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3673,f3529,f2822,f2310,f9455]) ).

fof(f9455,plain,
    ( spl0_625
  <=> null_class = intersection(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f3673,plain,
    ( null_class = intersection(singleton_relation,complement(subset_relation))
    | ~ spl0_235
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(forward_demodulation,[],[f3664,f2312]) ).

fof(f3664,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3659]) ).

fof(f3659,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_293
    | ~ spl0_352 ),
    inference(resolution,[],[f3530,f2823]) ).

fof(f9397,plain,
    ( spl0_624
    | ~ spl0_235
    | ~ spl0_619 ),
    inference(avatar_split_clause,[],[f9369,f9366,f2310,f9395]) ).

fof(f9395,plain,
    ( spl0_624
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f9366,plain,
    ( spl0_619
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f9369,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))) )
    | ~ spl0_235
    | ~ spl0_619 ),
    inference(forward_demodulation,[],[f9367,f2312]) ).

fof(f9367,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
    | ~ spl0_619 ),
    inference(avatar_component_clause,[],[f9366]) ).

fof(f9393,plain,
    ( spl0_623
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(avatar_split_clause,[],[f9364,f9359,f2310,f9391]) ).

fof(f9391,plain,
    ( spl0_623
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f9359,plain,
    ( spl0_618
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f9364,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) )
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9363,f2312]) ).

fof(f9363,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9362,f2312]) ).

fof(f9362,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9360,f2312]) ).

fof(f9360,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_618 ),
    inference(avatar_component_clause,[],[f9359]) ).

fof(f9381,plain,
    ( spl0_621
    | ~ spl0_622
    | ~ spl0_61
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1878,f1868,f524,f9378,f9375]) ).

fof(f9375,plain,
    ( spl0_621
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f9378,plain,
    ( spl0_622
  <=> subclass(composition_function,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f1878,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_61
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f525]) ).

fof(f9373,plain,
    ( spl0_620
    | ~ spl0_38
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1623,f1620,f372,f9371]) ).

fof(f9371,plain,
    ( spl0_620
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f1623,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_38
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f373]) ).

fof(f9368,plain,
    ( spl0_619
    | ~ spl0_125
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1396,f1365,f959,f9366]) ).

fof(f1396,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
    | ~ spl0_125
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f960]) ).

fof(f9361,plain,
    ( spl0_618
    | ~ spl0_124
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1394,f1365,f955,f9359]) ).

fof(f1394,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_124
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f956]) ).

fof(f9356,plain,
    ( spl0_617
    | ~ spl0_135
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1214,f1167,f1087,f9354]) ).

fof(f9354,plain,
    ( spl0_617
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
        | member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
        | subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f1214,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
        | member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
        | subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) )
    | ~ spl0_135
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f1088]) ).

fof(f9352,plain,
    ( spl0_616
    | ~ spl0_128
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3668,f3529,f1004,f9350]) ).

fof(f3668,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_128
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3647]) ).

fof(f3647,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(X0))
        | null_class = intersection(X0,complement(X0)) )
    | ~ spl0_128
    | ~ spl0_352 ),
    inference(resolution,[],[f3530,f1005]) ).

fof(f9347,plain,
    ( spl0_615
    | ~ spl0_134
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1207,f1167,f1083,f9345]) ).

fof(f9345,plain,
    ( spl0_615
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
        | member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
        | subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f1207,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
        | member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
        | subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) )
    | ~ spl0_134
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f1084]) ).

fof(f9340,plain,
    ( spl0_614
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1200,f1163,f1087,f9338]) ).

fof(f9338,plain,
    ( spl0_614
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
        | subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1200,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
        | subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) )
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f1088]) ).

fof(f9333,plain,
    ( spl0_613
    | ~ spl0_134
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1193,f1163,f1083,f9331]) ).

fof(f9331,plain,
    ( spl0_613
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
        | subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1193,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
        | subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) )
    | ~ spl0_134
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f1084]) ).

fof(f9329,plain,
    ( spl0_612
    | ~ spl0_88
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f882,f823,f677,f9327]) ).

fof(f9327,plain,
    ( spl0_612
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f677,plain,
    ( spl0_88
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f882,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) )
    | ~ spl0_88
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f678]) ).

fof(f678,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f677]) ).

fof(f9236,plain,
    ( spl0_611
    | ~ spl0_294
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3666,f3529,f2826,f9233]) ).

fof(f9233,plain,
    ( spl0_611
  <=> null_class = intersection(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f3666,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_294
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3650]) ).

fof(f3650,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_294
    | ~ spl0_352 ),
    inference(resolution,[],[f3530,f2827]) ).

fof(f9209,plain,
    ( spl0_610
    | ~ spl0_86
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1722,f1711,f669,f9207]) ).

fof(f9207,plain,
    ( spl0_610
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f669,plain,
    ( spl0_86
  <=> ! [X4,X0,X1] :
        ( member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1722,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_86
    | ~ spl0_198 ),
    inference(superposition,[],[f670,f1712]) ).

fof(f670,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
        | member(X1,domain_of(X0)) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f669]) ).

fof(f9205,plain,
    ( spl0_609
    | ~ spl0_85
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1721,f1711,f664,f9203]) ).

fof(f9203,plain,
    ( spl0_609
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f1721,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_85
    | ~ spl0_198 ),
    inference(superposition,[],[f665,f1712]) ).

fof(f9201,plain,
    ( spl0_608
    | ~ spl0_31
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1627,f1620,f335,f9199]) ).

fof(f9199,plain,
    ( spl0_608
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f1627,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_31
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f336]) ).

fof(f9197,plain,
    ( spl0_607
    | ~ spl0_32
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1626,f1620,f339,f9195]) ).

fof(f9195,plain,
    ( spl0_607
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f1626,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_32
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f340]) ).

fof(f9193,plain,
    ( spl0_606
    | ~ spl0_130
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1574,f1556,f1012,f9191]) ).

fof(f9191,plain,
    ( spl0_606
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f1574,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f1013]) ).

fof(f9189,plain,
    ( spl0_605
    | ~ spl0_44
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1393,f1365,f424,f9187]) ).

fof(f9187,plain,
    ( spl0_605
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
        | subclass(X0,intersection(X1,complement(X2)))
        | member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f1393,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
        | subclass(X0,intersection(X1,complement(X2)))
        | member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) )
    | ~ spl0_44
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f425]) ).

fof(f9185,plain,
    ( spl0_604
    | ~ spl0_79
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f974,f919,f628,f9183]) ).

fof(f9183,plain,
    ( spl0_604
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | null_class = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f974,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | null_class = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) )
    | ~ spl0_79
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f629]) ).

fof(f9142,plain,
    ( spl0_603
    | ~ spl0_129
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3640,f3525,f1008,f9140]) ).

fof(f3640,plain,
    ( ! [X0] : null_class = intersection(complement(X0),X0)
    | ~ spl0_129
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3617]) ).

fof(f3617,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(X0),X0)
        | null_class = intersection(complement(X0),X0) )
    | ~ spl0_129
    | ~ spl0_351 ),
    inference(resolution,[],[f3526,f1009]) ).

fof(f9132,plain,
    ( ~ spl0_602
    | ~ spl0_235
    | spl0_601 ),
    inference(avatar_split_clause,[],[f9127,f9123,f2310,f9129]) ).

fof(f9129,plain,
    ( spl0_602
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f9123,plain,
    ( spl0_601
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f9127,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_235
    | spl0_601 ),
    inference(forward_demodulation,[],[f9124,f2312]) ).

fof(f9124,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | spl0_601 ),
    inference(avatar_component_clause,[],[f9123]) ).

fof(f9126,plain,
    ( ~ spl0_548
    | spl0_233
    | spl0_601
    | ~ spl0_43
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1702,f1660,f393,f9123,f2300,f8196]) ).

fof(f8196,plain,
    ( spl0_548
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f2300,plain,
    ( spl0_233
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f1702,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ member(identity_relation,universal_class)
    | ~ spl0_43
    | ~ spl0_196 ),
    inference(superposition,[],[f1661,f395]) ).

fof(f9121,plain,
    ( spl0_600
    | ~ spl0_20
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1629,f1620,f287,f9119]) ).

fof(f9119,plain,
    ( spl0_600
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f1629,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_20
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f288]) ).

fof(f9116,plain,
    ( spl0_599
    | ~ spl0_129
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1213,f1167,f1008,f9114]) ).

fof(f9114,plain,
    ( spl0_599
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
        | member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f1213,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
        | member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_129
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f1009]) ).

fof(f9111,plain,
    ( spl0_598
    | ~ spl0_128
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1211,f1167,f1004,f9109]) ).

fof(f9109,plain,
    ( spl0_598
  <=> ! [X0] :
        ( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
        | member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f1211,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
        | member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_128
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f1005]) ).

fof(f9104,plain,
    ( spl0_597
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1199,f1163,f1008,f9102]) ).

fof(f9102,plain,
    ( spl0_597
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
        | member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
        | null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f1199,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
        | member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
        | null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f1009]) ).

fof(f9097,plain,
    ( spl0_596
    | ~ spl0_128
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1197,f1163,f1004,f9095]) ).

fof(f9095,plain,
    ( spl0_596
  <=> ! [X0] :
        ( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
        | member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
        | null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f1197,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
        | member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
        | null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_128
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f1005]) ).

fof(f9093,plain,
    ( spl0_595
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f970,f915,f568,f452,f9091]) ).

fof(f9091,plain,
    ( spl0_595
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
        | subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f970,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
        | subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_115 ),
    inference(forward_demodulation,[],[f969,f453]) ).

fof(f969,plain,
    ( ! [X0,X1] :
        ( subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class),X0) )
    | ~ spl0_70
    | ~ spl0_115 ),
    inference(resolution,[],[f916,f569]) ).

fof(f9079,plain,
    ( spl0_594
    | ~ spl0_300
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3638,f3525,f2930,f9076]) ).

fof(f9076,plain,
    ( spl0_594
  <=> null_class = intersection(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f3638,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_300
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3620]) ).

fof(f3620,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_300
    | ~ spl0_351 ),
    inference(resolution,[],[f3526,f2931]) ).

fof(f9065,plain,
    ( spl0_593
    | ~ spl0_235
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f8996,f8993,f2310,f9063]) ).

fof(f9063,plain,
    ( spl0_593
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f8993,plain,
    ( spl0_590
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f8996,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_235
    | ~ spl0_590 ),
    inference(forward_demodulation,[],[f8994,f2312]) ).

fof(f8994,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_590 ),
    inference(avatar_component_clause,[],[f8993]) ).

fof(f9004,plain,
    ( spl0_592
    | ~ spl0_72
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1755,f1745,f584,f9002]) ).

fof(f9002,plain,
    ( spl0_592
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose_class(X3))
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f1755,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose_class(X3))
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) )
    | ~ spl0_72
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f585]) ).

fof(f9000,plain,
    ( spl0_591
    | ~ spl0_97
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1637,f1620,f731,f8998]) ).

fof(f8998,plain,
    ( spl0_591
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f1637,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_97
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f732]) ).

fof(f8995,plain,
    ( spl0_590
    | ~ spl0_103
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1635,f1620,f761,f8993]) ).

fof(f1635,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f762]) ).

fof(f8991,plain,
    ( spl0_589
    | ~ spl0_116
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1571,f1556,f919,f8989]) ).

fof(f8989,plain,
    ( spl0_589
  <=> ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f1571,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f920]) ).

fof(f8987,plain,
    ( spl0_588
    | ~ spl0_89
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f832,f802,f682,f8985]) ).

fof(f832,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_89
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f683]) ).

fof(f8983,plain,
    ( spl0_587
    | ~ spl0_312
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3636,f3525,f3118,f8980]) ).

fof(f8980,plain,
    ( spl0_587
  <=> null_class = intersection(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f3636,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_312
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3629]) ).

fof(f3629,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_312
    | ~ spl0_351 ),
    inference(resolution,[],[f3526,f3119]) ).

fof(f8856,plain,
    ( spl0_586
    | ~ spl0_77
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1719,f1711,f613,f8854]) ).

fof(f8854,plain,
    ( spl0_586
  <=> ! [X0,X3,X2,X1] :
        ( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),X3)
        | ~ member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f1719,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),X3)
        | ~ member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_77
    | ~ spl0_198 ),
    inference(superposition,[],[f614,f1712]) ).

fof(f8849,plain,
    ( ~ spl0_584
    | spl0_274
    | spl0_585
    | ~ spl0_76
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1700,f1660,f608,f8846,f2535,f8842]) ).

fof(f8842,plain,
    ( spl0_584
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f8846,plain,
    ( spl0_585
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f1700,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_76
    | ~ spl0_196 ),
    inference(superposition,[],[f1661,f610]) ).

fof(f8840,plain,
    ( spl0_583
    | ~ spl0_152
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1643,f1639,f1247,f8838]) ).

fof(f8838,plain,
    ( spl0_583
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(complement(X0),universal_class)
        | ~ subclass(universal_class,X0)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f1643,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(complement(X0),universal_class)
        | ~ subclass(universal_class,X0)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_152
    | ~ spl0_194 ),
    inference(resolution,[],[f1640,f1248]) ).

fof(f8836,plain,
    ( spl0_582
    | ~ spl0_28
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3129,f3092,f323,f8834]) ).

fof(f8834,plain,
    ( spl0_582
  <=> ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f3129,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_310 ),
    inference(duplicate_literal_removal,[],[f3121]) ).

fof(f3121,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,subset_relation) )
    | ~ spl0_28
    | ~ spl0_310 ),
    inference(resolution,[],[f3093,f324]) ).

fof(f8832,plain,
    ( spl0_581
    | ~ spl0_38
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1582,f1578,f372,f8830]) ).

fof(f8830,plain,
    ( spl0_581
  <=> ! [X2,X0,X1] :
        ( ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class)
        | ~ subclass(compose_class(X0),X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1582,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class)
        | ~ subclass(compose_class(X0),X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) )
    | ~ spl0_38
    | ~ spl0_186 ),
    inference(resolution,[],[f1579,f373]) ).

fof(f8828,plain,
    ( ~ spl0_579
    | spl0_580
    | ~ spl0_106
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1573,f1556,f802,f8826,f8822]) ).

fof(f8822,plain,
    ( spl0_579
  <=> subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f8826,plain,
    ( spl0_580
  <=> ! [X0,X1] :
        ( member(unordered_pair(X0,X1),subset_relation)
        | ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1573,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(X0,X1),subset_relation)
        | ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_106
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f803]) ).

fof(f8820,plain,
    ( spl0_578
    | ~ spl0_76
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1401,f1365,f608,f8818]) ).

fof(f8818,plain,
    ( spl0_578
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f1401,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) )
    | ~ spl0_76
    | ~ spl0_164 ),
    inference(superposition,[],[f1366,f610]) ).

fof(f8816,plain,
    ( spl0_577
    | ~ spl0_130
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1314,f1294,f1012,f8814]) ).

fof(f8814,plain,
    ( spl0_577
  <=> ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f1314,plain,
    ( ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_158 ),
    inference(resolution,[],[f1295,f1013]) ).

fof(f8729,plain,
    ( spl0_576
    | ~ spl0_28
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f3103,f2940,f323,f8727]) ).

fof(f8727,plain,
    ( spl0_576
  <=> ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f3103,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_302 ),
    inference(duplicate_literal_removal,[],[f3095]) ).

fof(f3095,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,element_relation) )
    | ~ spl0_28
    | ~ spl0_302 ),
    inference(resolution,[],[f2941,f324]) ).

fof(f8725,plain,
    ( spl0_575
    | ~ spl0_64
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1756,f1745,f539,f8723]) ).

fof(f8723,plain,
    ( spl0_575
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f1756,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) )
    | ~ spl0_64
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f540]) ).

fof(f8721,plain,
    ( spl0_574
    | ~ spl0_114
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1385,f1361,f892,f8719]) ).

fof(f8719,plain,
    ( spl0_574
  <=> ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
        | not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
        | function(unordered_pair(X0,X1))
        | ~ single_valued_class(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f1385,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
        | not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
        | function(unordered_pair(X0,X1))
        | ~ single_valued_class(unordered_pair(X0,X1)) )
    | ~ spl0_114
    | ~ spl0_163 ),
    inference(resolution,[],[f1362,f893]) ).

fof(f8717,plain,
    ( spl0_573
    | ~ spl0_142
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1270,f1247,f1159,f8715]) ).

fof(f8715,plain,
    ( spl0_573
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f1270,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 )
    | ~ spl0_142
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f1160]) ).

fof(f8713,plain,
    ( spl0_572
    | ~ spl0_435
    | ~ spl0_143
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1265,f1247,f1163,f5514,f8711]) ).

fof(f8711,plain,
    ( spl0_572
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f1265,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation) )
    | ~ spl0_143
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f1164]) ).

fof(f8709,plain,
    ( spl0_571
    | ~ spl0_76
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1256,f1243,f608,f8707]) ).

fof(f8707,plain,
    ( spl0_571
  <=> ! [X0,X1] :
        ( ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f1243,plain,
    ( spl0_151
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1256,plain,
    ( ! [X0,X1] :
        ( ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X1,X0) )
    | ~ spl0_76
    | ~ spl0_151 ),
    inference(superposition,[],[f1244,f610]) ).

fof(f1244,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1243]) ).

fof(f8705,plain,
    ( spl0_570
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f899,f884,f568,f452,f8703]) ).

fof(f8703,plain,
    ( spl0_570
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f899,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(forward_demodulation,[],[f898,f453]) ).

fof(f898,plain,
    ( ! [X0] :
        ( null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
    | ~ spl0_70
    | ~ spl0_112 ),
    inference(resolution,[],[f885,f569]) ).

fof(f8670,plain,
    ( spl0_569
    | ~ spl0_4
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f2961,f2814,f219,f8668]) ).

fof(f2814,plain,
    ( spl0_291
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f2961,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_291 ),
    inference(resolution,[],[f2815,f220]) ).

fof(f2815,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f2814]) ).

fof(f8358,plain,
    ( spl0_568
    | ~ spl0_61
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1751,f1745,f524,f8356]) ).

fof(f8356,plain,
    ( spl0_568
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f1751,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_61
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f525]) ).

fof(f8354,plain,
    ( spl0_567
    | ~ spl0_72
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1718,f1711,f584,f8352]) ).

fof(f8352,plain,
    ( spl0_567
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f1718,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_72
    | ~ spl0_198 ),
    inference(superposition,[],[f585,f1712]) ).

fof(f8350,plain,
    ( spl0_566
    | ~ spl0_103
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2870,f2310,f761,f8348]) ).

fof(f8348,plain,
    ( spl0_566
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f2870,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103
    | ~ spl0_235 ),
    inference(superposition,[],[f762,f2312]) ).

fof(f8346,plain,
    ( spl0_565
    | ~ spl0_134
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1606,f1584,f1083,f8344]) ).

