%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET232-6 : 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 : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:17:54 EDT 2024

% Result   : Unsatisfiable 14.76s 2.49s
% Output   : Refutation 14.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1351
% Syntax   : Number of formulae    : 4209 ( 137 unt;   0 def)
%            Number of atoms       : 15704 (1446 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 20496 (9001   ~;10249   |;   0   &)
%                                         (1246 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   28 (   4 avg)
%            Number of predicates  : 1258 (1256 usr;1247 prp; 0-3 aty)
%            Number of functors    :   41 (  41 usr;  15 con; 0-3 aty)
%            Number of variables   : 5661 (5661   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f27087,plain,
    $false,
    inference(avatar_sat_refutation,[],[f208,f213,f218,f223,f227,f232,f236,f240,f244,f248,f253,f258,f262,f266,f271,f275,f279,f283,f287,f291,f295,f299,f303,f307,f312,f317,f323,f327,f331,f335,f339,f343,f347,f351,f355,f359,f363,f367,f380,f384,f388,f392,f397,f402,f432,f436,f440,f444,f452,f456,f460,f464,f468,f472,f476,f480,f507,f511,f515,f519,f524,f532,f536,f540,f547,f551,f560,f564,f568,f572,f577,f581,f592,f596,f600,f604,f617,f621,f632,f636,f645,f653,f658,f662,f672,f677,f681,f685,f690,f694,f700,f704,f710,f726,f731,f735,f739,f743,f747,f753,f758,f765,f769,f787,f797,f812,f819,f823,f827,f831,f892,f896,f900,f923,f927,f936,f946,f955,f959,f963,f967,f971,f976,f1012,f1016,f1020,f1024,f1028,f1032,f1091,f1095,f1104,f1108,f1112,f1116,f1163,f1167,f1171,f1175,f1179,f1229,f1238,f1247,f1251,f1255,f1286,f1290,f1294,f1298,f1302,f1306,f1324,f1328,f1359,f1369,f1373,f1377,f1381,f1385,f1452,f1456,f1460,f1464,f1473,f1481,f1485,f1523,f1531,f1538,f1551,f1557,f1564,f1586,f1592,f1605,f1610,f1622,f1628,f1647,f1664,f1668,f1713,f1719,f1753,f1781,f1802,f1807,f1817,f1821,f1877,f1915,f1922,f1932,f1944,f1954,f2003,f2007,f2035,f2065,f2076,f2089,f2102,f2106,f2119,f2129,f2133,f2146,f2148,f2232,f2236,f2266,f2270,f2274,f2286,f2296,f2314,f2320,f2343,f2351,f2356,f2361,f2365,f2369,f2373,f2381,f2386,f2390,f2395,f2403,f2411,f2419,f2423,f2433,f2442,f2453,f2457,f2461,f2465,f2470,f2488,f2497,f2504,f2508,f2512,f2528,f2534,f2538,f2547,f2565,f2693,f2745,f2749,f2757,f2763,f2767,f2769,f2774,f2786,f2790,f2794,f2798,f2806,f2872,f2876,f2880,f2884,f2888,f2893,f2897,f2918,f2970,f2981,f2989,f2993,f3000,f3005,f3010,f3014,f3018,f3107,f3118,f3126,f3131,f3136,f3181,f3202,f3221,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3256,f3260,f3265,f3271,f3277,f3285,f3294,f3298,f3302,f3306,f3336,f3396,f3410,f3414,f3418,f3433,f3547,f3556,f3562,f3567,f3576,f3583,f3606,f3610,f3614,f3618,f3623,f3628,f3632,f3636,f3640,f3644,f3649,f3653,f3733,f3737,f3867,f3871,f3875,f3879,f3883,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3925,f3929,f3933,f3937,f3941,f3945,f3949,f3979,f4286,f4369,f4373,f4377,f4381,f4385,f4400,f4404,f4408,f4412,f4416,f4420,f4425,f4429,f4438,f4442,f4716,f4813,f4932,f4936,f4942,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4976,f4981,f4985,f4989,f4999,f5003,f5007,f5021,f5025,f5317,f5321,f5522,f5644,f5653,f5660,f5665,f5675,f5685,f5690,f5694,f5702,f5708,f5716,f5725,f5729,f5733,f5737,f5741,f5745,f5750,f5761,f5996,f6000,f6061,f6070,f6075,f6079,f6083,f6088,f6093,f6097,f6101,f6105,f6120,f6199,f6203,f6363,f6368,f6373,f6385,f6389,f6393,f6401,f6407,f6411,f6416,f6420,f6581,f6585,f6592,f6596,f6601,f6606,f6610,f6614,f6618,f6622,f6626,f6630,f6635,f6643,f6777,f6781,f6992,f6997,f7001,f7005,f7010,f7014,f7018,f7022,f7026,f7030,f7180,f7184,f7188,f7192,f7196,f7200,f7204,f7209,f7213,f7217,f7221,f7498,f7502,f7506,f7510,f7523,f7531,f7536,f7541,f7546,f7562,f7571,f7576,f7580,f7584,f7588,f7592,f7596,f7600,f7604,f7943,f8277,f8286,f8290,f8294,f8298,f8302,f8331,f8342,f8349,f8360,f8364,f8368,f8374,f8378,f8382,f8386,f8393,f8398,f8402,f8406,f8420,f8429,f8433,f8437,f8441,f8661,f8791,f8795,f8799,f8803,f8808,f8812,f8901,f8905,f8913,f8917,f8921,f8925,f8934,f8941,f9072,f9076,f9080,f9085,f9089,f9151,f9159,f9182,f9186,f9193,f9200,f9205,f9210,f9215,f9223,f9272,f9276