fof(f8344,plain,
    ( spl0_565
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f1584,plain,
    ( spl0_187
  <=> ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f1606,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0)) )
    | ~ spl0_134
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1601]) ).

fof(f1601,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0))
        | subclass(intersection(universal_class,X1),domain_of(X0)) )
    | ~ spl0_134
    | ~ spl0_187 ),
    inference(resolution,[],[f1585,f1084]) ).

fof(f1585,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1584]) ).

fof(f8342,plain,
    ( spl0_564
    | ~ spl0_135
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1605,f1584,f1087,f8340]) ).

fof(f8340,plain,
    ( spl0_564
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f1605,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0)) )
    | ~ spl0_135
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1602]) ).

fof(f1602,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0))
        | subclass(intersection(X1,universal_class),domain_of(X0)) )
    | ~ spl0_135
    | ~ spl0_187 ),
    inference(resolution,[],[f1585,f1088]) ).

fof(f8338,plain,
    ( spl0_563
    | ~ spl0_63
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1437,f1373,f532,f8336]) ).

fof(f8336,plain,
    ( spl0_563
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f532,plain,
    ( spl0_63
  <=> ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1373,plain,
    ( spl0_166
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f1437,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | ~ inductive(X1) )
    | ~ spl0_63
    | ~ spl0_166 ),
    inference(resolution,[],[f1374,f533]) ).

fof(f533,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f532]) ).

fof(f1374,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),X2)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,X2) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1373]) ).

fof(f8324,plain,
    ( spl0_562
    | ~ spl0_14
    | ~ spl0_85
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1411,f1369,f664,f262,f8322]) ).

fof(f1411,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | ~ member(X0,domain_of(X0)) )
    | ~ spl0_85
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f665]) ).

fof(f8320,plain,
    ( spl0_561
    | ~ spl0_123
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1397,f1365,f951,f8318]) ).

fof(f8318,plain,
    ( spl0_561
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
        | subclass(X0,intersection(X1,regular(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f1397,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
        | subclass(X0,intersection(X1,regular(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
        | null_class = X2 )
    | ~ spl0_123
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f952]) ).

fof(f8316,plain,
    ( spl0_560
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1390,f1365,f823,f8314]) ).

fof(f8314,plain,
    ( spl0_560
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f1390,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) )
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f824]) ).

fof(f8311,plain,
    ( spl0_559
    | ~ spl0_27
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1206,f1167,f319,f8309]) ).

fof(f8309,plain,
    ( spl0_559
  <=> ! [X0] :
        ( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
        | member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
        | subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f1206,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
        | member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
        | subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_27
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f320]) ).

fof(f8304,plain,
    ( spl0_558
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1192,f1163,f319,f8302]) ).

fof(f8302,plain,
    ( spl0_558
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
        | member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
        | subclass(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f1192,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
        | member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
        | subclass(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f320]) ).

fof(f8300,plain,
    ( spl0_557
    | ~ spl0_135
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1186,f1159,f1087,f8298]) ).

fof(f8298,plain,
    ( spl0_557
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | null_class = X1
        | subclass(intersection(X0,regular(X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f1186,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | null_class = X1
        | subclass(intersection(X0,regular(X1)),X2) )
    | ~ spl0_135
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f1088]) ).

fof(f8237,plain,
    ( spl0_556
    | ~ spl0_134
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1179,f1159,f1083,f8235]) ).

fof(f8235,plain,
    ( spl0_556
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | null_class = X0
        | subclass(intersection(regular(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f1179,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | null_class = X0
        | subclass(intersection(regular(X0),X1),X2) )
    | ~ spl0_134
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f1084]) ).

fof(f8233,plain,
    ( spl0_555
    | ~ spl0_48
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1131,f1087,f444,f8231]) ).

fof(f8231,plain,
    ( spl0_555
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f1131,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 )
    | ~ spl0_48
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f445]) ).

fof(f8229,plain,
    ( spl0_554
    | ~ spl0_48
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1113,f1083,f444,f8227]) ).

fof(f8227,plain,
    ( spl0_554
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(unordered_pair(X0,X1),X2),X3)
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f1113,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(unordered_pair(X0,X1),X2),X3)
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 )
    | ~ spl0_48
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f445]) ).

fof(f8225,plain,
    ( spl0_553
    | ~ spl0_85
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f878,f823,f664,f8223]) ).

fof(f8223,plain,
    ( spl0_553
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f878,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_85
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f665]) ).

fof(f8221,plain,
    ( ~ spl0_2
    | ~ spl0_551
    | spl0_552
    | ~ spl0_63
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f872,f819,f532,f8218,f8214,f209]) ).

fof(f209,plain,
    ( spl0_2
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f8214,plain,
    ( spl0_551
  <=> inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f8218,plain,
    ( spl0_552
  <=> omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f872,plain,
    ( omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))
    | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))))
    | ~ inductive(omega)
    | ~ spl0_63
    | ~ spl0_110 ),
    inference(resolution,[],[f820,f533]) ).

fof(f8210,plain,
    ( ~ spl0_550
    | ~ spl0_235
    | spl0_549 ),
    inference(avatar_split_clause,[],[f8204,f8200,f2310,f8207]) ).

fof(f8207,plain,
    ( spl0_550
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f8200,plain,
    ( spl0_549
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f8204,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_235
    | spl0_549 ),
    inference(forward_demodulation,[],[f8201,f2312]) ).

fof(f8201,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | spl0_549 ),
    inference(avatar_component_clause,[],[f8200]) ).

fof(f8203,plain,
    ( spl0_233
    | ~ spl0_548
    | spl0_549
    | ~ spl0_84
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f776,f761,f654,f8200,f8196,f2300]) ).

fof(f776,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ member(identity_relation,universal_class)
    | null_class = identity_relation
    | ~ spl0_84
    | ~ spl0_103 ),
    inference(resolution,[],[f762,f655]) ).

fof(f8194,plain,
    ( spl0_547
    | ~ spl0_55
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f7331,f5170,f477,f8191]) ).

fof(f8191,plain,
    ( spl0_547
  <=> universal_class = intersection(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f7331,plain,
    ( universal_class = intersection(universal_class,universal_class)
    | ~ spl0_55
    | ~ spl0_423 ),
    inference(resolution,[],[f5171,f478]) ).

fof(f8187,plain,
    ( spl0_231
    | ~ spl0_545
    | spl0_546
    | ~ spl0_84
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f772,f731,f654,f8184,f8180,f2282]) ).

fof(f8180,plain,
    ( spl0_545
  <=> member(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f8184,plain,
    ( spl0_546
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f772,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
    | ~ member(singleton_relation,universal_class)
    | null_class = singleton_relation
    | ~ spl0_84
    | ~ spl0_97 ),
    inference(resolution,[],[f732,f655]) ).

fof(f8161,plain,
    ( spl0_544
    | ~ spl0_67
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1749,f1745,f556,f8159]) ).

fof(f8159,plain,
    ( spl0_544
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f1749,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),X4) )
    | ~ spl0_67
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f557]) ).

fof(f8157,plain,
    ( spl0_543
    | ~ spl0_68
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1748,f1745,f560,f8155]) ).

fof(f8155,plain,
    ( spl0_543
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f1748,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),X3) )
    | ~ spl0_68
    | ~ spl0_199 ),
    inference(resolution,[],[f1746,f561]) ).

fof(f8152,plain,
    ( spl0_542
    | ~ spl0_228
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f7330,f5170,f2265,f8149]) ).

fof(f8149,plain,
    ( spl0_542
  <=> member(null_class,intersection(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f7330,plain,
    ( member(null_class,intersection(universal_class,universal_class))
    | ~ spl0_228
    | ~ spl0_423 ),
    inference(resolution,[],[f5171,f2266]) ).

fof(f8147,plain,
    ( spl0_541
    | ~ spl0_39
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1383,f1361,f376,f8145]) ).

fof(f8145,plain,
    ( spl0_541
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | ~ subclass(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f1383,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | ~ subclass(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = X2 )
    | ~ spl0_39
    | ~ spl0_163 ),
    inference(resolution,[],[f1362,f377]) ).

fof(f8143,plain,
    ( spl0_540
    | ~ spl0_106
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1313,f1294,f802,f8141]) ).

fof(f8141,plain,
    ( spl0_540
  <=> ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f1313,plain,
    ( ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) )
    | ~ spl0_106
    | ~ spl0_158 ),
    inference(resolution,[],[f1295,f803]) ).

fof(f8139,plain,
    ( spl0_539
    | ~ spl0_48
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1260,f1247,f444,f8137]) ).

fof(f8137,plain,
    ( spl0_539
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f1260,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
    | ~ spl0_48
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f445]) ).

fof(f7473,plain,
    ( spl0_538
    | ~ spl0_64
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1715,f1711,f539,f7471]) ).

fof(f7471,plain,
    ( spl0_538
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_relation)
        | second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1715,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_relation)
        | second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_64
    | ~ spl0_198 ),
    inference(superposition,[],[f540,f1712]) ).

fof(f7469,plain,
    ( spl0_537
    | ~ spl0_22
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1554,f1549,f295,f7467]) ).

fof(f7467,plain,
    ( spl0_537
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ function(cross_product(X1,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f1554,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ function(cross_product(X1,X3)) )
    | ~ spl0_22
    | ~ spl0_184 ),
    inference(resolution,[],[f1550,f296]) ).

fof(f7465,plain,
    ( spl0_536
    | ~ spl0_38
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1513,f1477,f372,f7463]) ).

fof(f7463,plain,
    ( spl0_536
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(element_relation,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1513,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(element_relation,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_38
    | ~ spl0_176 ),
    inference(resolution,[],[f1478,f373]) ).

fof(f7461,plain,
    ( spl0_535
    | ~ spl0_38
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1498,f1456,f372,f7459]) ).

fof(f7459,plain,
    ( spl0_535
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1498,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) )
    | ~ spl0_38
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f373]) ).

fof(f7457,plain,
    ( spl0_534
    | ~ spl0_38
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1480,f1452,f372,f7455]) ).

fof(f7455,plain,
    ( spl0_534
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,X1)
        | ~ member(X2,universal_class)
        | ~ subclass(X1,X3)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f1480,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,X1)
        | ~ member(X2,universal_class)
        | ~ subclass(X1,X3)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
    | ~ spl0_38
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f373]) ).

fof(f7447,plain,
    ( spl0_533
    | ~ spl0_57
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1436,f1373,f503,f7445]) ).

fof(f7445,plain,
    ( spl0_533
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,domain_of(domain_of(X1)))
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f503,plain,
    ( spl0_57
  <=> ! [X8] :
        ( ~ operation(X8)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1436,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,domain_of(domain_of(X1)))
        | ~ operation(X1) )
    | ~ spl0_57
    | ~ spl0_166 ),
    inference(resolution,[],[f1374,f504]) ).

fof(f504,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f503]) ).

fof(f7443,plain,
    ( spl0_532
    | ~ spl0_110
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1384,f1361,f819,f7441]) ).

fof(f7441,plain,
    ( spl0_532
  <=> ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),omega) = X1
        | not_subclass_element(unordered_pair(X0,X1),omega) = X0
        | unordered_pair(X0,X1) = omega
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f1384,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),omega) = X1
        | not_subclass_element(unordered_pair(X0,X1),omega) = X0
        | unordered_pair(X0,X1) = omega
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_110
    | ~ spl0_163 ),
    inference(resolution,[],[f1362,f820]) ).

fof(f7439,plain,
    ( spl0_531
    | ~ spl0_116
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1311,f1294,f919,f7437]) ).

fof(f7437,plain,
    ( spl0_531
  <=> ! [X0] :
        ( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f1311,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_158 ),
    inference(resolution,[],[f1295,f920]) ).

fof(f7434,plain,
    ( ~ spl0_530
    | ~ spl0_235
    | spl0_528 ),
    inference(avatar_split_clause,[],[f7426,f7418,f2310,f7431]) ).

fof(f7431,plain,
    ( spl0_530
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f7418,plain,
    ( spl0_528
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f7426,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
    | ~ spl0_235
    | spl0_528 ),
    inference(forward_demodulation,[],[f7419,f2312]) ).

fof(f7419,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | spl0_528 ),
    inference(avatar_component_clause,[],[f7418]) ).

fof(f7425,plain,
    ( spl0_527
    | spl0_528
    | ~ spl0_529
    | ~ spl0_23
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1210,f1167,f299,f7422,f7418,f7414]) ).

fof(f1210,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
    | member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_23
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f300]) ).

fof(f7401,plain,
    ( ~ spl0_526
    | ~ spl0_235
    | spl0_522 ),
    inference(avatar_split_clause,[],[f7385,f7376,f2310,f7398]) ).

fof(f7398,plain,
    ( spl0_526
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f7376,plain,
    ( spl0_522
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f7385,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
    | ~ spl0_235
    | spl0_522 ),
    inference(forward_demodulation,[],[f7377,f2312]) ).

fof(f7377,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | spl0_522 ),
    inference(avatar_component_clause,[],[f7376]) ).

fof(f7396,plain,
    ( ~ spl0_525
    | ~ spl0_235
    | spl0_523 ),
    inference(avatar_split_clause,[],[f7384,f7380,f2310,f7393]) ).

fof(f7380,plain,
    ( spl0_523
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f7384,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
    | ~ spl0_235
    | spl0_523 ),
    inference(forward_demodulation,[],[f7382,f2312]) ).

fof(f7382,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | spl0_523 ),
    inference(avatar_component_clause,[],[f7380]) ).

fof(f7391,plain,
    ( ~ spl0_524
    | ~ spl0_235
    | spl0_521 ),
    inference(avatar_split_clause,[],[f7386,f7372,f2310,f7388]) ).

fof(f7386,plain,
    ( null_class != complement(compose(element_relation,complement(singleton_relation)))
    | ~ spl0_235
    | spl0_521 ),
    inference(forward_demodulation,[],[f7373,f2312]) ).

fof(f7373,plain,
    ( null_class != complement(compose(element_relation,complement(identity_relation)))
    | spl0_521 ),
    inference(avatar_component_clause,[],[f7372]) ).

fof(f7383,plain,
    ( spl0_521
    | spl0_522
    | ~ spl0_523
    | ~ spl0_23
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1196,f1163,f299,f7380,f7376,f7372]) ).

fof(f1196,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_23
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f300]) ).

fof(f7370,plain,
    ( spl0_520
    | ~ spl0_129
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1185,f1159,f1008,f7368]) ).

fof(f7368,plain,
    ( spl0_520
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),null_class)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | null_class = X1
        | null_class = intersection(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f1185,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),null_class)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | null_class = X1
        | null_class = intersection(X0,regular(X1)) )
    | ~ spl0_129
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f1009]) ).

fof(f7366,plain,
    ( spl0_519
    | ~ spl0_128
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1183,f1159,f1004,f7364]) ).

fof(f7364,plain,
    ( spl0_519
  <=> ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),null_class)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | null_class = X0
        | null_class = intersection(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f1183,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),null_class)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | null_class = X0
        | null_class = intersection(regular(X0),X1) )
    | ~ spl0_128
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f1005]) ).

fof(f7362,plain,
    ( spl0_518
    | ~ spl0_48
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1044,f1008,f444,f7360]) ).

fof(f7360,plain,
    ( spl0_518
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f1044,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
    | ~ spl0_48
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f445]) ).

fof(f7358,plain,
    ( spl0_517
    | ~ spl0_48
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1028,f1004,f444,f7356]) ).

fof(f7356,plain,
    ( spl0_517
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f1028,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
    | ~ spl0_48
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f445]) ).

fof(f7049,plain,
    ( spl0_516
    | ~ spl0_61
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1714,f1711,f524,f7047]) ).

fof(f7047,plain,
    ( spl0_516
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f1714,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_61
    | ~ spl0_198 ),
    inference(superposition,[],[f525,f1712]) ).

fof(f7037,plain,
    ( spl0_515
    | ~ spl0_130
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1604,f1584,f1012,f7035]) ).

fof(f1604,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class) )
    | ~ spl0_130
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1603]) ).

fof(f1603,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class)
        | subclass(X1,domain_of(X0)) )
    | ~ spl0_130
    | ~ spl0_187 ),
    inference(resolution,[],[f1585,f1013]) ).

fof(f7033,plain,
    ( ~ spl0_514
    | ~ spl0_182
    | spl0_192
    | ~ spl0_12
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1563,f1556,f254,f1613,f1538,f7030]) ).

fof(f7030,plain,
    ( spl0_514
  <=> inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f1613,plain,
    ( spl0_192
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f1563,plain,
    ( member(null_class,subset_relation)
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_12
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f255]) ).

fof(f7028,plain,
    ( spl0_513
    | ~ spl0_31
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1502,f1456,f335,f7026]) ).

fof(f7026,plain,
    ( spl0_513
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f1502,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) )
    | ~ spl0_31
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f336]) ).

fof(f7024,plain,
    ( spl0_512
    | ~ spl0_32
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1501,f1456,f339,f7022]) ).

fof(f7022,plain,
    ( spl0_512
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f1501,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) )
    | ~ spl0_32
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f340]) ).

fof(f7020,plain,
    ( spl0_511
    | ~ spl0_31
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1484,f1452,f335,f7018]) ).

fof(f7018,plain,
    ( spl0_511
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f1484,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) )
    | ~ spl0_31
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f336]) ).

fof(f7016,plain,
    ( spl0_510
    | ~ spl0_32
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1483,f1452,f339,f7014]) ).

fof(f7014,plain,
    ( spl0_510
  <=> ! [X0,X3,X2,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f1483,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) )
    | ~ spl0_32
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f340]) ).

fof(f7012,plain,
    ( spl0_509
    | ~ spl0_38
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1422,f1369,f372,f7010]) ).

fof(f7010,plain,
    ( spl0_509
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f1422,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) )
    | ~ spl0_38
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f373]) ).

fof(f7008,plain,
    ( spl0_508
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1346,f1316,f1159,f7006]) ).

fof(f7006,plain,
    ( spl0_508
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f1346,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1325]) ).

fof(f1325,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(superposition,[],[f1160,f1317]) ).

fof(f7004,plain,
    ( spl0_507
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1341,f1316,f1159,f7002]) ).

fof(f7002,plain,
    ( spl0_507
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f1341,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1330]) ).

fof(f1330,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_142
    | ~ spl0_160 ),
    inference(superposition,[],[f1160,f1317]) ).

fof(f6992,plain,
    ( spl0_506
    | ~ spl0_49
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f967,f915,f448,f6990]) ).

fof(f6990,plain,
    ( spl0_506
  <=> ! [X2,X0,X1] :
        ( subclass(complement(intersection(X0,X1)),X2)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f967,plain,
    ( ! [X2,X0,X1] :
        ( subclass(complement(intersection(X0,X1)),X2)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) )
    | ~ spl0_49
    | ~ spl0_115 ),
    inference(resolution,[],[f916,f449]) ).

fof(f6844,plain,
    ( spl0_505
    | ~ spl0_235
    | ~ spl0_497 ),
    inference(avatar_split_clause,[],[f6806,f6803,f2310,f6842]) ).

fof(f6842,plain,
    ( spl0_505
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f6803,plain,
    ( spl0_497
  <=> ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f6806,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_235
    | ~ spl0_497 ),
    inference(forward_demodulation,[],[f6804,f2312]) ).

fof(f6804,plain,
    ( ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_497 ),
    inference(avatar_component_clause,[],[f6803]) ).

fof(f6834,plain,
    ( spl0_504
    | ~ spl0_68
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1875,f1868,f560,f6832]) ).

fof(f1875,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f561]) ).

fof(f6830,plain,
    ( spl0_503
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1503,f1456,f287,f6828]) ).

fof(f6828,plain,
    ( spl0_503
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f1503,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) )
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(resolution,[],[f1457,f288]) ).

fof(f6826,plain,
    ( spl0_502
    | ~ spl0_20
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1485,f1452,f287,f6824]) ).

fof(f6824,plain,
    ( spl0_502
  <=> ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(X1))
        | ~ member(X2,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f1485,plain,
    ( ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(X1))
        | ~ member(X2,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) )
    | ~ spl0_20
    | ~ spl0_170 ),
    inference(resolution,[],[f1453,f288]) ).

fof(f6822,plain,
    ( spl0_501
    | ~ spl0_31
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1426,f1369,f335,f6820]) ).

fof(f6820,plain,
    ( spl0_501
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f1426,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) )
    | ~ spl0_31
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f336]) ).

fof(f6818,plain,
    ( spl0_500
    | ~ spl0_32
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1425,f1369,f339,f6816]) ).

fof(f6816,plain,
    ( spl0_500
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f1425,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) )
    | ~ spl0_32
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f340]) ).

fof(f6814,plain,
    ( spl0_499
    | ~ spl0_109
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1382,f1361,f815,f6812]) ).

fof(f6812,plain,
    ( spl0_499
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(null_class,X2)
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f1382,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(null_class,X2)
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_109
    | ~ spl0_163 ),
    inference(resolution,[],[f1362,f816]) ).

fof(f6810,plain,
    ( spl0_498
    | ~ spl0_38
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1356,f1351,f372,f6808]) ).

fof(f6808,plain,
    ( spl0_498
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f1356,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_162 ),
    inference(resolution,[],[f1352,f373]) ).

fof(f6805,plain,
    ( spl0_497
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1217,f1167,f568,f452,f6803]) ).

fof(f1217,plain,
    ( ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_144 ),
    inference(forward_demodulation,[],[f1204,f453]) ).

fof(f1204,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
    | ~ spl0_70
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f569]) ).

fof(f6599,plain,
    ( spl0_496
    | ~ spl0_235
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f6418,f6415,f2310,f6597]) ).

fof(f6597,plain,
    ( spl0_496
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | ~ member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f6415,plain,
    ( spl0_483
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),subset_relation)
        | member(not_subclass_element(X0,X1),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f6418,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | ~ member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_235
    | ~ spl0_483 ),
    inference(forward_demodulation,[],[f6416,f2312]) ).

fof(f6416,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),subset_relation)
        | member(not_subclass_element(X0,X1),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f6415]) ).

fof(f6595,plain,
    ( spl0_495
    | ~ spl0_235
    | ~ spl0_482 ),
    inference(avatar_split_clause,[],[f6413,f6410,f2310,f6593]) ).

fof(f6593,plain,
    ( spl0_495
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f6410,plain,
    ( spl0_482
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f6413,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1) )
    | ~ spl0_235
    | ~ spl0_482 ),
    inference(forward_demodulation,[],[f6411,f2312]) ).

fof(f6411,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) )
    | ~ spl0_482 ),
    inference(avatar_component_clause,[],[f6410]) ).

fof(f6463,plain,
    ( spl0_493
    | ~ spl0_494
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1872,f1868,f669,f6460,f6457]) ).

fof(f6457,plain,
    ( spl0_493
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f6460,plain,
    ( spl0_494
  <=> subclass(composition_function,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f1872,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X1,domain_of(X0)) )
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(resolution,[],[f1869,f670]) ).

fof(f6455,plain,
    ( spl0_492
    | ~ spl0_68
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1717,f1711,f560,f6453]) ).

fof(f1717,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_68
    | ~ spl0_198 ),
    inference(superposition,[],[f561,f1712]) ).

fof(f6451,plain,
    ( spl0_491
    | ~ spl0_67
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1716,f1711,f556,f6449]) ).

fof(f1716,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_67
    | ~ spl0_198 ),
    inference(superposition,[],[f557,f1712]) ).

fof(f6447,plain,
    ( spl0_490
    | ~ spl0_22
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1440,f1373,f295,f6445]) ).

fof(f6445,plain,
    ( spl0_490
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f1440,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(X1)) )
    | ~ spl0_22
    | ~ spl0_166 ),
    inference(resolution,[],[f1374,f296]) ).

fof(f6443,plain,
    ( spl0_489
    | ~ spl0_20
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1427,f1369,f287,f6441]) ).

fof(f1427,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) )
    | ~ spl0_20
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f288]) ).

fof(f6439,plain,
    ( spl0_488
    | ~ spl0_131
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1381,f1361,f1016,f6437]) ).

fof(f6437,plain,
    ( spl0_488
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f1381,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_131
    | ~ spl0_163 ),
    inference(resolution,[],[f1362,f1017]) ).

fof(f6435,plain,
    ( spl0_487
    | ~ spl0_132
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1380,f1361,f1020,f6433]) ).

fof(f6433,plain,
    ( spl0_487
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f1380,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_132
    | ~ spl0_163 ),
    inference(resolution,[],[f1362,f1021]) ).

fof(f6431,plain,
    ( ~ spl0_485
    | spl0_486
    | ~ spl0_114
    | ~ spl0_398 ),
    inference(avatar_split_clause,[],[f6328,f4364,f892,f6428,f6424]) ).

fof(f6424,plain,
    ( spl0_485
  <=> single_valued_class(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f6428,plain,
    ( spl0_486
  <=> function(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f4364,plain,
    ( spl0_398
  <=> subclass(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f6328,plain,
    ( function(singleton_relation)
    | ~ single_valued_class(singleton_relation)
    | ~ spl0_114
    | ~ spl0_398 ),
    inference(resolution,[],[f4366,f893]) ).

fof(f4366,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_398 ),
    inference(avatar_component_clause,[],[f4364]) ).

fof(f6422,plain,
    ( spl0_484
    | ~ spl0_38
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1347,f1320,f372,f6420]) ).

fof(f6420,plain,
    ( spl0_484
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f1320,plain,
    ( spl0_161
  <=> ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f1347,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) )
    | ~ spl0_38
    | ~ spl0_161 ),
    inference(resolution,[],[f1321,f373]) ).

fof(f1321,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1320]) ).

fof(f6417,plain,
    ( spl0_483
    | ~ spl0_130
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1216,f1167,f1012,f6415]) ).

fof(f1216,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),subset_relation)
        | member(not_subclass_element(X0,X1),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f1013]) ).

fof(f6412,plain,
    ( spl0_482
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1202,f1163,f1012,f6410]) ).

fof(f1202,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f1013]) ).

fof(f6408,plain,
    ( spl0_481
    | ~ spl0_130
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1188,f1159,f1012,f6406]) ).

fof(f1188,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | ~ member(not_subclass_element(X0,X1),X2)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) )
    | ~ spl0_130
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f1013]) ).

fof(f6404,plain,
    ( spl0_480
    | ~ spl0_76
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1143,f1087,f608,f6402]) ).

fof(f6402,plain,
    ( spl0_480
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f1143,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_135 ),
    inference(superposition,[],[f1088,f610]) ).

fof(f6400,plain,
    ( spl0_479
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f896,f884,f448,f6398]) ).

fof(f6398,plain,
    ( spl0_479
  <=> ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f896,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(resolution,[],[f885,f449]) ).

fof(f6236,plain,
    ( spl0_478
    | ~ spl0_27
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1607,f1584,f319,f6234]) ).

fof(f6234,plain,
    ( spl0_478
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f1607,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0)) )
    | ~ spl0_27
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1600]) ).

fof(f1600,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0))
        | subclass(universal_class,domain_of(X0)) )
    | ~ spl0_27
    | ~ spl0_187 ),
    inference(resolution,[],[f1585,f320]) ).

fof(f6232,plain,
    ( spl0_477
    | ~ spl0_49
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1576,f1556,f448,f6230]) ).

fof(f6230,plain,
    ( spl0_477
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f1576,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_49
    | ~ spl0_185 ),
    inference(duplicate_literal_removal,[],[f1560]) ).

fof(f1560,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_49
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f449]) ).

fof(f6228,plain,
    ( ~ spl0_476
    | ~ spl0_235
    | spl0_475 ),
    inference(avatar_split_clause,[],[f6223,f6219,f2310,f6225]) ).

fof(f6225,plain,
    ( spl0_476
  <=> subclass(domain_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f6219,plain,
    ( spl0_475
  <=> subclass(domain_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f6223,plain,
    ( ~ subclass(domain_relation,singleton_relation)
    | ~ spl0_235
    | spl0_475 ),
    inference(forward_demodulation,[],[f6221,f2312]) ).

fof(f6221,plain,
    ( ~ subclass(domain_relation,identity_relation)
    | spl0_475 ),
    inference(avatar_component_clause,[],[f6219]) ).

fof(f6222,plain,
    ( spl0_474
    | ~ spl0_475
    | ~ spl0_103
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1433,f1369,f761,f6219,f6216]) ).

fof(f6216,plain,
    ( spl0_474
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f1433,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,identity_relation)
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) )
    | ~ spl0_103
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f762]) ).

fof(f6214,plain,
    ( spl0_473
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1344,f1316,f919,f6212]) ).

fof(f1344,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1327]) ).

fof(f1327,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(superposition,[],[f920,f1317]) ).

fof(f6210,plain,
    ( spl0_472
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1339,f1316,f919,f6208]) ).

fof(f1339,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1332]) ).

fof(f1332,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_116
    | ~ spl0_160 ),
    inference(superposition,[],[f920,f1317]) ).

fof(f6206,plain,
    ( spl0_471
    | ~ spl0_27
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1178,f1159,f319,f6204]) ).

fof(f6204,plain,
    ( spl0_471
  <=> ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),null_class)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | null_class = X0
        | subclass(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f1178,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),null_class)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | null_class = X0
        | subclass(regular(X0),X1) )
    | ~ spl0_27
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f320]) ).

fof(f6194,plain,
    ( spl0_274
    | spl0_470
    | ~ spl0_76
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1056,f1008,f608,f6191,f2535]) ).

fof(f1056,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = subset_relation
    | ~ spl0_76
    | ~ spl0_129 ),
    inference(superposition,[],[f1009,f610]) ).

fof(f6189,plain,
    ( spl0_469
    | ~ spl0_44
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f968,f915,f424,f6187]) ).

fof(f6187,plain,
    ( spl0_469
  <=> ! [X0,X1] :
        ( subclass(complement(complement(X0)),X1)
        | member(not_subclass_element(complement(complement(X0)),X1),X0)
        | ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f968,plain,
    ( ! [X0,X1] :
        ( subclass(complement(complement(X0)),X1)
        | member(not_subclass_element(complement(complement(X0)),X1),X0)
        | ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) )
    | ~ spl0_44
    | ~ spl0_115 ),
    inference(resolution,[],[f916,f425]) ).

fof(f6185,plain,
    ( spl0_468
    | ~ spl0_79
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f875,f823,f628,f6183]) ).

fof(f6183,plain,
    ( spl0_468
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f875,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
    | ~ spl0_79
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f629]) ).

fof(f6180,plain,
    ( spl0_466
    | ~ spl0_467
    | ~ spl0_85
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f828,f802,f664,f6177,f6174]) ).

fof(f6174,plain,
    ( spl0_466
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f6177,plain,
    ( spl0_467
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f828,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_85
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f665]) ).

fof(f6022,plain,
    ( spl0_465
    | ~ spl0_235
    | ~ spl0_457 ),
    inference(avatar_split_clause,[],[f5904,f5901,f2310,f6020]) ).

fof(f6020,plain,
    ( spl0_465
  <=> ! [X0] :
        ( member(regular(X0),singleton_relation)
        | ~ member(regular(X0),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f5901,plain,
    ( spl0_457
  <=> ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f5904,plain,
    ( ! [X0] :
        ( member(regular(X0),singleton_relation)
        | ~ member(regular(X0),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_235
    | ~ spl0_457 ),
    inference(forward_demodulation,[],[f5902,f2312]) ).

fof(f5902,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_457 ),
    inference(avatar_component_clause,[],[f5901]) ).

fof(f6018,plain,
    ( spl0_464
    | ~ spl0_235
    | ~ spl0_456 ),
    inference(avatar_split_clause,[],[f5899,f5896,f2310,f6016]) ).

fof(f6016,plain,
    ( spl0_464
  <=> ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f5896,plain,
    ( spl0_456
  <=> ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f5899,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | null_class = X0 )
    | ~ spl0_235
    | ~ spl0_456 ),
    inference(forward_demodulation,[],[f5897,f2312]) ).

fof(f5897,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 )
    | ~ spl0_456 ),
    inference(avatar_component_clause,[],[f5896]) ).

fof(f5929,plain,
    ( spl0_463
    | ~ spl0_235
    | ~ spl0_453 ),
    inference(avatar_split_clause,[],[f5886,f5883,f2310,f5927]) ).

fof(f5927,plain,
    ( spl0_463
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f5883,plain,
    ( spl0_453
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f5886,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_235
    | ~ spl0_453 ),
    inference(forward_demodulation,[],[f5884,f2312]) ).

fof(f5884,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_453 ),
    inference(avatar_component_clause,[],[f5883]) ).

fof(f5925,plain,
    ( spl0_462
    | ~ spl0_235
    | ~ spl0_452 ),
    inference(avatar_split_clause,[],[f5881,f5877,f2310,f5923]) ).

fof(f5923,plain,
    ( spl0_462
  <=> ! [X0] :
        ( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
        | ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f5877,plain,
    ( spl0_452
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f5881,plain,
    ( ! [X0] :
        ( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
        | ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f5880,f2312]) ).

fof(f5880,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_235
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f5878,f2312]) ).

fof(f5878,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_452 ),
    inference(avatar_component_clause,[],[f5877]) ).

fof(f5921,plain,
    ( spl0_461
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1343,f1316,f380,f5919]) ).

fof(f5919,plain,
    ( spl0_461
  <=> ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f1343,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1328]) ).

fof(f1328,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(superposition,[],[f381,f1317]) ).

fof(f5917,plain,
    ( ~ spl0_459
    | spl0_460
    | ~ spl0_114
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f5810,f4206,f892,f5914,f5910]) ).

fof(f5910,plain,
    ( spl0_459
  <=> single_valued_class(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f5914,plain,
    ( spl0_460
  <=> function(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f4206,plain,
    ( spl0_383
  <=> subclass(subset_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f5810,plain,
    ( function(subset_relation)
    | ~ single_valued_class(subset_relation)
    | ~ spl0_114
    | ~ spl0_383 ),
    inference(resolution,[],[f4208,f893]) ).

fof(f4208,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f4206]) ).

fof(f5908,plain,
    ( spl0_458
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1338,f1316,f380,f5906]) ).

fof(f5906,plain,
    ( spl0_458
  <=> ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f1338,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1333]) ).

fof(f1333,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(superposition,[],[f381,f1317]) ).

fof(f5903,plain,
    ( spl0_457
    | ~ spl0_116
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1212,f1167,f919,f5901]) ).

fof(f1212,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f920]) ).

fof(f5898,plain,
    ( spl0_456
    | ~ spl0_116
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1198,f1163,f919,f5896]) ).

fof(f1198,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f920]) ).

fof(f5894,plain,
    ( spl0_455
    | ~ spl0_116
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1184,f1159,f919,f5892]) ).

fof(f1184,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_116
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f920]) ).

fof(f5890,plain,
    ( spl0_454
    | ~ spl0_48
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1062,f1012,f444,f5888]) ).

fof(f5888,plain,
    ( spl0_454
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = X1
        | not_subclass_element(X0,X3) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f1062,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = X1
        | not_subclass_element(X0,X3) = X2 )
    | ~ spl0_48
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f445]) ).

fof(f5885,plain,
    ( spl0_453
    | ~ spl0_115
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f999,f959,f915,f5883]) ).

fof(f999,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_115
    | ~ spl0_125 ),
    inference(resolution,[],[f960,f916]) ).

fof(f5879,plain,
    ( spl0_452
    | ~ spl0_115
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f995,f955,f915,f5877]) ).

fof(f995,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_115
    | ~ spl0_124 ),
    inference(resolution,[],[f956,f916]) ).

fof(f5818,plain,
    ( spl0_451
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f5566,f5561,f2310,f5816]) ).

fof(f5561,plain,
    ( spl0_446
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f5566,plain,
    ( ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) )
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5565,f2312]) ).

fof(f5565,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | subclass(X0,identity_relation) )
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5564,f2312]) ).

fof(f5564,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_235
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5562,f2312]) ).

fof(f5562,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_446 ),
    inference(avatar_component_clause,[],[f5561]) ).

fof(f5809,plain,
    ( spl0_450
    | ~ spl0_235
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f5559,f5556,f2310,f5807]) ).

fof(f5556,plain,
    ( spl0_445
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f5559,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_445 ),
    inference(forward_demodulation,[],[f5557,f2312]) ).

fof(f5557,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_445 ),
    inference(avatar_component_clause,[],[f5556]) ).

fof(f5578,plain,
    ( spl0_448
    | ~ spl0_449
    | ~ spl0_78
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1414,f1369,f624,f5575,f5572]) ).

fof(f5572,plain,
    ( spl0_448
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f5575,plain,
    ( spl0_449
  <=> subclass(domain_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1414,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,successor_relation)
        | ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
    | ~ spl0_78
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f625]) ).

fof(f5570,plain,
    ( spl0_447
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3452,f3332,f323,f5568]) ).

fof(f5568,plain,
    ( spl0_447
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f3452,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation)
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3439]) ).

fof(f3439,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),subset_relation)
        | subclass(intersection(X0,singleton_relation),subset_relation) )
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(resolution,[],[f3333,f324]) ).

fof(f5563,plain,
    ( spl0_446
    | ~ spl0_43
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1403,f1365,f393,f5561]) ).

fof(f1403,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_43
    | ~ spl0_164 ),
    inference(superposition,[],[f1366,f395]) ).

fof(f5558,plain,
    ( spl0_445
    | ~ spl0_41
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1402,f1365,f384,f5556]) ).

fof(f1402,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_41
    | ~ spl0_164 ),
    inference(superposition,[],[f1366,f386]) ).

fof(f5554,plain,
    ( spl0_444
    | ~ spl0_40
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1398,f1365,f380,f5552]) ).