,f9280,f9284,f9288,f9292,f9297,f9301,f9405,f9409,f9417,f9421,f9428,f9433,f9438,f9445,f9450,f9458,f9470,f9503,f9619,f9623,f9631,f9694,f9774,f9781,f9788,f9792,f9799,f9803,f9812,f9816,f9829,f9871,f9875,f9879,f9883,f9887,f9891,f10014,f10020,f10028,f10034,f10042,f10047,f10051,f10055,f10059,f10063,f10067,f10071,f10075,f10079,f10083,f10087,f10179,f10422,f10433,f10437,f10441,f10445,f10545,f10549,f10554,f10558,f10566,f10599,f10603,f10607,f10784,f10789,f10794,f11020,f11024,f11028,f11032,f11036,f11040,f11044,f11420,f11466,f11471,f11475,f11493,f11497,f11599,f11603,f11607,f11637,f11644,f11649,f11660,f11666,f11672,f11683,f11687,f11701,f11706,f11735,f11739,f11743,f11772,f11777,f11781,f11785,f11876,f11880,f11884,f11924,f11929,f11934,f11938,f11946,f11952,f11956,f11960,f11964,f11968,f12314,f12319,f12386,f12391,f12399,f12598,f12604,f12608,f12613,f12632,f12651,f12655,f12738,f12840,f12847,f12934,f12938,f12942,f13123,f13127,f13131,f13135,f13139,f13143,f13147,f13151,f13155,f13253,f13492,f13563,f13567,f13599,f13603,f13607,f13611,f13615,f13657,f13754,f13758,f13762,f13766,f13770,f13863,f13867,f13871,f13875,f13879,f13883,f13892,f13896,f14137,f14202,f14206,f14210,f14214,f14218,f14392,f14396,f14400,f14404,f14487,f14521,f14567,f14571,f14579,f14586,f14594,f14716,f14720,f14724,f14728,f14733,f14945,f14949,f15150,f15172,f15180,f15185,f15190,f15219,f15228,f15234,f15238,f15242,f15250,f15256,f15260,f15264,f15471,f15475,f15503,f15507,f15512,f15517,f15521,f15525,f15529,f15542,f15551,f15555,f15649,f15653,f15713,f15720,f15754,f15758,f15776,f15848,f15856,f15861,f15869,f15874,f15878,f15882,f15886,f15891,f15991,f15995,f16012,f16034,f16042,f16133,f16137,f16188,f16192,f16197,f16269,f16273,f16281,f16287,f16295,f16300,f16304,f16432,f16437,f16442,f16446,f16451,f16457,f16461,f16465,f16469,f16495,f16499,f16623,f16627,f16631,f16635,f16639,f16681,f16687,f16732,f16773,f16777,f16781,f16803,f16807,f16811,f16866,f16874,f16883,f16887,f16896,f16903,f17052,f17056,f17189,f17225,f17255,f17272,f17279,f17304,f17309,f17313,f17317,f17321,f17328,f17379,f17387,f17391,f17395,f17399,f17403,f17407,f17631,f17727,f17753,f17757,f17761,f17898,f17902,f18106,f18110,f18166,f18170,f18205,f18348,f18352,f18393,f18430,f18435,f18485,f18489,f18493,f18497,f18501,f18505,f18536,f18687,f18770,f18774,f18778,f18802,f18806,f18810,f18964,f18970,f18974,f19024,f19029,f19079,f19083,f19087,f19112,f19157,f19161,f19187,f19191,f19196,f19200,f19256,f19260,f19265,f19342,f19346,f19394,f19443,f19447,f19451,f19492,f19496,f19545,f19550,f19554,f19558,f19583,f19613,f19621,f19625,f19667,f19817,f19825,f19850,f19864,f19868,f19908,f19912,f19956,f19971,f20003,f20007,f20011,f20015,f20019,f20023,f20027,f20031,f20035,f20205,f20229,f20240,f20257,f20287,f20317,f20326,f20335,f20354,f20400,f20430,f20464,f20508,f20514,f20571,f20579,f20580,f20585,f20594,f20599,f20603,f20607,f20612,f20616,f20621,f20625,f20630,f20635,f20640,f20753,f20794,f20800,f20806,f20828,f20832,f20836,f20841,f20846,f20850,f20855,f20859,f20864,f20868,f20873,f20878,f22100,f22115,f22119,f22435,f22443,f22456,f22462,f22467,f22471,f22476,f22481,f22486,f22490,f22495,f22500,f22504,f22508,f22512,f22517,f22521,f22525,f22530,f22535,f22540,f22544,f22548,f22552,f22556,f22560,f22564,f22568,f22572,f22576,f22580,f22584,f22588,f22592,f22596,f22600,f22604,f22609,f22614,f22622,f22627,f22632,f22637,f22642,f22647,f22852,f23429,f23437,f23443,f23455,f23477,f23478,f23592,f23598,f23607,f23611,f23615,f23620,f23633,f23637,f23641,f23645,f23649,f23653,f23657,f23661,f23665,f23669,f23673,f23677,f23682,f23686,f23690,f23694,f23698,f23702,f24690,f24760,f24769,f24772,f24790,f24794,f24798,f24803,f24807,f24812,f24816,f24820,f24824,f24828,f24833,f24837,f24842,f24847,f24851,f24855,f24859,f24863,f24867,f24871,f24875,f24879,f24883,f24887,f24891,f24895,f24899,f24903,f24907,f24911,f24915,f24923,f24927,f24931,f24935,f24939,f24943,f24947,f25453,f26209,f26242,f26253,f26259,f26263,f26267,f26272,f26281,f26288,f26293,f26306,f26315,f26320,f26324,f26328,f26332,f26336,f26340,f26344,f26348,f26352,f26356,f26360,f26365,f26369,f26373,f26377,f26381,f26385,f26389,f26393,f26397,f26401,f26406,f26410,f26414,f26419,f26432,f26437,f26442,f26446,f26450,f26454,f26725,f27086]) ).

fof(f27086,plain,
    ( spl0_1
    | spl0_2
    | ~ spl0_27
    | ~ spl0_663 ),
    inference(avatar_split_clause,[],[f20560,f10177,f321,f210,f205]) ).

fof(f205,plain,
    ( spl0_1
  <=> subclass(cross_product(x,y),z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f210,plain,
    ( spl0_2
  <=> member(first(not_subclass_element(cross_product(x,y),z)),x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f321,plain,
    ( spl0_27
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f10177,plain,
    ( spl0_663
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | member(first(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f20560,plain,
    ( member(first(not_subclass_element(cross_product(x,y),z)),x)
    | subclass(cross_product(x,y),z)
    | ~ spl0_27
    | ~ spl0_663 ),
    inference(resolution,[],[f10178,f322]) ).

fof(f322,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f321]) ).

fof(f10178,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | member(first(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_663 ),
    inference(avatar_component_clause,[],[f10177]) ).

fof(f26725,plain,
    ( spl0_1246
    | ~ spl0_538
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f20707,f20614,f7941,f26723]) ).

fof(f26723,plain,
    ( spl0_1246
  <=> ! [X0] :
        ( ~ subclass(intersection(universal_class,universal_class),X0)
        | member(not_subclass_element(cross_product(x,y),z),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f7941,plain,
    ( spl0_538
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(not_subclass_element(cross_product(x,y),z),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f20614,plain,
    ( spl0_1048
  <=> ! [X0] : subclass(X0,intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f20707,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(universal_class,universal_class),X0)
        | member(not_subclass_element(cross_product(x,y),z),X0) )
    | ~ spl0_538
    | ~ spl0_1048 ),
    inference(resolution,[],[f20615,f7942]) ).

fof(f7942,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(not_subclass_element(cross_product(x,y),z),X1) )
    | ~ spl0_538 ),
    inference(avatar_component_clause,[],[f7941]) ).

fof(f20615,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_1048 ),
    inference(avatar_component_clause,[],[f20614]) ).

fof(f26454,plain,
    ( spl0_1245
    | ~ spl0_348
    | ~ spl0_735 ),
    inference(avatar_split_clause,[],[f12393,f12383,f3581,f26452]) ).

fof(f26452,plain,
    ( spl0_1245
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f3581,plain,
    ( spl0_348
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f12383,plain,
    ( spl0_735
  <=> subclass(application_function,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f12393,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),composition_function) )
    | ~ spl0_348
    | ~ spl0_735 ),
    inference(resolution,[],[f12385,f3582]) ).

fof(f3582,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X1,X2)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),X2) )
    | ~ spl0_348 ),
    inference(avatar_component_clause,[],[f3581]) ).

fof(f12385,plain,
    ( subclass(application_function,composition_function)
    | ~ spl0_735 ),
    inference(avatar_component_clause,[],[f12383]) ).

fof(f26450,plain,
    ( spl0_1244
    | ~ spl0_109
    | ~ spl0_681 ),
    inference(avatar_split_clause,[],[f10979,f10791,f817,f26448]) ).

fof(f26448,plain,
    ( spl0_1244
  <=> ! [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_1244])]) ).

fof(f817,plain,
    ( spl0_109
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f10791,plain,
    ( spl0_681
  <=> 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_681])]) ).

fof(f10979,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_681 ),
    inference(superposition,[],[f818,f10793]) ).

fof(f10793,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_681 ),
    inference(avatar_component_clause,[],[f10791]) ).

fof(f818,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f817]) ).