fof(f5552,plain,
    ( spl0_444
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),regular(X0))
        | ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f1398,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),regular(X0))
        | ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_164 ),
    inference(superposition,[],[f1366,f381]) ).

fof(f5550,plain,
    ( spl0_443
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1345,f1316,f951,f5548]) ).

fof(f5548,plain,
    ( spl0_443
  <=> ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f1345,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1326]) ).

fof(f1326,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(superposition,[],[f952,f1317]) ).

fof(f5546,plain,
    ( spl0_442
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1340,f1316,f951,f5544]) ).

fof(f5544,plain,
    ( spl0_442
  <=> ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f1340,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1331]) ).

fof(f1331,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_123
    | ~ spl0_160 ),
    inference(superposition,[],[f952,f1317]) ).

fof(f5542,plain,
    ( spl0_441
    | ~ spl0_38
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1259,f1247,f372,f5540]) ).

fof(f1259,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
    | ~ spl0_38
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f373]) ).

fof(f5538,plain,
    ( ~ spl0_439
    | spl0_440
    | ~ spl0_106
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1215,f1167,f802,f5536,f5532]) ).

fof(f5532,plain,
    ( spl0_439
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f5536,plain,
    ( spl0_440
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f1215,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation)
        | ~ subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_106
    | ~ spl0_144 ),
    inference(resolution,[],[f1168,f803]) ).

fof(f5530,plain,
    ( ~ spl0_438
    | ~ spl0_235
    | spl0_435 ),
    inference(avatar_split_clause,[],[f5521,f5514,f2310,f5527]) ).

fof(f5527,plain,
    ( spl0_438
  <=> subclass(universal_class,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f5521,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_435 ),
    inference(forward_demodulation,[],[f5516,f2312]) ).

fof(f5516,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
    | spl0_435 ),
    inference(avatar_component_clause,[],[f5514]) ).

fof(f5525,plain,
    ( spl0_437
    | ~ spl0_28
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f3413,f3310,f323,f5523]) ).

fof(f5523,plain,
    ( spl0_437
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f3413,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation)
    | ~ spl0_28
    | ~ spl0_332 ),
    inference(duplicate_literal_removal,[],[f3400]) ).

fof(f3400,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),subset_relation)
        | subclass(intersection(singleton_relation,X0),subset_relation) )
    | ~ spl0_28
    | ~ spl0_332 ),
    inference(resolution,[],[f3311,f324]) ).

fof(f5520,plain,
    ( ~ spl0_435
    | spl0_436
    | ~ spl0_106
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1201,f1163,f802,f5518,f5514]) ).

fof(f5518,plain,
    ( spl0_436
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1201,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation)
        | ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_106
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f803]) ).

fof(f5512,plain,
    ( spl0_434
    | ~ spl0_106
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1187,f1159,f802,f5510]) ).

fof(f1187,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | ~ member(unordered_pair(X0,X1),X2)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) )
    | ~ spl0_106
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f803]) ).

fof(f5508,plain,
    ( spl0_433
    | ~ spl0_23
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1182,f1159,f299,f5506]) ).

fof(f5506,plain,
    ( spl0_433
  <=> ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f1182,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) )
    | ~ spl0_23
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f300]) ).

fof(f5503,plain,
    ( ~ spl0_432
    | ~ spl0_235
    | spl0_431 ),
    inference(avatar_split_clause,[],[f5498,f5494,f2310,f5500]) ).

fof(f5500,plain,
    ( spl0_432
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f5494,plain,
    ( spl0_431
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f5498,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
    | ~ spl0_235
    | spl0_431 ),
    inference(forward_demodulation,[],[f5496,f2312]) ).

fof(f5496,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | spl0_431 ),
    inference(avatar_component_clause,[],[f5494]) ).

fof(f5497,plain,
    ( spl0_430
    | ~ spl0_431
    | ~ spl0_112
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1001,f959,f884,f5494,f5490]) ).

fof(f1001,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_112
    | ~ spl0_125 ),
    inference(resolution,[],[f960,f885]) ).

fof(f5487,plain,
    ( ~ spl0_429
    | ~ spl0_235
    | spl0_426 ),
    inference(avatar_split_clause,[],[f5471,f5467,f2310,f5484]) ).

fof(f5484,plain,
    ( spl0_429
  <=> member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f5467,plain,
    ( spl0_426
  <=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f5471,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
    | ~ spl0_235
    | spl0_426 ),
    inference(forward_demodulation,[],[f5469,f2312]) ).

fof(f5469,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | spl0_426 ),
    inference(avatar_component_clause,[],[f5467]) ).

fof(f5482,plain,
    ( spl0_428
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3386,f3210,f2364,f2310,f5479]) ).

fof(f3386,plain,
    ( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(forward_demodulation,[],[f3371,f2312]) ).

fof(f3371,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3362]) ).

fof(f3362,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_244
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f2365]) ).

fof(f5477,plain,
    ( ~ spl0_427
    | ~ spl0_235
    | spl0_425 ),
    inference(avatar_split_clause,[],[f5472,f5463,f2310,f5474]) ).

fof(f5474,plain,
    ( spl0_427
  <=> null_class = complement(complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f5472,plain,
    ( null_class != complement(complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | spl0_425 ),
    inference(forward_demodulation,[],[f5464,f2312]) ).

fof(f5464,plain,
    ( null_class != complement(complement(compose(element_relation,complement(identity_relation))))
    | spl0_425 ),
    inference(avatar_component_clause,[],[f5463]) ).

fof(f5470,plain,
    ( spl0_425
    | ~ spl0_426
    | ~ spl0_112
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f996,f955,f884,f5467,f5463]) ).

fof(f996,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_112
    | ~ spl0_124 ),
    inference(resolution,[],[f956,f885]) ).

fof(f5461,plain,
    ( spl0_424
    | ~ spl0_44
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f897,f884,f424,f5459]) ).

fof(f5459,plain,
    ( spl0_424
  <=> ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f897,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_44
    | ~ spl0_112 ),
    inference(resolution,[],[f885,f425]) ).

fof(f5172,plain,
    ( spl0_423
    | ~ spl0_27
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3380,f3210,f319,f5170]) ).

fof(f3380,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_27
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3345]) ).

fof(f3345,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(X0,X0))
        | subclass(X0,intersection(X0,X0)) )
    | ~ spl0_27
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f320]) ).

fof(f5145,plain,
    ( spl0_422
    | ~ spl0_235
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f4810,f4807,f2310,f5143]) ).

fof(f5143,plain,
    ( spl0_422
  <=> ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f4807,plain,
    ( spl0_411
  <=> ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f4810,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_235
    | ~ spl0_411 ),
    inference(forward_demodulation,[],[f4808,f2312]) ).

fof(f4808,plain,
    ( ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_411 ),
    inference(avatar_component_clause,[],[f4807]) ).

fof(f5141,plain,
    ( spl0_421
    | ~ spl0_235
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f4801,f4798,f2310,f5139]) ).

fof(f5139,plain,
    ( spl0_421
  <=> ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f4798,plain,
    ( spl0_409
  <=> ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f4801,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_235
    | ~ spl0_409 ),
    inference(forward_demodulation,[],[f4799,f2312]) ).

fof(f4799,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f4798]) ).

fof(f4856,plain,
    ( spl0_420
    | ~ spl0_243
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3375,f3210,f2360,f4853]) ).

fof(f3375,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_243
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3351]) ).

fof(f3351,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_243
    | ~ spl0_327 ),
    inference(resolution,[],[f3211,f2361]) ).

fof(f4851,plain,
    ( spl0_419
    | ~ spl0_235
    | ~ spl0_403 ),
    inference(avatar_split_clause,[],[f4776,f4773,f2310,f4849]) ).

fof(f4773,plain,
    ( spl0_403
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f4776,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_235
    | ~ spl0_403 ),
    inference(forward_demodulation,[],[f4774,f2312]) ).

fof(f4774,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_403 ),
    inference(avatar_component_clause,[],[f4773]) ).

fof(f4847,plain,
    ( spl0_418
    | ~ spl0_235
    | ~ spl0_402 ),
    inference(avatar_split_clause,[],[f4771,f4767,f2310,f4845]) ).

fof(f4767,plain,
    ( spl0_402
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f4771,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) )
    | ~ spl0_235
    | ~ spl0_402 ),
    inference(forward_demodulation,[],[f4770,f2312]) ).

fof(f4770,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_235
    | ~ spl0_402 ),
    inference(forward_demodulation,[],[f4768,f2312]) ).

fof(f4768,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_402 ),
    inference(avatar_component_clause,[],[f4767]) ).

fof(f4834,plain,
    ( spl0_417
    | ~ spl0_134
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1406,f1365,f1083,f4832]) ).

fof(f1406,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_134
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1387]) ).

fof(f1387,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0))
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_134
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f1084]) ).

fof(f4830,plain,
    ( spl0_416
    | ~ spl0_135
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1405,f1365,f1087,f4828]) ).

fof(f1405,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_135
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1388]) ).

fof(f1388,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1))
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_135
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f1088]) ).

fof(f4826,plain,
    ( spl0_415
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1342,f1316,f299,f4824]) ).

fof(f4824,plain,
    ( spl0_415
  <=> ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f1342,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1329]) ).

fof(f1329,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(superposition,[],[f300,f1317]) ).

fof(f4822,plain,
    ( spl0_414
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1337,f1316,f299,f4820]) ).

fof(f4820,plain,
    ( spl0_414
  <=> ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f1337,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1334]) ).

fof(f1334,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_160 ),
    inference(superposition,[],[f300,f1317]) ).

fof(f4818,plain,
    ( spl0_413
    | ~ spl0_31
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1263,f1247,f335,f4816]) ).

fof(f4816,plain,
    ( spl0_413
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f1263,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) )
    | ~ spl0_31
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f336]) ).

fof(f4814,plain,
    ( spl0_412
    | ~ spl0_32
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1262,f1247,f339,f4812]) ).

fof(f4812,plain,
    ( spl0_412
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f1262,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) )
    | ~ spl0_32
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f340]) ).

fof(f4809,plain,
    ( spl0_411
    | ~ spl0_43
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1258,f1243,f393,f4807]) ).

fof(f1258,plain,
    ( ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_43
    | ~ spl0_151 ),
    inference(superposition,[],[f1244,f395]) ).

fof(f4805,plain,
    ( spl0_410
    | ~ spl0_28
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f3344,f3193,f323,f4803]) ).

fof(f4803,plain,
    ( spl0_410
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f3344,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),element_relation)
    | ~ spl0_28
    | ~ spl0_324 ),
    inference(duplicate_literal_removal,[],[f3335]) ).

fof(f3335,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),element_relation)
        | subclass(intersection(X0,singleton_relation),element_relation) )
    | ~ spl0_28
    | ~ spl0_324 ),
    inference(resolution,[],[f3194,f324]) ).

fof(f4800,plain,
    ( spl0_409
    | ~ spl0_41
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1257,f1243,f384,f4798]) ).

fof(f1257,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_41
    | ~ spl0_151 ),
    inference(superposition,[],[f1244,f386]) ).

fof(f4796,plain,
    ( spl0_408
    | ~ spl0_40
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1253,f1243,f380,f4794]) ).

fof(f4794,plain,
    ( spl0_408
  <=> ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f1253,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_151 ),
    inference(superposition,[],[f1244,f381]) ).

fof(f4792,plain,
    ( spl0_407
    | ~ spl0_31
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1134,f1087,f335,f4790]) ).

fof(f1134,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_31
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f336]) ).

fof(f4788,plain,
    ( spl0_406
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1133,f1087,f339,f4786]) ).

fof(f1133,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f340]) ).

fof(f4784,plain,
    ( spl0_405
    | ~ spl0_31
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1116,f1083,f335,f4782]) ).

fof(f1116,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_31
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f336]) ).

fof(f4780,plain,
    ( spl0_404
    | ~ spl0_32
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1115,f1083,f339,f4778]) ).

fof(f1115,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_32
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f340]) ).

fof(f4775,plain,
    ( spl0_403
    | ~ spl0_28
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f998,f959,f323,f4773]) ).

fof(f998,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_28
    | ~ spl0_125 ),
    inference(resolution,[],[f960,f324]) ).

fof(f4769,plain,
    ( spl0_402
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f994,f955,f323,f4767]) ).

fof(f994,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(resolution,[],[f956,f324]) ).

fof(f4765,plain,
    ( spl0_401
    | ~ spl0_48
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f973,f919,f444,f4763]) ).

fof(f973,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_48
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f445]) ).

fof(f4738,plain,
    ( spl0_400
    | ~ spl0_28
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f3322,f3172,f323,f4736]) ).

fof(f4736,plain,
    ( spl0_400
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f3322,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),element_relation)
    | ~ spl0_28
    | ~ spl0_320 ),
    inference(duplicate_literal_removal,[],[f3313]) ).

fof(f3313,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),element_relation)
        | subclass(intersection(singleton_relation,X0),element_relation) )
    | ~ spl0_28
    | ~ spl0_320 ),
    inference(resolution,[],[f3173,f324]) ).

fof(f4643,plain,
    ( spl0_399
    | ~ spl0_235
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4246,f4243,f2310,f4641]) ).

fof(f4641,plain,
    ( spl0_399
  <=> ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f4243,plain,
    ( spl0_392
  <=> ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f4246,plain,
    ( ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_235
    | ~ spl0_392 ),
    inference(forward_demodulation,[],[f4244,f2312]) ).

fof(f4244,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_392 ),
    inference(avatar_component_clause,[],[f4243]) ).

fof(f4367,plain,
    ( spl0_398
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3237,f3137,f2364,f2310,f4364]) ).

fof(f3237,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_235
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(forward_demodulation,[],[f3236,f2312]) ).

fof(f3236,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3225]) ).

fof(f3225,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_244
    | ~ spl0_313 ),
    inference(resolution,[],[f3138,f2365]) ).

fof(f4272,plain,
    ( spl0_397
    | ~ spl0_130
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1404,f1365,f1012,f4270]) ).

fof(f1404,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_130
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1389]) ).

fof(f1389,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_130
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f1013]) ).

fof(f4268,plain,
    ( ~ spl0_395
    | spl0_396
    | ~ spl0_12
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1310,f1294,f254,f4265,f4261]) ).

fof(f4261,plain,
    ( spl0_395
  <=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f4265,plain,
    ( spl0_396
  <=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1310,plain,
    ( null_class = cross_product(unordered_pair(null_class,null_class),universal_class)
    | ~ inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class))))
    | ~ spl0_12
    | ~ spl0_158 ),
    inference(resolution,[],[f1295,f255]) ).

fof(f4259,plain,
    ( spl0_394
    | ~ spl0_20
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1264,f1247,f287,f4257]) ).

fof(f4257,plain,
    ( spl0_394
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1264,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) )
    | ~ spl0_20
    | ~ spl0_152 ),
    inference(resolution,[],[f1248,f288]) ).

fof(f4251,plain,
    ( spl0_182
    | ~ spl0_6
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f2511,f2479,f228,f1538]) ).

fof(f2479,plain,
    ( spl0_265
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f2511,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_265 ),
    inference(resolution,[],[f2480,f229]) ).

fof(f2480,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f2479]) ).

fof(f4250,plain,
    ( spl0_393
    | ~ spl0_22
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1252,f1243,f295,f4248]) ).

fof(f4248,plain,
    ( spl0_393
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f1252,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) )
    | ~ spl0_22
    | ~ spl0_151 ),
    inference(resolution,[],[f1244,f296]) ).

fof(f4245,plain,
    ( spl0_392
    | ~ spl0_44
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1191,f1163,f424,f4243]) ).

fof(f1191,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_44
    | ~ spl0_143 ),
    inference(resolution,[],[f1164,f425]) ).

fof(f4241,plain,
    ( spl0_391
    | ~ spl0_113
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1136,f1087,f888,f4239]) ).

fof(f1136,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 )
    | ~ spl0_113
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f889]) ).

fof(f4237,plain,
    ( spl0_390
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1130,f1087,f372,f4235]) ).

fof(f1130,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f373]) ).

fof(f4233,plain,
    ( spl0_389
    | ~ spl0_113
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1118,f1083,f888,f4231]) ).

fof(f1118,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 )
    | ~ spl0_113
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f889]) ).

fof(f4229,plain,
    ( spl0_388
    | ~ spl0_38
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1112,f1083,f372,f4227]) ).

fof(f1112,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_38
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f373]) ).

fof(f4225,plain,
    ( spl0_387
    | ~ spl0_31
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1047,f1008,f335,f4223]) ).

fof(f1047,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_31
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f336]) ).

fof(f4221,plain,
    ( spl0_386
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1046,f1008,f339,f4219]) ).

fof(f1046,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f340]) ).

fof(f4217,plain,
    ( spl0_385
    | ~ spl0_31
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1031,f1004,f335,f4215]) ).

fof(f1031,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_31
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f336]) ).

fof(f4213,plain,
    ( spl0_384
    | ~ spl0_32
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1030,f1004,f339,f4211]) ).

fof(f1030,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_32
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f340]) ).

fof(f4209,plain,
    ( spl0_383
    | ~ spl0_76
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2238,f2223,f608,f4206]) ).

fof(f2238,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_76
    | ~ spl0_223 ),
    inference(superposition,[],[f2224,f610]) ).

fof(f4204,plain,
    ( spl0_382
    | ~ spl0_115
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f990,f951,f915,f4202]) ).

fof(f4202,plain,
    ( spl0_382
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f990,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) )
    | ~ spl0_115
    | ~ spl0_123 ),
    inference(resolution,[],[f952,f916]) ).

fof(f4200,plain,
    ( spl0_381
    | ~ spl0_48
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f846,f802,f444,f4198]) ).

fof(f4198,plain,
    ( spl0_381
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f846,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_48
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f445]) ).

fof(f3836,plain,
    ( spl0_380
    | ~ spl0_106
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1737,f1711,f802,f3834]) ).

fof(f1737,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_106
    | ~ spl0_198 ),
    inference(superposition,[],[f803,f1712]) ).

fof(f3832,plain,
    ( spl0_379
    | ~ spl0_32
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1354,f1351,f339,f3830]) ).

fof(f1354,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_32
    | ~ spl0_162 ),
    inference(resolution,[],[f1352,f340]) ).

fof(f3828,plain,
    ( spl0_378
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1336,f1316,f3826]) ).

fof(f3826,plain,
    ( spl0_378
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f1336,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_160 ),
    inference(equality_factoring,[],[f1317]) ).

fof(f3824,plain,
    ( spl0_377
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1335,f1316,f3822]) ).

fof(f1335,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_160 ),
    inference(equality_factoring,[],[f1317]) ).

fof(f3820,plain,
    ( spl0_376
    | ~ spl0_134
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1307,f1290,f1083,f3818]) ).

fof(f1290,plain,
    ( spl0_157
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f1307,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_134
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1302]) ).

fof(f1302,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1))
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_134
    | ~ spl0_157 ),
    inference(resolution,[],[f1291,f1084]) ).

fof(f1291,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1)) )
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f1290]) ).

fof(f3816,plain,
    ( spl0_375
    | ~ spl0_135
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1306,f1290,f1087,f3814]) ).

fof(f1306,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1303]) ).

fof(f1303,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1))
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_157 ),
    inference(resolution,[],[f1291,f1088]) ).

fof(f3812,plain,
    ( spl0_374
    | ~ spl0_22
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1176,f1155,f295,f3810]) ).

fof(f3810,plain,
    ( spl0_374
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f1155,plain,
    ( spl0_141
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1176,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_22
    | ~ spl0_141 ),
    inference(resolution,[],[f1156,f296]) ).

fof(f1156,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1155]) ).

fof(f3808,plain,
    ( spl0_373
    | ~ spl0_20
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1135,f1087,f287,f3806]) ).

fof(f1135,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_20
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f288]) ).

fof(f3804,plain,
    ( spl0_372
    | ~ spl0_20
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1117,f1083,f287,f3802]) ).

fof(f1117,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_20
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f288]) ).

fof(f3800,plain,
    ( ~ spl0_370
    | spl0_371
    | ~ spl0_114
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f3158,f2727,f892,f3797,f3793]) ).

fof(f3793,plain,
    ( spl0_370
  <=> single_valued_class(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f3797,plain,
    ( spl0_371
  <=> function(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f3158,plain,
    ( function(null_class)
    | ~ single_valued_class(null_class)
    | ~ spl0_114
    | ~ spl0_284 ),
    inference(resolution,[],[f2728,f893]) ).

fof(f3791,plain,
    ( spl0_369
    | ~ spl0_113
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1067,f1012,f888,f3789]) ).

fof(f3789,plain,
    ( spl0_369
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f1067,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 )
    | ~ spl0_113
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f889]) ).

fof(f3787,plain,
    ( spl0_368
    | ~ spl0_38
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1061,f1012,f372,f3785]) ).

fof(f1061,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_38
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f373]) ).

fof(f3783,plain,
    ( spl0_367
    | ~ spl0_113
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1049,f1008,f888,f3781]) ).

fof(f3781,plain,
    ( spl0_367
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f1049,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 )
    | ~ spl0_113
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f889]) ).

fof(f3779,plain,
    ( spl0_366
    | ~ spl0_38
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1043,f1008,f372,f3777]) ).

fof(f1043,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_38
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f373]) ).

fof(f3775,plain,
    ( spl0_365
    | ~ spl0_113
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1033,f1004,f888,f3773]) ).

fof(f3773,plain,
    ( spl0_365
  <=> ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f1033,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 )
    | ~ spl0_113
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f889]) ).

fof(f3771,plain,
    ( spl0_364
    | ~ spl0_38
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1027,f1004,f372,f3769]) ).

fof(f1027,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_38
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f373]) ).

fof(f3767,plain,
    ( spl0_363
    | ~ spl0_112
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f991,f951,f884,f3765]) ).

fof(f3765,plain,
    ( spl0_363
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f991,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) )
    | ~ spl0_112
    | ~ spl0_123 ),
    inference(resolution,[],[f952,f885]) ).

fof(f3763,plain,
    ( spl0_362
    | ~ spl0_111
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f966,f915,f823,f3761]) ).

fof(f966,plain,
    ( ! [X0] :
        ( subclass(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) )
    | ~ spl0_111
    | ~ spl0_115 ),
    inference(resolution,[],[f916,f824]) ).

fof(f3759,plain,
    ( spl0_361
    | ~ spl0_67
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f880,f823,f556,f3757]) ).

fof(f880,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_67
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f557]) ).

fof(f3755,plain,
    ( spl0_360
    | ~ spl0_68
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f879,f823,f560,f3753]) ).

fof(f879,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f561]) ).

fof(f3747,plain,
    ( spl0_359
    | ~ spl0_57
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f858,f815,f503,f3745]) ).

fof(f3745,plain,
    ( spl0_359
  <=> ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f858,plain,
    ( ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_57
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f504]) ).

fof(f3616,plain,
    ( spl0_358
    | ~ spl0_235
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f3518,f3515,f2310,f3614]) ).

fof(f3515,plain,
    ( spl0_349
  <=> ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f3518,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_235
    | ~ spl0_349 ),
    inference(forward_demodulation,[],[f3516,f2312]) ).

fof(f3516,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f3515]) ).

fof(f3597,plain,
    ( spl0_357
    | ~ spl0_235
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3513,f3510,f2310,f3595]) ).

fof(f3510,plain,
    ( spl0_348
  <=> ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f3513,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_235
    | ~ spl0_348 ),
    inference(forward_demodulation,[],[f3511,f2312]) ).

fof(f3511,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_348 ),
    inference(avatar_component_clause,[],[f3510]) ).

fof(f3547,plain,
    ( spl0_356
    | ~ spl0_72
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1416,f1369,f584,f3545]) ).

fof(f3545,plain,
    ( spl0_356
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f1416,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) )
    | ~ spl0_72
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f585]) ).

fof(f3543,plain,
    ( spl0_355
    | ~ spl0_130
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1305,f1290,f1012,f3541]) ).

fof(f1305,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_130
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1304]) ).

fof(f1304,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_130
    | ~ spl0_157 ),
    inference(resolution,[],[f1291,f1013]) ).

fof(f3539,plain,
    ( spl0_354
    | ~ spl0_31
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1065,f1012,f335,f3537]) ).

fof(f1065,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_31
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f336]) ).

fof(f3535,plain,
    ( spl0_353
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1064,f1012,f339,f3533]) ).

fof(f1064,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f340]) ).

fof(f3531,plain,
    ( spl0_352
    | ~ spl0_20
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1048,f1008,f287,f3529]) ).

fof(f1048,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_20
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f288]) ).

fof(f3527,plain,
    ( spl0_351
    | ~ spl0_20
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1032,f1004,f287,f3525]) ).

fof(f1032,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_20
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f288]) ).

fof(f3523,plain,
    ( spl0_350
    | ~ spl0_234
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2876,f2310,f2304,f3520]) ).

fof(f2876,plain,
    ( member(regular(singleton_relation),subset_relation)
    | ~ spl0_234
    | ~ spl0_235 ),
    inference(superposition,[],[f2306,f2312]) ).

fof(f3517,plain,
    ( spl0_349
    | ~ spl0_38
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f997,f959,f372,f3515]) ).

fof(f997,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_125 ),
    inference(resolution,[],[f960,f373]) ).

fof(f3512,plain,
    ( spl0_348
    | ~ spl0_38
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f993,f955,f372,f3510]) ).

fof(f993,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_124 ),
    inference(resolution,[],[f956,f373]) ).

fof(f3508,plain,
    ( spl0_347
    | ~ spl0_28
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f989,f951,f323,f3506]) ).

fof(f989,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_28
    | ~ spl0_123 ),
    inference(resolution,[],[f952,f324]) ).

fof(f3504,plain,
    ( spl0_346
    | ~ spl0_38
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f988,f951,f372,f3502]) ).

fof(f3502,plain,
    ( spl0_346
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f988,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_123 ),
    inference(resolution,[],[f952,f373]) ).

fof(f3500,plain,
    ( spl0_345
    | ~ spl0_38
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f972,f919,f372,f3498]) ).

fof(f972,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_38
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f373]) ).

fof(f3493,plain,
    ( ~ spl0_343
    | spl0_344
    | ~ spl0_111
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f895,f884,f823,f3490,f3486]) ).

fof(f895,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | ~ spl0_111
    | ~ spl0_112 ),
    inference(resolution,[],[f885,f824]) ).

fof(f3484,plain,
    ( spl0_342
    | spl0_339
    | ~ spl0_51
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f866,f815,f456,f3465,f3482]) ).

fof(f3482,plain,
    ( spl0_342
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f3465,plain,
    ( spl0_339
  <=> member(null_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f866,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f457]) ).

fof(f3480,plain,
    ( spl0_341
    | ~ spl0_4
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f2484,f2452,f219,f3477]) ).

fof(f2484,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_4
    | ~ spl0_262 ),
    inference(resolution,[],[f2453,f220]) ).

fof(f3474,plain,
    ( ~ spl0_340
    | ~ spl0_235
    | spl0_339 ),
    inference(avatar_split_clause,[],[f3469,f3465,f2310,f3471]) ).

fof(f3471,plain,
    ( spl0_340
  <=> member(null_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f3469,plain,
    ( ~ member(null_class,singleton_relation)
    | ~ spl0_235
    | spl0_339 ),
    inference(forward_demodulation,[],[f3466,f2312]) ).

fof(f3466,plain,
    ( ~ member(null_class,identity_relation)
    | spl0_339 ),
    inference(avatar_component_clause,[],[f3465]) ).

fof(f3468,plain,
    ( spl0_338
    | spl0_339
    | ~ spl0_52
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f865,f815,f460,f3465,f3462]) ).

fof(f3462,plain,
    ( spl0_338
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f865,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f461]) ).

fof(f3460,plain,
    ( spl0_336
    | ~ spl0_337
    | ~ spl0_78
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f831,f802,f624,f3457,f3454]) ).

fof(f3454,plain,
    ( spl0_336
  <=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f3457,plain,
    ( spl0_337
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f831,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_78
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f625]) ).

fof(f3334,plain,
    ( spl0_335
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3191,f3187,f2310,f3332]) ).

fof(f3187,plain,
    ( spl0_323
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f3191,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3190,f2312]) ).

fof(f3190,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3188,f2312]) ).

fof(f3188,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f3187]) ).

fof(f3330,plain,
    ( spl0_334
    | ~ spl0_235
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3185,f3181,f2310,f3328]) ).

fof(f3181,plain,
    ( spl0_322
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f3185,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_235
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f3184,f2312]) ).

fof(f3184,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_235
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f3182,f2312]) ).

fof(f3182,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f3181]) ).

fof(f3326,plain,
    ( spl0_333
    | ~ spl0_235
    | ~ spl0_321 ),
    inference(avatar_split_clause,[],[f3179,f3176,f2310,f3324]) ).

fof(f3176,plain,
    ( spl0_321
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f3179,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_235
    | ~ spl0_321 ),
    inference(forward_demodulation,[],[f3177,f2312]) ).

fof(f3177,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f3176]) ).

fof(f3312,plain,
    ( spl0_332
    | ~ spl0_235
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3170,f3166,f2310,f3310]) ).

fof(f3166,plain,
    ( spl0_319
  <=> ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f3170,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_235
    | ~ spl0_319 ),
    inference(forward_demodulation,[],[f3169,f2312]) ).

fof(f3169,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_235
    | ~ spl0_319 ),
    inference(forward_demodulation,[],[f3167,f2312]) ).

fof(f3167,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f3166]) ).

fof(f3308,plain,
    ( spl0_331
    | ~ spl0_235
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2880,f2466,f2310,f3305]) ).

fof(f3305,plain,
    ( spl0_331
  <=> subclass(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f2880,plain,
    ( subclass(singleton_relation,subset_relation)
    | ~ spl0_235
    | ~ spl0_264 ),
    inference(superposition,[],[f2468,f2312]) ).

fof(f3224,plain,
    ( spl0_330
    | ~ spl0_6
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1442,f1377,f228,f3222]) ).

fof(f3222,plain,
    ( spl0_330
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f1377,plain,
    ( spl0_167
  <=> ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1442,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_6
    | ~ spl0_167 ),
    inference(resolution,[],[f1378,f229]) ).

fof(f1378,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1)))
        | ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,X1) )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1377]) ).

fof(f3220,plain,
    ( spl0_329
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1441,f1377,f503,f3218]) ).

fof(f3218,plain,
    ( spl0_329
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f1441,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(resolution,[],[f1378,f504]) ).

fof(f3216,plain,
    ( spl0_328
    | ~ spl0_67
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1410,f1369,f556,f3214]) ).

fof(f1410,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_67
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f557]) ).

fof(f3212,plain,
    ( spl0_327
    | ~ spl0_27
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1407,f1365,f319,f3210]) ).

fof(f1407,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_164 ),
    inference(duplicate_literal_removal,[],[f1386]) ).

fof(f1386,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0))
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_164 ),
    inference(resolution,[],[f1366,f320]) ).

fof(f3203,plain,
    ( spl0_325
    | spl0_326
    | ~ spl0_12
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1180,f1159,f254,f3200,f3197]) ).

fof(f3197,plain,
    ( spl0_325
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f3200,plain,
    ( spl0_326
  <=> member(null_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f1180,plain,
    ( ! [X0] :
        ( member(null_class,null_class)
        | ~ member(null_class,X0)
        | null_class = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_12
    | ~ spl0_142 ),
    inference(resolution,[],[f1160,f255]) ).

fof(f3195,plain,
    ( spl0_324
    | ~ spl0_97
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1139,f1087,f731,f3193]) ).

fof(f1139,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f732]) ).

fof(f3189,plain,
    ( spl0_323
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1138,f1087,f761,f3187]) ).

fof(f1138,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f762]) ).

fof(f3183,plain,
    ( spl0_322
    | ~ spl0_43
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1127,f1083,f393,f3181]) ).

fof(f1127,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_43
    | ~ spl0_134 ),
    inference(superposition,[],[f1084,f395]) ).

fof(f3178,plain,
    ( spl0_321
    | ~ spl0_41
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1126,f1083,f384,f3176]) ).

fof(f1126,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_41
    | ~ spl0_134 ),
    inference(superposition,[],[f1084,f386]) ).

fof(f3174,plain,
    ( spl0_320
    | ~ spl0_97
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1121,f1083,f731,f3172]) ).

fof(f1121,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f732]) ).

fof(f3168,plain,
    ( spl0_319
    | ~ spl0_103
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1120,f1083,f761,f3166]) ).

fof(f1120,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f762]) ).

fof(f3164,plain,
    ( spl0_318
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1078,f1020,f295,f3162]) ).

fof(f3162,plain,
    ( spl0_318
  <=> ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f1078,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(resolution,[],[f1021,f296]) ).

fof(f3155,plain,
    ( spl0_317
    | ~ spl0_22
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1075,f1016,f295,f3153]) ).

fof(f3153,plain,
    ( spl0_317
  <=> ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f1075,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_131 ),
    inference(resolution,[],[f1017,f296]) ).

fof(f3151,plain,
    ( spl0_316
    | ~ spl0_20
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1066,f1012,f287,f3149]) ).

fof(f1066,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_20
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f288]) ).

fof(f3147,plain,
    ( spl0_315
    | ~ spl0_31
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f976,f919,f335,f3145]) ).

fof(f976,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_31
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f336]) ).

fof(f3143,plain,
    ( spl0_314
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f975,f919,f339,f3141]) ).

fof(f975,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f340]) ).

fof(f3139,plain,
    ( spl0_313
    | ~ spl0_28
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f877,f823,f323,f3137]) ).

fof(f877,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_28
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f324]) ).

fof(f3120,plain,
    ( spl0_312
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f3051,f2923,f2310,f3118]) ).

fof(f2923,plain,
    ( spl0_299
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f3051,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2926,f2312]) ).

fof(f2926,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2924,f2312]) ).

fof(f2924,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f2923]) ).

fof(f3108,plain,
    ( ~ spl0_311
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_262
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2586,f2499,f2452,f240,f219,f3105]) ).

fof(f3105,plain,
    ( spl0_311
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f2586,plain,
    ( ~ subclass(universal_class,null_class)
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_262
    | ~ spl0_268 ),
    inference(forward_demodulation,[],[f2565,f2484]) ).

fof(f2565,plain,
    ( ~ subclass(universal_class,complement(universal_class))
    | ~ spl0_9
    | ~ spl0_268 ),
    inference(resolution,[],[f2500,f241]) ).

fof(f3094,plain,
    ( spl0_310
    | ~ spl0_235
    | ~ spl0_301 ),
    inference(avatar_split_clause,[],[f2938,f2935,f2310,f3092]) ).

fof(f2935,plain,
    ( spl0_301
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f2938,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_235
    | ~ spl0_301 ),
    inference(forward_demodulation,[],[f2936,f2312]) ).

fof(f2936,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_301 ),
    inference(avatar_component_clause,[],[f2935]) ).

fof(f3073,plain,
    ( spl0_309
    | ~ spl0_235
    | ~ spl0_296 ),
    inference(avatar_split_clause,[],[f3057,f2851,f2310,f3070]) ).

fof(f2851,plain,
    ( spl0_296
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f3057,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_235
    | ~ spl0_296 ),
    inference(forward_demodulation,[],[f2853,f2312]) ).

fof(f2853,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_296 ),
    inference(avatar_component_clause,[],[f2851]) ).

fof(f3068,plain,
    ( spl0_308
    | ~ spl0_235
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f3052,f2830,f2310,f3065]) ).

fof(f2830,plain,
    ( spl0_295
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f3052,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_235
    | ~ spl0_295 ),
    inference(forward_demodulation,[],[f2832,f2312]) ).

fof(f2832,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f2830]) ).

fof(f3063,plain,
    ( ~ spl0_307
    | ~ spl0_111
    | spl0_298 ),
    inference(avatar_split_clause,[],[f2919,f2915,f823,f3060]) ).

fof(f3060,plain,
    ( spl0_307
  <=> member(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f2915,plain,
    ( spl0_298
  <=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f2919,plain,
    ( ~ member(singleton_relation,subset_relation)
    | ~ spl0_111
    | spl0_298 ),
    inference(resolution,[],[f2917,f824]) ).

fof(f2917,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | spl0_298 ),
    inference(avatar_component_clause,[],[f2915]) ).

fof(f3055,plain,
    ( spl0_231
    | ~ spl0_233
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2864,f2310,f2300,f2282]) ).

fof(f2864,plain,
    ( null_class = singleton_relation
    | ~ spl0_233
    | ~ spl0_235 ),
    inference(forward_demodulation,[],[f2302,f2312]) ).

fof(f2302,plain,
    ( null_class = identity_relation
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2300]) ).

fof(f3044,plain,
    ( spl0_306
    | ~ spl0_231
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f2928,f2923,f2310,f2282,f3042]) ).

fof(f3042,plain,
    ( spl0_306
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f2928,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) )
    | ~ spl0_231
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2927,f2312]) ).

fof(f2927,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_231
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2926,f2284]) ).

fof(f2284,plain,
    ( null_class = singleton_relation
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f2282]) ).

fof(f2955,plain,
    ( spl0_305
    | ~ spl0_9
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1733,f1711,f240,f2953]) ).

fof(f2953,plain,
    ( spl0_305
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f1733,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_9
    | ~ spl0_198 ),
    inference(superposition,[],[f241,f1712]) ).

fof(f2951,plain,
    ( spl0_304
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1409,f1369,f560,f2949]) ).

fof(f2949,plain,
    ( spl0_304
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f1409,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f561]) ).

fof(f2947,plain,
    ( ~ spl0_303
    | ~ spl0_3
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2920,f2503,f214,f2944]) ).