fof(f26446,plain,
    ( spl0_1243
    | ~ spl0_109
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10905,f10786,f817,f26444]) ).

fof(f26444,plain,
    ( spl0_1243
  <=> ! [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_1243])]) ).

fof(f10786,plain,
    ( spl0_680
  <=> 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_680])]) ).

fof(f10905,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_680 ),
    inference(superposition,[],[f818,f10788]) ).

fof(f10788,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_680 ),
    inference(avatar_component_clause,[],[f10786]) ).

fof(f26442,plain,
    ( spl0_1242
    | ~ spl0_109
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f10831,f10781,f817,f26440]) ).

fof(f26440,plain,
    ( spl0_1242
  <=> ! [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_1242])]) ).

fof(f10781,plain,
    ( spl0_679
  <=> 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_679])]) ).

fof(f10831,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_679 ),
    inference(superposition,[],[f818,f10783]) ).

fof(f10783,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_679 ),
    inference(avatar_component_clause,[],[f10781]) ).

fof(f26437,plain,
    ( spl0_1241
    | spl0_913
    | ~ spl0_166
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f6953,f6616,f1375,f16898,f26435]) ).

fof(f26435,plain,
    ( spl0_1241
  <=> ! [X1] :
        ( ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f16898,plain,
    ( spl0_913
  <=> ! [X2] : ~ member(X2,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f1375,plain,
    ( spl0_166
  <=> ! [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_166])]) ).

fof(f6616,plain,
    ( spl0_485
  <=> ! [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_485])]) ).

fof(f6953,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1) )
    | ~ spl0_166
    | ~ spl0_485 ),
    inference(duplicate_literal_removal,[],[f6929]) ).

fof(f6929,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_166
    | ~ spl0_485 ),
    inference(resolution,[],[f6617,f1376]) ).

fof(f1376,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_166 ),
    inference(avatar_component_clause,[],[f1375]) ).

fof(f6617,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_485 ),
    inference(avatar_component_clause,[],[f6616]) ).

fof(f26432,plain,
    ( spl0_1240
    | spl0_913
    | ~ spl0_109
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f6930,f6616,f817,f16898,f26430]) ).

fof(f26430,plain,
    ( spl0_1240
  <=> ! [X1] :
        ( ~ subclass(domain_relation,complement(X1))
        | ~ subclass(universal_class,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f6930,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(universal_class,X1) )
    | ~ spl0_109
    | ~ spl0_485 ),
    inference(resolution,[],[f6617,f818]) ).

fof(f26419,plain,
    ( ~ spl0_276
    | spl0_1239
    | ~ spl0_186
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f6376,f6370,f1562,f26416,f2544]) ).

fof(f2544,plain,
    ( spl0_276
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f26416,plain,
    ( spl0_1239
  <=> member(regular(subset_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f1562,plain,
    ( spl0_186
  <=> ! [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_186])]) ).

fof(f6370,plain,
    ( spl0_467
  <=> 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_467])]) ).

fof(f6376,plain,
    ( member(regular(subset_relation),subset_relation)
    | ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_186
    | ~ spl0_467 ),
    inference(resolution,[],[f6372,f1563]) ).

fof(f1563,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_186 ),
    inference(avatar_component_clause,[],[f1562]) ).

fof(f6372,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_467 ),
    inference(avatar_component_clause,[],[f6370]) ).

fof(f26414,plain,
    ( spl0_1238
    | ~ spl0_131
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5540,f5023,f1018,f26412]) ).

fof(f26412,plain,
    ( spl0_1238
  <=> ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f1018,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f5023,plain,
    ( spl0_421
  <=> ! [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_421])]) ).

fof(f5540,plain,
    ( ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_131
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5529]) ).

fof(f5529,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_131
    | ~ spl0_421 ),
    inference(resolution,[],[f5024,f1019]) ).

fof(f1019,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1018]) ).

fof(f5024,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_421 ),
    inference(avatar_component_clause,[],[f5023]) ).

fof(f26410,plain,
    ( spl0_1237
    | ~ spl0_131
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5511,f5019,f1018,f26408]) ).

fof(f26408,plain,
    ( spl0_1237
  <=> ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f5019,plain,
    ( spl0_420
  <=> ! [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_420])]) ).

fof(f5511,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_131
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5500]) ).

fof(f5500,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_131
    | ~ spl0_420 ),
    inference(resolution,[],[f5020,f1019]) ).

fof(f5020,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_420 ),
    inference(avatar_component_clause,[],[f5019]) ).

fof(f26406,plain,
    ( ~ spl0_1236
    | spl0_825
    | ~ spl0_1137 ),
    inference(avatar_split_clause,[],[f23772,f23631,f15247,f26403]) ).

fof(f26403,plain,
    ( spl0_1236
  <=> subclass(composition_function,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f15247,plain,
    ( spl0_825
  <=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f23631,plain,
    ( spl0_1137
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f23772,plain,
    ( ~ subclass(composition_function,subset_relation)
    | spl0_825
    | ~ spl0_1137 ),
    inference(resolution,[],[f23632,f15249]) ).