fof(f2944,plain,
    ( spl0_303
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f214,plain,
    ( spl0_3
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f2920,plain,
    ( ~ inductive(choice)
    | ~ spl0_3
    | ~ spl0_269 ),
    inference(resolution,[],[f2504,f216]) ).

fof(f216,plain,
    ( function(choice)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f214]) ).

fof(f2942,plain,
    ( spl0_302
    | ~ spl0_97
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1070,f1012,f731,f2940]) ).

fof(f1070,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f732]) ).

fof(f2937,plain,
    ( spl0_301
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1069,f1012,f761,f2935]) ).

fof(f1069,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f762]) ).

fof(f2932,plain,
    ( spl0_300
    | ~ spl0_97
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1052,f1008,f731,f2930]) ).

fof(f1052,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) )
    | ~ spl0_97
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f732]) ).

fof(f2925,plain,
    ( spl0_299
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1051,f1008,f761,f2923]) ).

fof(f1051,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(resolution,[],[f1009,f762]) ).

fof(f2918,plain,
    ( ~ spl0_298
    | ~ spl0_235
    | spl0_257 ),
    inference(avatar_split_clause,[],[f2911,f2423,f2310,f2915]) ).

fof(f2423,plain,
    ( spl0_257
  <=> member(identity_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f2911,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_235
    | spl0_257 ),
    inference(forward_demodulation,[],[f2424,f2312]) ).

fof(f2424,plain,
    ( ~ member(identity_relation,cross_product(universal_class,universal_class))
    | spl0_257 ),
    inference(avatar_component_clause,[],[f2423]) ).

fof(f2907,plain,
    ( spl0_297
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f2892,f2423,f2310,f372,f2905]) ).

fof(f2905,plain,
    ( spl0_297
  <=> ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f2892,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) )
    | ~ spl0_38
    | ~ spl0_235
    | ~ spl0_257 ),
    inference(forward_demodulation,[],[f2886,f2312]) ).

fof(f2886,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(identity_relation,X0) )
    | ~ spl0_38
    | ~ spl0_257 ),
    inference(resolution,[],[f2425,f373]) ).

fof(f2425,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_257 ),
    inference(avatar_component_clause,[],[f2423]) ).

fof(f2854,plain,
    ( spl0_233
    | spl0_296
    | ~ spl0_43
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1042,f1004,f393,f2851,f2300]) ).

fof(f1042,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ spl0_43
    | ~ spl0_128 ),
    inference(superposition,[],[f1005,f395]) ).

fof(f2833,plain,
    ( spl0_231
    | spl0_295
    | ~ spl0_41
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1041,f1004,f384,f2830,f2282]) ).

fof(f1041,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | null_class = singleton_relation
    | ~ spl0_41
    | ~ spl0_128 ),
    inference(superposition,[],[f1005,f386]) ).

fof(f2828,plain,
    ( spl0_294
    | ~ spl0_97
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1036,f1004,f731,f2826]) ).

fof(f1036,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) )
    | ~ spl0_97
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f732]) ).

fof(f2824,plain,
    ( spl0_293
    | ~ spl0_103
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1035,f1004,f761,f2822]) ).

fof(f1035,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_128 ),
    inference(resolution,[],[f1005,f762]) ).

fof(f2820,plain,
    ( spl0_292
    | ~ spl0_20
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f977,f919,f287,f2818]) ).

fof(f977,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_20
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f288]) ).

fof(f2816,plain,
    ( spl0_291
    | ~ spl0_38
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f876,f823,f372,f2814]) ).

fof(f876,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_111 ),
    inference(resolution,[],[f824,f373]) ).

fof(f2812,plain,
    ( spl0_290
    | ~ spl0_38
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f845,f802,f372,f2810]) ).

fof(f2810,plain,
    ( spl0_290
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f845,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_38
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f373]) ).

fof(f2749,plain,
    ( spl0_288
    | ~ spl0_289
    | ~ spl0_61
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1412,f1369,f524,f2746,f2743]) ).

fof(f2743,plain,
    ( spl0_288
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f2746,plain,
    ( spl0_289
  <=> subclass(domain_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f1412,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,element_relation)
        | ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) )
    | ~ spl0_61
    | ~ spl0_165 ),
    inference(resolution,[],[f1370,f525]) ).

fof(f2741,plain,
    ( spl0_287
    | ~ spl0_27
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1308,f1290,f319,f2739]) ).

fof(f1308,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_157 ),
    inference(duplicate_literal_removal,[],[f1301]) ).

fof(f1301,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_157 ),
    inference(resolution,[],[f1291,f320]) ).

fof(f2737,plain,
    ( spl0_286
    | ~ spl0_76
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1125,f1083,f608,f2735]) ).

fof(f1125,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_134 ),
    inference(superposition,[],[f1084,f610]) ).

fof(f2733,plain,
    ( spl0_285
    | ~ spl0_97
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f981,f919,f731,f2731]) ).

fof(f981,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) )
    | ~ spl0_97
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f732]) ).

fof(f2729,plain,
    ( spl0_284
    | ~ spl0_4
    | ~ spl0_262
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2488,f2456,f2452,f219,f2727]) ).

fof(f2456,plain,
    ( spl0_263
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f2488,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_4
    | ~ spl0_262
    | ~ spl0_263 ),
    inference(forward_demodulation,[],[f2486,f2484]) ).

fof(f2486,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_4
    | ~ spl0_263 ),
    inference(resolution,[],[f2457,f220]) ).

fof(f2457,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2456]) ).

fof(f2725,plain,
    ( spl0_283
    | ~ spl0_103
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f980,f919,f761,f2723]) ).

fof(f980,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) )
    | ~ spl0_103
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f762]) ).

fof(f2713,plain,
    ( spl0_281
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f2712,f2698,f2535,f2704]) ).

fof(f2704,plain,
    ( spl0_281
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f2712,plain,
    ( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(forward_demodulation,[],[f2700,f2537]) ).

fof(f2537,plain,
    ( null_class = subset_relation
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2535]) ).

fof(f2711,plain,
    ( spl0_282
    | spl0_280
    | ~ spl0_34
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f861,f815,f347,f2698,f2709]) ).

fof(f2709,plain,
    ( spl0_282
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f861,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_34
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f348]) ).

fof(f2707,plain,
    ( ~ spl0_281
    | ~ spl0_274
    | spl0_280 ),
    inference(avatar_split_clause,[],[f2702,f2698,f2535,f2704]) ).

fof(f2702,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_274
    | spl0_280 ),
    inference(forward_demodulation,[],[f2699,f2537]) ).

fof(f2699,plain,
    ( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_280 ),
    inference(avatar_component_clause,[],[f2698]) ).

fof(f2701,plain,
    ( spl0_279
    | spl0_280
    | ~ spl0_33
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f860,f815,f343,f2698,f2695]) ).

fof(f2695,plain,
    ( spl0_279
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f860,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_33
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f344]) ).

fof(f2691,plain,
    ( spl0_278
    | ~ spl0_31
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f849,f802,f335,f2689]) ).

fof(f2689,plain,
    ( spl0_278
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f849,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_31
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f336]) ).

fof(f2687,plain,
    ( spl0_277
    | ~ spl0_32
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f848,f802,f339,f2685]) ).

fof(f2685,plain,
    ( spl0_277
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f848,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_32
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f340]) ).

fof(f2560,plain,
    ( spl0_276
    | ~ spl0_4
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1250,f1243,f219,f2558]) ).

fof(f1250,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_151 ),
    inference(resolution,[],[f1244,f220]) ).

fof(f2542,plain,
    ( spl0_274
    | spl0_275
    | ~ spl0_76
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1040,f1004,f608,f2539,f2535]) ).

fof(f1040,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_76
    | ~ spl0_128 ),
    inference(superposition,[],[f1005,f610]) ).

fof(f2531,plain,
    ( spl0_273
    | ~ spl0_20
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f992,f955,f287,f2529]) ).

fof(f992,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_20
    | ~ spl0_124 ),
    inference(resolution,[],[f956,f288]) ).

fof(f2527,plain,
    ( ~ spl0_272
    | spl0_271
    | ~ spl0_25
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f870,f815,f308,f2518,f2524]) ).

fof(f2524,plain,
    ( spl0_272
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f2518,plain,
    ( spl0_271
  <=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f870,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_25
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f310]) ).

fof(f2521,plain,
    ( ~ spl0_270
    | spl0_271
    | ~ spl0_24
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f868,f815,f303,f2518,f2514]) ).

fof(f2514,plain,
    ( spl0_270
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f868,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_24
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f305]) ).

fof(f2505,plain,
    ( spl0_269
    | spl0_182
    | ~ spl0_22
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f856,f815,f295,f1538,f2503]) ).

fof(f856,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f296]) ).

fof(f2501,plain,
    ( spl0_268
    | ~ spl0_20
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f850,f802,f287,f2499]) ).

fof(f850,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_20
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f288]) ).

fof(f2497,plain,
    ( ~ spl0_267
    | ~ spl0_111
    | spl0_230 ),
    inference(avatar_split_clause,[],[f2280,f2276,f823,f2494]) ).

fof(f2494,plain,
    ( spl0_267
  <=> member(omega,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2276,plain,
    ( spl0_230
  <=> member(omega,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f2280,plain,
    ( ~ member(omega,subset_relation)
    | ~ spl0_111
    | spl0_230 ),
    inference(resolution,[],[f2277,f824]) ).

fof(f2277,plain,
    ( ~ member(omega,cross_product(universal_class,universal_class))
    | spl0_230 ),
    inference(avatar_component_clause,[],[f2276]) ).

fof(f2492,plain,
    ( spl0_266
    | ~ spl0_72
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f833,f802,f584,f2490]) ).

fof(f2490,plain,
    ( spl0_266
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f833,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_72
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f585]) ).

fof(f2481,plain,
    ( spl0_265
    | ~ spl0_38
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2429,f1538,f372,f2479]) ).

fof(f2429,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_182 ),
    inference(resolution,[],[f1539,f373]) ).

fof(f2469,plain,
    ( spl0_264
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2251,f2227,f393,f2466]) ).

fof(f2251,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(superposition,[],[f2228,f395]) ).

fof(f2458,plain,
    ( spl0_263
    | ~ spl0_115
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1071,f1012,f915,f2456]) ).

fof(f1071,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_115
    | ~ spl0_130 ),
    inference(duplicate_literal_removal,[],[f1060]) ).

fof(f1060,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_115
    | ~ spl0_130 ),
    inference(resolution,[],[f1013,f916]) ).

fof(f2454,plain,
    ( spl0_262
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f982,f919,f884,f2452]) ).

fof(f982,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(duplicate_literal_removal,[],[f971]) ).

fof(f971,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(resolution,[],[f920,f885]) ).

fof(f2450,plain,
    ( spl0_261
    | ~ spl0_21
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f911,f892,f291,f2448]) ).

fof(f2448,plain,
    ( spl0_261
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f911,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_114 ),
    inference(resolution,[],[f893,f292]) ).

fof(f2446,plain,
    ( ~ spl0_259
    | spl0_260
    | ~ spl0_6
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f906,f892,f228,f2443,f2439]) ).

fof(f2439,plain,
    ( spl0_259
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f2443,plain,
    ( spl0_260
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f906,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_114 ),
    inference(resolution,[],[f893,f229]) ).

fof(f2435,plain,
    ( ~ spl0_258
    | ~ spl0_111
    | spl0_257 ),
    inference(avatar_split_clause,[],[f2430,f2423,f823,f2432]) ).

fof(f2432,plain,
    ( spl0_258
  <=> member(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f2430,plain,
    ( ~ member(identity_relation,subset_relation)
    | ~ spl0_111
    | spl0_257 ),
    inference(resolution,[],[f2424,f824]) ).

fof(f2426,plain,
    ( spl0_257
    | ~ spl0_182
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2421,f2300,f1538,f2423]) ).

fof(f2421,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_182
    | ~ spl0_233 ),
    inference(forward_demodulation,[],[f1539,f2302]) ).

fof(f2416,plain,
    ( spl0_256
    | spl0_182
    | ~ spl0_18
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f867,f815,f279,f1538,f2414]) ).

fof(f2414,plain,
    ( spl0_256
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f867,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f280]) ).

fof(f2412,plain,
    ( spl0_254
    | ~ spl0_255
    | ~ spl0_97
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f853,f802,f731,f2409,f2406]) ).

fof(f2406,plain,
    ( spl0_254
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f2409,plain,
    ( spl0_255
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f853,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_97
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f732]) ).

fof(f2404,plain,
    ( spl0_252
    | ~ spl0_253
    | ~ spl0_103
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f852,f802,f761,f2401,f2398]) ).

fof(f2398,plain,
    ( spl0_252
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f2401,plain,
    ( spl0_253
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f852,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f762]) ).

fof(f2396,plain,
    ( spl0_251
    | ~ spl0_41
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2250,f2227,f384,f2393]) ).

fof(f2250,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_41
    | ~ spl0_224 ),
    inference(superposition,[],[f2228,f386]) ).

fof(f2391,plain,
    ( spl0_249
    | ~ spl0_250
    | ~ spl0_87
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f837,f802,f673,f2388,f2385]) ).

fof(f2385,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f2388,plain,
    ( spl0_250
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f837,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_87
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f674]) ).

fof(f2383,plain,
    ( spl0_248
    | ~ spl0_67
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f827,f802,f556,f2381]) ).

fof(f2381,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f827,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f557]) ).

fof(f2379,plain,
    ( spl0_247
    | ~ spl0_68
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f826,f802,f560,f2377]) ).

fof(f2377,plain,
    ( spl0_247
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f826,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f561]) ).

fof(f2374,plain,
    ( spl0_245
    | ~ spl0_246
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f782,f389,f380,f2371,f2368]) ).

fof(f2368,plain,
    ( spl0_245
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f2371,plain,
    ( spl0_246
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f389,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f782,plain,
    ( ! [X0] :
        ( ~ inductive(null_class)
        | member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(superposition,[],[f390,f381]) ).

fof(f390,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(null_class,X0) )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f389]) ).

fof(f2366,plain,
    ( spl0_244
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f774,f761,f319,f2364]) ).

fof(f774,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(resolution,[],[f762,f320]) ).

fof(f2362,plain,
    ( spl0_243
    | ~ spl0_27
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f770,f731,f319,f2360]) ).

fof(f770,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_27
    | ~ spl0_97 ),
    inference(resolution,[],[f732,f320]) ).

fof(f2358,plain,
    ( spl0_242
    | ~ spl0_37
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f537,f511,f359,f2356]) ).

fof(f2356,plain,
    ( spl0_242
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f511,plain,
    ( spl0_59
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f537,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_37
    | ~ spl0_59 ),
    inference(resolution,[],[f512,f360]) ).

fof(f512,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f511]) ).

fof(f2354,plain,
    ( ~ spl0_241
    | spl0_182
    | ~ spl0_14
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f869,f815,f262,f1538,f2351]) ).

fof(f2351,plain,
    ( spl0_241
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f869,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_14
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f264]) ).

fof(f2349,plain,
    ( ~ spl0_240
    | spl0_182
    | ~ spl0_11
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f862,f815,f249,f1538,f2346]) ).

fof(f2346,plain,
    ( spl0_240
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f862,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_11
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f251]) ).

fof(f2344,plain,
    ( spl0_238
    | ~ spl0_239
    | ~ spl0_86
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f836,f802,f669,f2341,f2338]) ).

fof(f2338,plain,
    ( spl0_238
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2341,plain,
    ( spl0_239
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f836,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_86
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f670]) ).

fof(f2336,plain,
    ( spl0_236
    | ~ spl0_237
    | ~ spl0_64
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f834,f802,f539,f2333,f2330]) ).

fof(f2330,plain,
    ( spl0_236
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f2333,plain,
    ( spl0_237
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f834,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_64
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f540]) ).

fof(f2313,plain,
    ( spl0_235
    | ~ spl0_231
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2308,f2300,f2282,f2310]) ).

fof(f2308,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_231
    | ~ spl0_233 ),
    inference(forward_demodulation,[],[f2302,f2284]) ).

fof(f2307,plain,
    ( spl0_233
    | spl0_234
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f777,f761,f299,f2304,f2300]) ).

fof(f777,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(resolution,[],[f762,f300]) ).

fof(f2289,plain,
    ( spl0_231
    | spl0_232
    | ~ spl0_23
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f773,f731,f299,f2286,f2282]) ).

fof(f773,plain,
    ( member(regular(singleton_relation),element_relation)
    | null_class = singleton_relation
    | ~ spl0_23
    | ~ spl0_97 ),
    inference(resolution,[],[f732,f300]) ).

fof(f2279,plain,
    ( ~ spl0_229
    | spl0_230
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f766,f439,f295,f2276,f2272]) ).

fof(f2272,plain,
    ( spl0_229
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f439,plain,
    ( spl0_47
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f766,plain,
    ( member(omega,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(resolution,[],[f440,f296]) ).

fof(f440,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f439]) ).

fof(f2267,plain,
    ( spl0_228
    | ~ spl0_38
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f2171,f636,f372,f2265]) ).

fof(f2171,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_80 ),
    inference(resolution,[],[f637,f373]) ).

fof(f2263,plain,
    ( spl0_227
    | ~ spl0_18
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f912,f892,f279,f2261]) ).

fof(f2261,plain,
    ( spl0_227
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f912,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_114 ),
    inference(resolution,[],[f893,f280]) ).

fof(f2259,plain,
    ( spl0_225
    | ~ spl0_226
    | ~ spl0_61
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f829,f802,f524,f2256,f2253]) ).

fof(f2253,plain,
    ( spl0_225
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2256,plain,
    ( spl0_226
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f829,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_61
    | ~ spl0_106 ),
    inference(resolution,[],[f803,f525]) ).

fof(f2229,plain,
    ( spl0_224
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1146,f1087,f323,f2227]) ).

fof(f1146,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(duplicate_literal_removal,[],[f1129]) ).

fof(f1129,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(resolution,[],[f1088,f324]) ).

fof(f2225,plain,
    ( spl0_223
    | ~ spl0_28
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1128,f1083,f323,f2223]) ).

fof(f1128,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_28
    | ~ spl0_134 ),
    inference(duplicate_literal_removal,[],[f1111]) ).

fof(f1111,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_28
    | ~ spl0_134 ),
    inference(resolution,[],[f1084,f324]) ).

fof(f2141,plain,
    ( ~ spl0_2
    | ~ spl0_222 ),
    inference(avatar_contradiction_clause,[],[f2140]) ).

fof(f2140,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_222 ),
    inference(resolution,[],[f2138,f211]) ).

fof(f211,plain,
    ( inductive(omega)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f209]) ).

fof(f2138,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f2137]) ).

fof(f2137,plain,
    ( spl0_222
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f2139,plain,
    ( spl0_222
    | spl0_80
    | ~ spl0_4
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f854,f815,f219,f636,f2137]) ).

fof(f854,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_4
    | ~ spl0_109 ),
    inference(resolution,[],[f816,f220]) ).

fof(f2126,plain,
    ( spl0_221
    | ~ spl0_90
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f706,f702,f686,f2124]) ).