fof(f15249,plain,
    ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
    | spl0_825 ),
    inference(avatar_component_clause,[],[f15247]) ).

fof(f23632,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_1137 ),
    inference(avatar_component_clause,[],[f23631]) ).

fof(f26401,plain,
    ( spl0_1235
    | ~ spl0_393
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5472,f5005,f4410,f26399]) ).

fof(f26399,plain,
    ( spl0_1235
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f4410,plain,
    ( spl0_393
  <=> ! [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_393])]) ).

fof(f5005,plain,
    ( spl0_419
  <=> ! [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_419])]) ).

fof(f5472,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2) )
    | ~ spl0_393
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5435]) ).

fof(f5435,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_393
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f4411]) ).

fof(f4411,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X3)
        | ~ subclass(X1,X3)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_393 ),
    inference(avatar_component_clause,[],[f4410]) ).

fof(f5006,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_419 ),
    inference(avatar_component_clause,[],[f5005]) ).

fof(f26397,plain,
    ( spl0_1234
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5471,f5005,f4402,f26395]) ).

fof(f26395,plain,
    ( spl0_1234
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f4402,plain,
    ( spl0_391
  <=> ! [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_391])]) ).

fof(f5471,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2) )
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5436]) ).

fof(f5436,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f4403]) ).

fof(f4403,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X3)
        | ~ subclass(X0,X3)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_391 ),
    inference(avatar_component_clause,[],[f4402]) ).

fof(f26393,plain,
    ( spl0_1233
    | ~ spl0_393
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5407,f5001,f4410,f26391]) ).

fof(f26391,plain,
    ( spl0_1233
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f5001,plain,
    ( spl0_418
  <=> ! [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_418])]) ).

fof(f5407,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2) )
    | ~ spl0_393
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5370]) ).

fof(f5370,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_393
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f4411]) ).

fof(f5002,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_418 ),
    inference(avatar_component_clause,[],[f5001]) ).

fof(f26389,plain,
    ( spl0_1232
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5406,f5001,f4402,f26387]) ).

fof(f26387,plain,
    ( spl0_1232
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f5406,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2) )
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5371]) ).

fof(f5371,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f4403]) ).

fof(f26385,plain,
    ( spl0_1231
    | ~ spl0_288
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f4887,f4440,f2792,f26383]) ).

fof(f26383,plain,
    ( spl0_1231
  <=> ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f2792,plain,
    ( spl0_288
  <=> ! [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_288])]) ).

fof(f4440,plain,
    ( spl0_400
  <=> ! [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_400])]) ).

fof(f4887,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0) )
    | ~ spl0_288
    | ~ spl0_400 ),
    inference(duplicate_literal_removal,[],[f4851]) ).

fof(f4851,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_288
    | ~ spl0_400 ),
    inference(resolution,[],[f4441,f2793]) ).

fof(f2793,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_288 ),
    inference(avatar_component_clause,[],[f2792]) ).

fof(f4441,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_400 ),
    inference(avatar_component_clause,[],[f4440]) ).

fof(f26381,plain,
    ( spl0_1230
    | ~ spl0_375
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4759,f4410,f3919,f26379]) ).

fof(f26379,plain,
    ( spl0_1230
  <=> ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f3919,plain,
    ( spl0_375
  <=> ! [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_375])]) ).

fof(f4759,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2) )
    | ~ spl0_375
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4720]) ).

fof(f4720,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2)
        | subclass(intersection(X1,complement(X0)),X2) )
    | ~ spl0_375
    | ~ spl0_393 ),
    inference(resolution,[],[f4411,f3920]) ).

fof(f3920,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f3919]) ).

fof(f26377,plain,
    ( spl0_1229
    | ~ spl0_315
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4758,f4410,f3219,f26375]) ).

fof(f26375,plain,
    ( spl0_1229
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f3219,plain,
    ( spl0_315
  <=> ! [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_315])]) ).

fof(f4758,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4721]) ).

fof(f4721,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_315
    | ~ spl0_393 ),
    inference(resolution,[],[f4411,f3220]) ).

fof(f3220,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3219]) ).

fof(f26373,plain,
    ( spl0_1228
    | ~ spl0_374
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4660,f4402,f3915,f26371]) ).

fof(f26371,plain,
    ( spl0_1228
  <=> ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f3915,plain,
    ( spl0_374
  <=> ! [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_374])]) ).

fof(f4660,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_374
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4619]) ).

fof(f4619,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_374
    | ~ spl0_391 ),
    inference(resolution,[],[f4403,f3916]) ).

fof(f3916,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_374 ),
    inference(avatar_component_clause,[],[f3915]) ).

fof(f26369,plain,
    ( spl0_1227
    | ~ spl0_315
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4658,f4402,f3219,f26367]) ).

fof(f26367,plain,
    ( spl0_1227
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f4658,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4621]) ).

fof(f4621,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_315
    | ~ spl0_391 ),
    inference(resolution,[],[f4403,f3220]) ).

fof(f26365,plain,
    ( spl0_1226
    | ~ spl0_355
    | ~ spl0_370 ),
    inference(avatar_split_clause,[],[f4077,f3899,f3630,f26363]) ).