fof(f706,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_90
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f687]) ).

fof(f2122,plain,
    ( spl0_220
    | ~ spl0_50
    | ~ spl0_90
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f755,f750,f686,f452,f2120]) ).

fof(f2120,plain,
    ( spl0_220
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f755,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_50
    | ~ spl0_90
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f753,f453]) ).

fof(f753,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_90
    | ~ spl0_101 ),
    inference(resolution,[],[f751,f687]) ).

fof(f2112,plain,
    ( spl0_219
    | ~ spl0_70
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f754,f750,f568,f2110]) ).

fof(f754,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_70
    | ~ spl0_101 ),
    inference(resolution,[],[f751,f569]) ).

fof(f2099,plain,
    ( spl0_218
    | ~ spl0_84
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f709,f702,f654,f2097]) ).

fof(f709,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_84
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f655]) ).

fof(f2095,plain,
    ( spl0_217
    | ~ spl0_79
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f659,f654,f628,f2093]) ).

fof(f2093,plain,
    ( spl0_217
  <=> ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f659,plain,
    ( ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_84 ),
    inference(resolution,[],[f655,f629]) ).

fof(f2082,plain,
    ( spl0_216
    | ~ spl0_27
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f707,f702,f319,f2080]) ).

fof(f707,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f320]) ).

fof(f2069,plain,
    ( spl0_215
    | ~ spl0_23
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f710,f702,f299,f2067]) ).

fof(f710,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f300]) ).

fof(f2058,plain,
    ( ~ spl0_214
    | spl0_192
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f775,f761,f254,f1613,f2055]) ).

fof(f2055,plain,
    ( spl0_214
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f775,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(resolution,[],[f762,f255]) ).

fof(f2053,plain,
    ( spl0_213
    | ~ spl0_77
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f748,f745,f613,f2051]) ).

fof(f748,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) )
    | ~ spl0_77
    | ~ spl0_100 ),
    inference(resolution,[],[f746,f614]) ).

fof(f2000,plain,
    ( spl0_212
    | ~ spl0_77
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f743,f739,f613,f1998]) ).

fof(f743,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_77
    | ~ spl0_99 ),
    inference(resolution,[],[f740,f614]) ).

fof(f1996,plain,
    ( spl0_211
    | ~ spl0_77
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f742,f735,f613,f1994]) ).

fof(f742,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_77
    | ~ spl0_98 ),
    inference(resolution,[],[f736,f614]) ).

fof(f1947,plain,
    ( spl0_210
    | ~ spl0_77
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f631,f628,f613,f1945]) ).

fof(f1945,plain,
    ( spl0_210
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f631,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) )
    | ~ spl0_77
    | ~ spl0_79 ),
    inference(resolution,[],[f629,f614]) ).

fof(f1937,plain,
    ( spl0_209
    | ~ spl0_40
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f715,f702,f380,f1935]) ).

fof(f715,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_93 ),
    inference(superposition,[],[f703,f381]) ).

fof(f1925,plain,
    ( spl0_208
    | ~ spl0_70
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f705,f702,f568,f1923]) ).

fof(f705,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_70
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f569]) ).

fof(f1915,plain,
    ( spl0_207
    | ~ spl0_48
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f658,f654,f444,f1913]) ).

fof(f658,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_84 ),
    inference(resolution,[],[f655,f445]) ).

fof(f1908,plain,
    ( spl0_206
    | ~ spl0_40
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f712,f702,f380,f1906]) ).

fof(f712,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_93 ),
    inference(superposition,[],[f703,f381]) ).

fof(f1870,plain,
    ( spl0_205
    | ~ spl0_38
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f700,f696,f372,f1868]) ).

fof(f700,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
    | ~ spl0_38
    | ~ spl0_92 ),
    inference(resolution,[],[f697,f373]) ).

fof(f1814,plain,
    ( spl0_204
    | ~ spl0_50
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f714,f702,f452,f1812]) ).

fof(f714,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_93 ),
    inference(superposition,[],[f703,f453]) ).

fof(f1810,plain,
    ( ~ spl0_203
    | ~ spl0_12
    | spl0_192 ),
    inference(avatar_split_clause,[],[f1707,f1613,f254,f1807]) ).

fof(f1807,plain,
    ( spl0_203
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1707,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_12
    | spl0_192 ),
    inference(resolution,[],[f1615,f255]) ).

fof(f1615,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_192 ),
    inference(avatar_component_clause,[],[f1613]) ).

fof(f1805,plain,
    ( spl0_202
    | ~ spl0_50
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f711,f702,f452,f1803]) ).

fof(f711,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_93 ),
    inference(superposition,[],[f703,f453]) ).

fof(f1795,plain,
    ( spl0_201
    | ~ spl0_12
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f708,f702,f254,f1793]) ).

fof(f708,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_12
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f255]) ).

fof(f1775,plain,
    ( spl0_200
    | ~ spl0_27
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f634,f628,f319,f1773]) ).

fof(f634,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_79 ),
    inference(resolution,[],[f629,f320]) ).

fof(f1747,plain,
    ( spl0_199
    | ~ spl0_38
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f689,f686,f372,f1745]) ).

fof(f689,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
    | ~ spl0_38
    | ~ spl0_90 ),
    inference(resolution,[],[f687,f373]) ).

fof(f1713,plain,
    ( spl0_198
    | ~ spl0_23
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f633,f628,f299,f1711]) ).

fof(f633,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_79 ),
    inference(resolution,[],[f629,f300]) ).

fof(f1706,plain,
    ( spl0_197
    | ~ spl0_77
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f721,f718,f613,f1704]) ).

fof(f721,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_94 ),
    inference(resolution,[],[f719,f614]) ).

fof(f1662,plain,
    ( spl0_196
    | ~ spl0_31
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f661,f654,f335,f1660]) ).

fof(f661,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_31
    | ~ spl0_84 ),
    inference(resolution,[],[f655,f336]) ).

fof(f1658,plain,
    ( spl0_195
    | ~ spl0_32
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f660,f654,f339,f1656]) ).

fof(f660,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_32
    | ~ spl0_84 ),
    inference(resolution,[],[f655,f340]) ).

fof(f1641,plain,
    ( spl0_194
    | ~ spl0_20
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f662,f654,f287,f1639]) ).

fof(f662,plain,
    ( ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_84 ),
    inference(resolution,[],[f655,f288]) ).

fof(f1622,plain,
    ( spl0_193
    | ~ spl0_38
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f657,f654,f372,f1620]) ).

fof(f657,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_38
    | ~ spl0_84 ),
    inference(resolution,[],[f655,f373]) ).

fof(f1616,plain,
    ( ~ spl0_192
    | ~ spl0_111
    | spl0_182 ),
    inference(avatar_split_clause,[],[f1546,f1538,f823,f1613]) ).

fof(f1546,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_111
    | spl0_182 ),
    inference(resolution,[],[f1540,f824]) ).

fof(f1611,plain,
    ( spl0_191
    | ~ spl0_39
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f535,f532,f376,f1609]) ).

fof(f535,plain,
    ( ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_39
    | ~ spl0_63 ),
    inference(resolution,[],[f533,f377]) ).

fof(f1599,plain,
    ( ~ spl0_188
    | ~ spl0_189
    | spl0_190
    | ~ spl0_73
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f616,f608,f588,f1596,f1592,f1588]) ).

fof(f1588,plain,
    ( spl0_188
  <=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f1592,plain,
    ( spl0_189
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1596,plain,
    ( spl0_190
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f588,plain,
    ( spl0_73
  <=> ! [X0,X8] :
        ( ~ function(X8)
        | ~ member(X0,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f616,plain,
    ( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(universal_class,universal_class)
    | ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_73
    | ~ spl0_76 ),
    inference(superposition,[],[f589,f610]) ).

fof(f589,plain,
    ( ! [X0,X8] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X8) )
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f588]) ).

fof(f1586,plain,
    ( spl0_187
    | ~ spl0_28
    | ~ spl0_50
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f582,f568,f452,f323,f1584]) ).

fof(f582,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_50
    | ~ spl0_70 ),
    inference(forward_demodulation,[],[f581,f453]) ).

fof(f581,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_70 ),
    inference(resolution,[],[f569,f324]) ).

fof(f1580,plain,
    ( spl0_186
    | ~ spl0_77
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f680,f677,f613,f1578]) ).

fof(f680,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_88 ),
    inference(resolution,[],[f678,f614]) ).

fof(f1558,plain,
    ( spl0_185
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f617,f608,f448,f1556]) ).

fof(f617,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(superposition,[],[f449,f610]) ).

fof(f1551,plain,
    ( spl0_184
    | ~ spl0_38
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f622,f613,f372,f1549]) ).

fof(f622,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_38
    | ~ spl0_77 ),
    inference(resolution,[],[f614,f373]) ).

fof(f1545,plain,
    ( ~ spl0_181
    | ~ spl0_182
    | spl0_183
    | ~ spl0_22
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f606,f596,f295,f1542,f1538,f1534]) ).

fof(f1534,plain,
    ( spl0_181
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1542,plain,
    ( spl0_183
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f596,plain,
    ( spl0_75
  <=> ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f606,plain,
    ( inductive(cross_product(universal_class,universal_class))
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | ~ spl0_22
    | ~ spl0_75 ),
    inference(resolution,[],[f597,f296]) ).

fof(f597,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f596]) ).

fof(f1532,plain,
    ( spl0_180
    | ~ spl0_39
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f514,f503,f376,f1530]) ).

fof(f1530,plain,
    ( spl0_180
  <=> ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f514,plain,
    ( ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
    | ~ spl0_39
    | ~ spl0_57 ),
    inference(resolution,[],[f504,f377]) ).

fof(f1525,plain,
    ( spl0_178
    | spl0_179
    | ~ spl0_40
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f601,f588,f380,f1522,f1519]) ).

fof(f1519,plain,
    ( spl0_178
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | null_class = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f601,plain,
    ( ! [X0] :
        ( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | null_class = cross_product(X0,universal_class) )
    | ~ spl0_40
    | ~ spl0_73 ),
    inference(superposition,[],[f589,f381]) ).

fof(f1517,plain,
    ( spl0_177
    | ~ spl0_63
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f547,f543,f532,f1515]) ).

fof(f1515,plain,
    ( spl0_177
  <=> ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f543,plain,
    ( spl0_65
  <=> ! [X1,X8] :
        ( ~ function(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | maps(X8,domain_of(X8),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f547,plain,
    ( ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) )
    | ~ spl0_63
    | ~ spl0_65 ),
    inference(resolution,[],[f544,f533]) ).

fof(f544,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f543]) ).

fof(f1479,plain,
    ( spl0_176
    | ~ spl0_77
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f667,f664,f613,f1477]) ).

fof(f667,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_85 ),
    inference(resolution,[],[f665,f614]) ).

fof(f1475,plain,
    ( ~ spl0_174
    | spl0_175
    | ~ spl0_14
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f913,f892,f262,f1472,f1468]) ).

fof(f1468,plain,
    ( spl0_174
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f1472,plain,
    ( spl0_175
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f913,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_14
    | ~ spl0_114 ),
    inference(resolution,[],[f893,f264]) ).

fof(f1466,plain,
    ( spl0_172
    | spl0_173
    | ~ spl0_12
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f632,f628,f254,f1463,f1460]) ).

fof(f1460,plain,
    ( spl0_172
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f632,plain,
    ( ! [X0,X1] :
        ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_79 ),
    inference(resolution,[],[f629,f255]) ).

fof(f1458,plain,
    ( spl0_171
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f603,f592,f372,f1456]) ).

fof(f592,plain,
    ( spl0_74
  <=> ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f603,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(resolution,[],[f593,f373]) ).

fof(f593,plain,
    ( ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f592]) ).

fof(f1454,plain,
    ( spl0_170
    | ~ spl0_38
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f599,f588,f372,f1452]) ).

fof(f599,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
    | ~ spl0_38
    | ~ spl0_73 ),
    inference(resolution,[],[f589,f373]) ).

fof(f1450,plain,
    ( spl0_169
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f494,f460,f376,f1448]) ).

fof(f1448,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f494,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(resolution,[],[f461,f377]) ).

fof(f1446,plain,
    ( spl0_168
    | ~ spl0_39
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f493,f456,f376,f1444]) ).

fof(f1444,plain,
    ( spl0_168
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f493,plain,
    ( ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_51 ),
    inference(resolution,[],[f457,f377]) ).

fof(f1379,plain,
    ( spl0_167
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f648,f645,f1377]) ).

fof(f645,plain,
    ( spl0_82
  <=> ! [X9,X11,X10] :
        ( ~ function(X9)
        | compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) != domain_of(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f648,plain,
    ( ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
    | ~ spl0_82 ),
    inference(equality_resolution,[],[f646]) ).

fof(f646,plain,
    ( ! [X10,X11,X9] :
        ( domain_of(domain_of(X10)) != domain_of(X9)
        | compatible(X9,X10,X11)
        | ~ function(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f645]) ).

fof(f1375,plain,
    ( spl0_166
    | ~ spl0_38
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f580,f568,f372,f1373]) ).

fof(f580,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_70 ),
    inference(resolution,[],[f569,f373]) ).

fof(f1371,plain,
    ( spl0_165
    | ~ spl0_38
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f572,f552,f372,f1369]) ).

fof(f572,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
    | ~ spl0_38
    | ~ spl0_66 ),
    inference(resolution,[],[f553,f373]) ).

fof(f1367,plain,
    ( spl0_164
    | ~ spl0_28
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f483,f448,f323,f1365]) ).

fof(f483,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_28
    | ~ spl0_49 ),
    inference(resolution,[],[f449,f324]) ).

fof(f1363,plain,
    ( spl0_163
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f475,f444,f319,f1361]) ).

fof(f475,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(resolution,[],[f445,f320]) ).

fof(f1353,plain,
    ( spl0_162
    | ~ spl0_32
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f618,f608,f339,f1351]) ).

fof(f618,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_32
    | ~ spl0_76 ),
    inference(superposition,[],[f340,f610]) ).

fof(f1322,plain,
    ( spl0_161
    | ~ spl0_50
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f600,f588,f452,f1320]) ).

fof(f600,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_50
    | ~ spl0_73 ),
    inference(superposition,[],[f589,f453]) ).

fof(f1318,plain,
    ( spl0_160
    | ~ spl0_23
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f474,f444,f299,f1316]) ).

fof(f474,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_48 ),
    inference(resolution,[],[f445,f300]) ).

fof(f1300,plain,
    ( spl0_159
    | ~ spl0_22
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f550,f543,f295,f1298]) ).

fof(f1298,plain,
    ( spl0_159
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f550,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_22
    | ~ spl0_65 ),
    inference(resolution,[],[f544,f296]) ).

fof(f1296,plain,
    ( spl0_158
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f522,f516,f380,f1294]) ).

fof(f516,plain,
    ( spl0_60
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f522,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(trivial_inequality_removal,[],[f520]) ).

fof(f520,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(superposition,[],[f517,f381]) ).

fof(f517,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f516]) ).

fof(f1292,plain,
    ( spl0_157
    | ~ spl0_28
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f437,f424,f323,f1290]) ).

fof(f437,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_28
    | ~ spl0_44 ),
    inference(resolution,[],[f425,f324]) ).

fof(f1288,plain,
    ( ~ spl0_155
    | spl0_156
    | ~ spl0_11
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f909,f892,f249,f1285,f1281]) ).

fof(f1281,plain,
    ( spl0_155
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1285,plain,
    ( spl0_156
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f909,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_11
    | ~ spl0_114 ),
    inference(resolution,[],[f893,f251]) ).

fof(f1279,plain,
    ( spl0_154
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f409,f376,f347,f1277]) ).

fof(f409,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f348]) ).

fof(f1275,plain,
    ( spl0_153
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f408,f376,f343,f1273]) ).

fof(f408,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f344]) ).

fof(f1249,plain,
    ( spl0_152
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f497,f468,f372,f1247]) ).

fof(f468,plain,
    ( spl0_54
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f497,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(resolution,[],[f469,f373]) ).

fof(f469,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f468]) ).

fof(f1245,plain,
    ( spl0_151
    | ~ spl0_38
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f482,f448,f372,f1243]) ).

fof(f482,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_38
    | ~ spl0_49 ),
    inference(resolution,[],[f449,f373]) ).

fof(f1241,plain,
    ( spl0_149
    | ~ spl0_150
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f416,f376,f308,f1238,f1234]) ).

fof(f1234,plain,
    ( spl0_149
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f416,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f310]) ).

fof(f1232,plain,
    ( spl0_147
    | ~ spl0_148
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f414,f376,f303,f1229,f1225]) ).

fof(f1225,plain,
    ( spl0_147
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f414,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f305]) ).

fof(f1223,plain,
    ( spl0_146
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f412,f376,f291,f1221]) ).

fof(f412,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f292]) ).

fof(f1173,plain,
    ( spl0_145
    | ~ spl0_50
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f519,f516,f452,f1171]) ).

fof(f519,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_50
    | ~ spl0_60 ),
    inference(superposition,[],[f517,f453]) ).

fof(f1169,plain,
    ( spl0_144
    | ~ spl0_43
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f486,f448,f393,f1167]) ).

fof(f486,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_49 ),
    inference(superposition,[],[f449,f395]) ).

fof(f1165,plain,
    ( spl0_143
    | ~ spl0_41
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f485,f448,f384,f1163]) ).

fof(f485,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_41
    | ~ spl0_49 ),
    inference(superposition,[],[f449,f386]) ).

fof(f1161,plain,
    ( spl0_142
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f484,f448,f380,f1159]) ).

fof(f484,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(superposition,[],[f449,f381]) ).

fof(f1157,plain,
    ( spl0_141
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f436,f424,f372,f1155]) ).

fof(f436,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(resolution,[],[f425,f373]) ).

fof(f1110,plain,
    ( spl0_140
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f549,f543,f228,f1108]) ).

fof(f1108,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f549,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(resolution,[],[f544,f229]) ).

fof(f1106,plain,
    ( ~ spl0_138
    | spl0_139
    | ~ spl0_10
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f907,f892,f244,f1103,f1099]) ).

fof(f1099,plain,
    ( spl0_138
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1103,plain,
    ( spl0_139
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f907,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_10
    | ~ spl0_114 ),
    inference(resolution,[],[f893,f246]) ).

fof(f1097,plain,
    ( spl0_137
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f413,f376,f279,f1095]) ).

fof(f413,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f280]) ).

fof(f1093,plain,
    ( spl0_136
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f406,f376,f295,f1091]) ).

fof(f406,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f296]) ).

fof(f1089,plain,
    ( spl0_135
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f370,f339,f319,f1087]) ).

fof(f370,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(resolution,[],[f340,f320]) ).

fof(f1085,plain,
    ( spl0_134
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f367,f335,f319,f1083]) ).

fof(f367,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(resolution,[],[f336,f320]) ).

fof(f1026,plain,
    ( spl0_133
    | ~ spl0_57
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f546,f543,f503,f1024]) ).

fof(f1024,plain,
    ( spl0_133
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f546,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_57
    | ~ spl0_65 ),
    inference(resolution,[],[f544,f504]) ).

fof(f1022,plain,
    ( spl0_132
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f403,f372,f331,f1020]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f332]) ).

fof(f1018,plain,
    ( spl0_131
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f402,f372,f327,f1016]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f328]) ).

fof(f1014,plain,
    ( spl0_130
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f401,f372,f319,f1012]) ).

fof(f401,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f320]) ).

fof(f1010,plain,
    ( spl0_129
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f369,f339,f299,f1008]) ).

fof(f369,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(resolution,[],[f340,f300]) ).

fof(f1006,plain,
    ( spl0_128
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f366,f335,f299,f1004]) ).

fof(f366,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(resolution,[],[f336,f300]) ).

fof(f987,plain,
    ( ~ spl0_127
    | ~ spl0_12
    | spl0_108 ),
    inference(avatar_split_clause,[],[f940,f810,f254,f984]) ).

fof(f984,plain,
    ( spl0_127
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f940,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_12
    | spl0_108 ),
    inference(resolution,[],[f811,f255]) ).

fof(f811,plain,
    ( ~ member(null_class,element_relation)
    | spl0_108 ),
    inference(avatar_component_clause,[],[f810]) ).

fof(f965,plain,
    ( spl0_126
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f473,f444,f254,f963]) ).

fof(f473,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(resolution,[],[f445,f255]) ).

fof(f961,plain,
    ( spl0_125
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f422,f393,f335,f959]) ).

fof(f422,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(superposition,[],[f336,f395]) ).

fof(f957,plain,
    ( spl0_124
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f420,f384,f335,f955]) ).

fof(f420,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(superposition,[],[f336,f386]) ).

fof(f953,plain,
    ( spl0_123
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f417,f380,f339,f951]) ).

fof(f417,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(superposition,[],[f340,f381]) ).

fof(f949,plain,
    ( spl0_121
    | ~ spl0_122
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f415,f376,f262,f946,f942]) ).

fof(f942,plain,
    ( spl0_121
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f415,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f264]) ).

fof(f939,plain,
    ( spl0_119
    | ~ spl0_120
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f410,f376,f249,f936,f932]) ).

fof(f932,plain,
    ( spl0_119
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f410,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f251]) ).

fof(f930,plain,
    ( spl0_117
    | ~ spl0_118
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f407,f376,f244,f927,f923]) ).

fof(f923,plain,
    ( spl0_117
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f407,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f246]) ).

fof(f921,plain,
    ( spl0_116
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f400,f372,f299,f919]) ).

fof(f400,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f300]) ).

fof(f917,plain,
    ( spl0_115
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f362,f319,f287,f915]) ).

fof(f362,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(resolution,[],[f320,f288]) ).

fof(f894,plain,
    ( spl0_114
    | ~ spl0_51
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f579,f564,f456,f892]) ).

fof(f579,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_69 ),
    inference(resolution,[],[f565,f457]) ).

fof(f890,plain,
    ( spl0_113
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f418,f380,f335,f888]) ).

fof(f418,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(superposition,[],[f336,f381]) ).

fof(f886,plain,
    ( spl0_112
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f317,f299,f287,f884]) ).

fof(f317,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(resolution,[],[f300,f288]) ).

fof(f825,plain,
    ( spl0_111
    | ~ spl0_31
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f619,f608,f335,f823]) ).

fof(f619,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_31
    | ~ spl0_76 ),
    inference(superposition,[],[f336,f610]) ).

fof(f821,plain,
    ( spl0_110
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f411,f376,f258,f819]) ).

fof(f411,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f259]) ).

fof(f817,plain,
    ( spl0_109
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f399,f372,f254,f815]) ).

fof(f399,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f255]) ).

fof(f813,plain,
    ( ~ spl0_107
    | spl0_108
    | ~ spl0_12
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f771,f731,f254,f810,f806]) ).

fof(f806,plain,
    ( spl0_107
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f771,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_12
    | ~ spl0_97 ),
    inference(resolution,[],[f732,f255]) ).

fof(f804,plain,
    ( spl0_106
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f398,f372,f240,f802]) ).

fof(f398,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f241]) ).

fof(f791,plain,
    ( spl0_105
    | ~ spl0_4
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f548,f543,f219,f789]) ).

fof(f789,plain,
    ( spl0_105
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f548,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_4
    | ~ spl0_65 ),
    inference(resolution,[],[f544,f220]) ).

fof(f781,plain,
    ( spl0_104
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f368,f339,f254,f779]) ).

fof(f779,plain,
    ( spl0_104
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f368,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(resolution,[],[f340,f255]) ).

fof(f763,plain,
    ( spl0_103
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f421,f393,f339,f761]) ).

fof(f421,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f340,f395]) ).

fof(f759,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f202,f757]) ).

fof(f757,plain,
    ( spl0_102
  <=> ! [X9,X11,X10] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
        | ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f202,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f201,f128]) ).

fof(f128,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/sandbox/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).

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(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,[],[f200,f128]) ).

fof(f200,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f199,f128]) ).

fof(f199,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(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,[],[f198,f128]) ).

fof(f198,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f197,f128]) ).

fof(f197,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,[],[f196,f128]) ).

fof(f196,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f195,f128]) ).

fof(f195,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(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,[],[f194,f128]) ).

fof(f194,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f193,f128]) ).

fof(f193,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,[],[f175,f128]) ).

fof(f175,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f91,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f118,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ordered_pair) ).

fof(f117,plain,
    ! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
    inference(definition_unfolding,[],[f68,f114,f116,f12]) ).

fof(f116,plain,
    ! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
    inference(definition_unfolding,[],[f42,f115,f29]) ).

fof(f115,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).

fof(f42,axiom,
    ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).

fof(f114,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f68,axiom,
    ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',homomorphism6) ).

fof(f752,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f192,f750]) ).

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(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,[],[f191,f128]) ).

fof(f191,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(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,[],[f190,f128]) ).

fof(f190,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,[],[f189,f128]) ).

fof(f189,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(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,[],[f188,f128]) ).

fof(f188,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,[],[f167,f128]) ).

fof(f167,plain,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f89,f118,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f89,axiom,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(ordered_pair(X0,X1),domain_of(X10))
      | apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).

fof(f747,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f187,f745]) ).

fof(f187,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,[],[f166,f128]) ).

fof(f166,plain,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(definition_unfolding,[],[f108,f118,f118,f117,f118,f118]) ).

fof(f108,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn4) ).

fof(f741,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f171,f739]) ).

fof(f171,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f37,f118,f118,f118,f118,f118,f118]) ).

fof(f37,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip3) ).

fof(f737,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f170,f735]) ).

fof(f170,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f34,f118,f118,f118,f118,f118,f118]) ).

fof(f34,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate3) ).

fof(f733,plain,
    ( spl0_97
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f419,f384,f339,f731]) ).

fof(f419,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(superposition,[],[f340,f386]) ).

fof(f729,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f155,f727]) ).

fof(f155,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
    inference(definition_unfolding,[],[f36,f118,f118,f118,f118]) ).

fof(f36,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip2) ).

fof(f725,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f154,f723]) ).

fof(f154,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
    inference(definition_unfolding,[],[f33,f118,f118,f118,f118]) ).

fof(f33,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate2) ).

fof(f720,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f178,f718]) ).

fof(f178,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,[],[f165]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f46,f124,f118,f118]) ).

fof(f124,plain,
    ! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
    inference(definition_unfolding,[],[f43,f26,f12]) ).

fof(f26,axiom,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

fof(f43,axiom,
    ! [X0] : union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',successor_relation3) ).

fof(f704,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f169,f702]) ).

fof(f169,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f59,f118,f118,f116,f116,f12]) ).

fof(f59,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X1,X4),compose(X7,X5))
      | ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).

fof(f698,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f152,f696]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
    inference(definition_unfolding,[],[f97,f118,f118,f118]) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function3) ).

fof(f693,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f183,f691]) ).

fof(f183,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,[],[f149,f128]) ).

fof(f149,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f107,f117,f118,f118]) ).

fof(f107,axiom,
    ! [X0,X1,X4] :
      ( apply(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn3) ).

fof(f688,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f174,f686]) ).

fof(f174,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
    inference(definition_unfolding,[],[f90,f118]) ).

fof(f90,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).

fof(f684,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f153,f682]) ).

fof(f153,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f58,f118,f116,f116,f12]) ).

fof(f58,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),compose(X7,X5))
      | member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).

fof(f679,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f179,f677]) ).

fof(f179,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,[],[f168]) ).

fof(f168,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f94,f118,f118]) ).

fof(f94,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(ordered_pair(X1,X4),compose_class(X0))
      | ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition3) ).

fof(f675,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f151,f673]) ).

fof(f151,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
    inference(definition_unfolding,[],[f96,f118,f118]) ).

fof(f96,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function2) ).

fof(f671,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f147,f669]) ).

fof(f147,plain,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f106,f118,f118]) ).

fof(f106,axiom,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn2) ).

fof(f666,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f162,f664]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f20,f118,f118]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(ordered_pair(X0,X1),element_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).

fof(f656,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f186,f654]) ).

fof(f186,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,[],[f185,f128]) ).

fof(f185,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,f128]) ).

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,f117]) ).

fof(f70,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(apply(choice,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).

fof(f652,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f172,f650]) ).

fof(f650,plain,
    ( spl0_83
  <=> ! [X8] :
        ( ~ function(X8)
        | operation(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f172,plain,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f81,f115]) ).

fof(f81,axiom,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(range_of(X8),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation4) ).

fof(f647,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f173,f645]) ).

fof(f173,plain,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f85,f115]) ).

fof(f85,axiom,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible4) ).

fof(f643,plain,
    ( ~ spl0_80
    | spl0_81
    | ~ spl0_4
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f605,f596,f219,f640,f636]) ).

fof(f640,plain,
    ( spl0_81
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f605,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_4
    | ~ spl0_75 ),
    inference(resolution,[],[f597,f220]) ).

fof(f630,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f148,f628]) ).

fof(f148,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
    inference(definition_unfolding,[],[f17,f118]) ).

fof(f17,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).

fof(f626,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f145,f624]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
    inference(definition_unfolding,[],[f45,f124,f118]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( successor(X0) = X1
      | ~ member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).

fof(f615,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f161,f613]) ).

fof(f161,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f16,f118]) ).

fof(f16,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f611,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f129,f608]) ).

fof(f129,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/sandbox/benchmark/theBenchmark.p',subset_relation) ).

fof(f598,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f184,f596]) ).

fof(f184,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,[],[f159,f128]) ).

fof(f159,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f116]) ).

fof(f49,axiom,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).

fof(f594,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f181,f592]) ).

fof(f181,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,[],[f136,f128]) ).

fof(f136,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
    inference(definition_unfolding,[],[f56,f125]) ).

fof(f125,plain,
    ! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
    inference(definition_unfolding,[],[f55,f116]) ).

fof(f55,axiom,
    ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).

fof(f56,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).

fof(f590,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f157,f588]) ).

fof(f157,plain,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
    inference(definition_unfolding,[],[f65,f116]) ).

fof(f65,axiom,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(image(X8,X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).

fof(f586,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f150,f584]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
    inference(definition_unfolding,[],[f93,f118]) ).

fof(f93,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition2) ).

fof(f577,plain,
    ( spl0_71
    | ~ spl0_3
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f536,f511,f214,f574]) ).

fof(f574,plain,
    ( spl0_71
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f536,plain,
    ( single_valued_class(choice)
    | ~ spl0_3
    | ~ spl0_59 ),
    inference(resolution,[],[f512,f216]) ).

fof(f570,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f164,f568]) ).

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/sandbox/benchmark/theBenchmark.p',domain2) ).

fof(f566,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f160,f564]) ).

fof(f160,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/sandbox/benchmark/theBenchmark.p',function3) ).

fof(f562,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f141,f560]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f14,f118]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f558,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f140,f556]) ).

fof(f140,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f15,f118]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f554,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f138,f552]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
    inference(definition_unfolding,[],[f100,f118]) ).

fof(f100,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation3) ).

fof(f545,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f158,f543]) ).

fof(f158,plain,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
      | maps(X8,domain_of(X8),X1) ),
    inference(definition_unfolding,[],[f112,f115]) ).

fof(f112,axiom,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(range_of(X8),X1)
      | maps(X8,domain_of(X8),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).

fof(f541,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f146,f539]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
    inference(definition_unfolding,[],[f99,f118]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(ordered_pair(X0,X1),domain_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation2) ).

fof(f534,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f180,f532]) ).

fof(f180,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,[],[f132,f128]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f48,f116]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).

fof(f530,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f144,f528]) ).

fof(f528,plain,
    ( spl0_62
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f144,plain,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f84,f115]) ).

fof(f84,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).

fof(f526,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f139,f524]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
    inference(definition_unfolding,[],[f19,f118]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).

fof(f518,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f142,f516]) ).

fof(f142,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/sandbox/benchmark/theBenchmark.p',domain1) ).

fof(f513,plain,
    ( spl0_59
    | ~ spl0_52
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f495,f464,f460,f511]) ).

fof(f495,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_53 ),
    inference(resolution,[],[f465,f461]) ).

fof(f509,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f143,f507]) ).

fof(f507,plain,
    ( spl0_58
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f143,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f115]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).

fof(f505,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f133,f503]) ).

fof(f133,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f115]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).

fof(f501,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f79,f499]) ).

fof(f499,plain,
    ( spl0_56
  <=> ! [X8] :
        ( ~ operation(X8)
        | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).

fof(f479,plain,
    ( spl0_55
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f404,f376,f219,f477]) ).

fof(f404,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(resolution,[],[f377,f220]) ).

fof(f470,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f182,f468]) ).

fof(f182,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f137,f128]) ).

fof(f137,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f114]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).

fof(f466,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f135,f464]) ).

fof(f135,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/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f462,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f134,f460]) ).

fof(f134,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/sandbox/benchmark/theBenchmark.p',function2) ).

fof(f458,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f130,f456]) ).

fof(f130,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/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f454,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f128,f452]) ).

fof(f450,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f23,f448]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).

fof(f446,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f8,f444]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f441,plain,
    ( spl0_47
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f397,f372,f223,f439]) ).

fof(f397,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(resolution,[],[f373,f225]) ).

fof(f434,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f156,f432]) ).

fof(f432,plain,
    ( spl0_46
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f156,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/sandbox/benchmark/theBenchmark.p',one_to_one3) ).

fof(f430,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f83,f428]) ).

fof(f428,plain,
    ( spl0_45
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).

fof(f426,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f25,f424]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).

fof(f396,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f127,f393]) ).

fof(f127,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/sandbox/benchmark/theBenchmark.p',identity_relation) ).

fof(f391,plain,
    ( spl0_42
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f365,f335,f254,f389]) ).

fof(f365,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(resolution,[],[f336,f255]) ).

fof(f387,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f104,f384]) ).

fof(f104,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_can_define_singleton) ).

fof(f382,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f67,f380]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).

fof(f378,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f7,f376]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f374,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1,f372]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).

fof(f361,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f131,f359]) ).

fof(f131,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/sandbox/benchmark/theBenchmark.p',one_to_one2) ).

fof(f357,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f110,f355]) ).

fof(f355,plain,
    ( spl0_36
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).

fof(f353,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f88,f351]) ).

fof(f351,plain,
    ( spl0_35
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).

fof(f349,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f35,f347]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).

fof(f345,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f32,f343]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).

fof(f341,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f22,f339]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).

fof(f337,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f21,f335]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).

fof(f333,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f10,f331]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f329,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f9,f327]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f325,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f3,f323]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f321,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f2,f319]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f316,plain,
    ( spl0_26
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f312,f287,f254,f314]) ).

fof(f314,plain,
    ( spl0_26
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f312,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(resolution,[],[f288,f255]) ).

fof(f311,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f105,f308]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f306,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f95,f303]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f301,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f66,f299]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).

fof(f297,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f62,f295]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).

fof(f293,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f57,f291]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).

fof(f289,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f24,f287]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).

fof(f285,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f109,f283]) ).

fof(f283,plain,
    ( spl0_19
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).

fof(f281,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f92,f279]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f277,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f87,f275]) ).

fof(f275,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).

fof(f273,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f86,f271]) ).

fof(f271,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).

fof(f269,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f82,f267]) ).

fof(f267,plain,
    ( spl0_15
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).

fof(f265,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f98,f262]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f260,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f51,f258]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f256,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f47,f254]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).

fof(f252,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f44,f249]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).

fof(f247,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f18,f244]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).

fof(f242,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f11,f240]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f238,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f78,f236]) ).

fof(f236,plain,
    ( spl0_8
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).

fof(f234,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f71,f232]) ).

fof(f232,plain,
    ( spl0_7
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).

fof(f230,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f176,f228]) ).

fof(f176,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).

fof(f226,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f52,f223]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f221,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f4,f219]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f217,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f69,f214]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).

fof(f212,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f50,f209]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f207,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f113,f204]) ).

fof(f113,axiom,
    ~ subclass(domain_of(intersection(x,y)),domain_of(x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_is_monotonic2_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET265-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 11:56:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (12920)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (12923)WARNING: value z3 for option sas not known
% 0.14/0.37  % (12927)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)
% 0.14/0.37  % (12921)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (12923)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)
% 0.14/0.37  % (12922)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (12926)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)
% 0.14/0.37  % (12924)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (12925)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]
% 0.20/0.48  TRYING [3]
% 1.37/0.54  TRYING [1]
% 1.37/0.55  TRYING [2]
% 1.37/0.56  TRYING [4]
% 1.37/0.63  TRYING [3]
% 3.45/0.87  TRYING [5]
% 6.21/1.26  TRYING [4]
% 7.71/1.48  TRYING [1]
% 7.71/1.48  TRYING [2]
% 7.71/1.49  TRYING [3]
% 8.33/1.53  TRYING [4]
% 8.71/1.66  TRYING [5]
% 11.93/2.08  TRYING [6]
% 17.07/2.85  TRYING [6]
% 18.58/3.08  % (12925)First to succeed.
% 19.16/3.16  % (12925)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12920"
% 19.16/3.17  % (12925)Refutation found. Thanks to Tanya!
% 19.16/3.17  % SZS status Unsatisfiable for theBenchmark
% 19.16/3.17  % SZS output start Proof for theBenchmark
% See solution above
% 19.84/3.20  % (12925)------------------------------
% 19.84/3.20  % (12925)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 19.84/3.20  % (12925)Termination reason: Refutation
% 19.84/3.20  
% 19.84/3.20  % (12925)Memory used [KB]: 32433
% 19.84/3.20  % (12925)Time elapsed: 2.771 s
% 19.84/3.20  % (12925)Instructions burned: 8038 (million)
% 19.84/3.20  % (12920)Success in time 2.827 s
%------------------------------------------------------------------------------