fof(f26363,plain,
    ( spl0_1226
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f3630,plain,
    ( spl0_355
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f3899,plain,
    ( spl0_370
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f4077,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0)) )
    | ~ spl0_355
    | ~ spl0_370 ),
    inference(duplicate_literal_removal,[],[f4048]) ).

fof(f4048,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0))
        | null_class = intersection(X1,complement(X0)) )
    | ~ spl0_355
    | ~ spl0_370 ),
    inference(resolution,[],[f3900,f3631]) ).

fof(f3631,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,complement(X1))),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_355 ),
    inference(avatar_component_clause,[],[f3630]) ).

fof(f3900,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X1,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_370 ),
    inference(avatar_component_clause,[],[f3899]) ).

fof(f26360,plain,
    ( spl0_1225
    | ~ spl0_354
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4011,f3891,f3626,f26358]) ).

fof(f26358,plain,
    ( spl0_1225
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f3626,plain,
    ( spl0_354
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f3891,plain,
    ( spl0_368
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f4011,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_354
    | ~ spl0_368 ),
    inference(duplicate_literal_removal,[],[f3980]) ).

fof(f3980,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_354
    | ~ spl0_368 ),
    inference(resolution,[],[f3892,f3627]) ).

fof(f3627,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(complement(X0),X1)),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_354 ),
    inference(avatar_component_clause,[],[f3626]) ).

fof(f3892,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X0,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_368 ),
    inference(avatar_component_clause,[],[f3891]) ).

fof(f26356,plain,
    ( spl0_1224
    | ~ spl0_7
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f3862,f3735,f234,f26354]) ).

fof(f26354,plain,
    ( spl0_1224
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f234,plain,
    ( spl0_7
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f3735,plain,
    ( spl0_362
  <=> ! [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_362])]) ).

fof(f3862,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_7
    | ~ spl0_362 ),
    inference(resolution,[],[f3736,f235]) ).

fof(f235,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f3736,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f3735]) ).

fof(f26352,plain,
    ( spl0_1223
    | ~ spl0_131
    | ~ spl0_351 ),
    inference(avatar_split_clause,[],[f3726,f3612,f1018,f26350]) ).

fof(f26350,plain,
    ( spl0_1223
  <=> ! [X0,X1] :
        ( null_class = X0
        | subclass(X1,regular(X0))
        | ~ subclass(X1,null_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f3612,plain,
    ( spl0_351
  <=> ! [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_351])]) ).

fof(f3726,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(X1,regular(X0))
        | ~ subclass(X1,null_class) )
    | ~ spl0_131
    | ~ spl0_351 ),
    inference(duplicate_literal_removal,[],[f3721]) ).

fof(f3721,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(X1,regular(X0))
        | ~ subclass(X1,null_class)
        | subclass(X1,regular(X0)) )
    | ~ spl0_131
    | ~ spl0_351 ),
    inference(resolution,[],[f3613,f1019]) ).

fof(f3613,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_351 ),
    inference(avatar_component_clause,[],[f3612]) ).

fof(f26348,plain,
    ( spl0_1222
    | ~ spl0_5
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3654,f3581,f225,f26346]) ).

fof(f26346,plain,
    ( spl0_1222
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f225,plain,
    ( spl0_5
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f3654,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) )
    | ~ spl0_5
    | ~ spl0_348 ),
    inference(resolution,[],[f3582,f226]) ).

fof(f226,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f26344,plain,
    ( spl0_1221
    | ~ spl0_131
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3379,f3236,f1018,f26342]) ).

fof(f26342,plain,
    ( spl0_1221
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f3236,plain,
    ( spl0_319
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f3379,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_131
    | ~ spl0_319 ),
    inference(duplicate_literal_removal,[],[f3357]) ).

fof(f3357,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2)
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_319 ),
    inference(resolution,[],[f3237,f1019]) ).

fof(f3237,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f3236]) ).

fof(f26340,plain,
    ( spl0_1220
    | ~ spl0_306
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3376,f3236,f3008,f26338]) ).

fof(f26338,plain,
    ( spl0_1220
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f3008,plain,
    ( spl0_306
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f3376,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_306
    | ~ spl0_319 ),
    inference(duplicate_literal_removal,[],[f3364]) ).

fof(f3364,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_306
    | ~ spl0_319 ),
    inference(resolution,[],[f3237,f3009]) ).

fof(f3009,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),element_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_306 ),
    inference(avatar_component_clause,[],[f3008]) ).

fof(f26336,plain,
    ( spl0_1219
    | ~ spl0_313
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3374,f3236,f3179,f26334]) ).

fof(f26334,plain,
    ( spl0_1219
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f3179,plain,
    ( spl0_313
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f3374,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_319 ),
    inference(duplicate_literal_removal,[],[f3373]) ).

fof(f3373,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_319 ),
    inference(resolution,[],[f3237,f3180]) ).

fof(f3180,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f3179]) ).

fof(f26332,plain,
    ( spl0_1218
    | ~ spl0_236
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3110,f2878,f2784,f2317,f26330]) ).

fof(f26330,plain,
    ( spl0_1218
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f2317,plain,
    ( spl0_236
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f2784,plain,
    ( spl0_286
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f2878,plain,
    ( spl0_294
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f3110,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(subset_relation)) )
    | ~ spl0_236
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(forward_demodulation,[],[f3050,f2319]) ).

fof(f2319,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f2317]) ).

fof(f3050,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f3045]) ).

fof(f3045,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(subset_relation))
        | null_class = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f2785]) ).

fof(f2785,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | null_class = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2784]) ).

fof(f2879,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_294 ),
    inference(avatar_component_clause,[],[f2878]) ).

fof(f26328,plain,
    ( spl0_1217
    | ~ spl0_117
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3053,f2878,f925,f26326]) ).

fof(f26326,plain,
    ( spl0_1217
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f925,plain,
    ( spl0_117
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f3053,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_117
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f3029]) ).

fof(f3029,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f926]) ).

fof(f926,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f925]) ).

fof(f26324,plain,
    ( spl0_1216
    | ~ spl0_287
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3051,f2878,f2788,f26322]) ).

fof(f26322,plain,
    ( spl0_1216
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f2788,plain,
    ( spl0_287
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f3051,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_287
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f3036]) ).

fof(f3036,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | null_class = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_287
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f2789]) ).

fof(f2789,plain,
    ( ! [X0] :
        ( member(regular(X0),element_relation)
        | null_class = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f2788]) ).

fof(f26320,plain,
    ( spl0_1
    | ~ spl0_1215
    | ~ spl0_131
    | spl0_1202 ),
    inference(avatar_split_clause,[],[f26244,f26239,f1018,f26317,f205]) ).

fof(f26317,plain,
    ( spl0_1215
  <=> subclass(cross_product(x,y),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f26239,plain,
    ( spl0_1202
  <=> member(not_subclass_element(cross_product(x,y),z),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).

fof(f26244,plain,
    ( ~ subclass(cross_product(x,y),successor_relation)
    | subclass(cross_product(x,y),z)
    | ~ spl0_131
    | spl0_1202 ),
    inference(resolution,[],[f26241,f1019]) ).

fof(f26241,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),successor_relation)
    | spl0_1202 ),
    inference(avatar_component_clause,[],[f26239]) ).

fof(f26315,plain,
    ( spl0_1214
    | ~ spl0_125
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2944,f2317,f961,f26313]) ).

fof(f26313,plain,
    ( spl0_1214
  <=> ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f961,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f2944,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_125
    | ~ spl0_236 ),
    inference(superposition,[],[f962,f2319]) ).

fof(f962,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f961]) ).

fof(f26306,plain,
    ( spl0_1213
    | spl0_1211
    | ~ spl0_98
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f2867,f2796,f737,f26285,f26303]) ).

fof(f26303,plain,
    ( spl0_1213
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f26285,plain,
    ( spl0_1211
  <=> subclass(universal_class,complement(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f737,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f2796,plain,
    ( spl0_289
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f2867,plain,
    ( subclass(universal_class,complement(singleton_relation))
    | member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation)
    | ~ spl0_98
    | ~ spl0_289 ),
    inference(resolution,[],[f2797,f738]) ).

fof(f738,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f737]) ).

fof(f2797,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_289 ),
    inference(avatar_component_clause,[],[f2796]) ).

fof(f26293,plain,
    ( spl0_1212
    | ~ spl0_236
    | ~ spl0_1209 ),
    inference(avatar_split_clause,[],[f26283,f26274,f2317,f26290]) ).

fof(f26290,plain,
    ( spl0_1212
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f26274,plain,
    ( spl0_1209
  <=> member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).

fof(f26283,plain,
    ( member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation)
    | ~ spl0_236
    | ~ spl0_1209 ),
    inference(forward_demodulation,[],[f26276,f2319]) ).

fof(f26276,plain,
    ( member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
    | ~ spl0_1209 ),
    inference(avatar_component_clause,[],[f26274]) ).

fof(f26288,plain,
    ( ~ spl0_1211
    | ~ spl0_236
    | spl0_1210 ),
    inference(avatar_split_clause,[],[f26282,f26278,f2317,f26285]) ).

fof(f26278,plain,
    ( spl0_1210
  <=> subclass(universal_class,complement(identity_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f26282,plain,
    ( ~ subclass(universal_class,complement(singleton_relation))
    | ~ spl0_236
    | spl0_1210 ),
    inference(forward_demodulation,[],[f26279,f2319]) ).

fof(f26279,plain,
    ( ~ subclass(universal_class,complement(identity_relation))
    | spl0_1210 ),
    inference(avatar_component_clause,[],[f26278]) ).

fof(f26281,plain,
    ( spl0_1209
    | spl0_1210
    | ~ spl0_103
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f2865,f2796,f763,f26278,f26274]) ).

fof(f763,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f2865,plain,
    ( subclass(universal_class,complement(identity_relation))
    | member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
    | ~ spl0_103
    | ~ spl0_289 ),
    inference(resolution,[],[f2797,f764]) ).

fof(f764,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f763]) ).

fof(f26272,plain,
    ( spl0_1208
    | ~ spl0_39
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f2782,f2754,f378,f26270]) ).

fof(f26270,plain,
    ( spl0_1208
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).

fof(f378,plain,
    ( spl0_39
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f2754,plain,
    ( spl0_282
  <=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f2782,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_39
    | ~ spl0_282 ),
    inference(resolution,[],[f2756,f379]) ).

fof(f379,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f378]) ).

fof(f2756,plain,
    ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_282 ),
    inference(avatar_component_clause,[],[f2754]) ).

fof(f26267,plain,
    ( spl0_913
    | spl0_1207
    | ~ spl0_166
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2566,f2506,f1375,f26265,f16898]) ).

fof(f26265,plain,
    ( spl0_1207
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(domain_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).

fof(f2506,plain,
    ( spl0_269
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f2566,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class) )
    | ~ spl0_166
    | ~ spl0_269 ),
    inference(resolution,[],[f2507,f1376]) ).

fof(f2507,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f2506]) ).

fof(f26263,plain,
    ( spl0_1206
    | ~ spl0_40
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2250,f2234,f382,f26261]) ).

fof(f26261,plain,
    ( spl0_1206
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).

fof(f382,plain,
    ( spl0_40
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f2234,plain,
    ( spl0_225
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2250,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 )
    | ~ spl0_40
    | ~ spl0_225 ),
    inference(resolution,[],[f2235,f383]) ).

fof(f383,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f382]) ).

fof(f2235,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f2234]) ).

fof(f26259,plain,
    ( spl0_1205
    | ~ spl0_40
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2239,f2230,f382,f26257]) ).

fof(f26257,plain,
    ( spl0_1205
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).

fof(f2230,plain,
    ( spl0_224
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f2239,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 )
    | ~ spl0_40
    | ~ spl0_224 ),
    inference(resolution,[],[f2231,f383]) ).

fof(f2231,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f2230]) ).

fof(f26253,plain,
    ( spl0_1203
    | ~ spl0_1158
    | ~ spl0_1204
    | ~ spl0_278
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f3390,f3240,f2690,f26250,f24762,f26246]) ).

fof(f26246,plain,
    ( spl0_1203
  <=> member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).

fof(f24762,plain,
    ( spl0_1158
  <=> member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f26250,plain,
    ( spl0_1204
  <=> function(not_subclass_element(cross_product(x,y),z)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).

fof(f2690,plain,
    ( spl0_278
  <=> not_subclass_element(cross_product(x,y),z) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f3240,plain,
    ( spl0_320
  <=> ! [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_320])]) ).

fof(f3390,plain,
    ( ~ function(not_subclass_element(cross_product(x,y),z))
    | ~ member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),universal_class)
    | member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),cross_product(universal_class,universal_class))
    | ~ spl0_278
    | ~ spl0_320 ),
    inference(superposition,[],[f3241,f2692]) ).

fof(f2692,plain,
    ( not_subclass_element(cross_product(x,y),z) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z)))))
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f2690]) ).

fof(f3241,plain,
    ( ! [X0,X1] :
        ( ~ function(unordered_pair(X0,X1))
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_320 ),
    inference(avatar_component_clause,[],[f3240]) ).

fof(f26242,plain,
    ( spl0_1201
    | ~ spl0_1202
    | ~ spl0_79
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2702,f2690,f630,f26239,f26235]) ).

fof(f26235,plain,
    ( spl0_1201
  <=> second(not_subclass_element(cross_product(x,y),z)) = complement(intersection(complement(first(not_subclass_element(cross_product(x,y),z))),complement(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).

fof(f630,plain,
    ( spl0_79
  <=> ! [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_79])]) ).

fof(f2702,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),successor_relation)
    | second(not_subclass_element(cross_product(x,y),z)) = complement(intersection(complement(first(not_subclass_element(cross_product(x,y),z))),complement(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))))))
    | ~ spl0_79
    | ~ spl0_278 ),
    inference(superposition,[],[f631,f2692]) ).

fof(f631,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_79 ),
    inference(avatar_component_clause,[],[f630]) ).

fof(f26209,plain,
    ( spl0_1191
    | ~ spl0_1200
    | ~ spl0_87
    | ~ spl0_1073 ),
    inference(avatar_split_clause,[],[f22315,f22117,f675,f26206,f24917]) ).

fof(f24917,plain,
    ( spl0_1191
  <=> ! [X0] : member(X0,domain_of(not_subclass_element(cross_product(x,y),z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f26206,plain,
    ( spl0_1200
  <=> subclass(universal_class,flip(application_function)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).

fof(f675,plain,
    ( spl0_87
  <=> ! [X4,X0,X1] :
        ( member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f22117,plain,
    ( spl0_1073
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)),unordered_pair(not_subclass_element(cross_product(x,y),z),unordered_pair(X0,X0))),X1)
        | ~ subclass(universal_class,flip(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f22315,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(application_function))
        | member(X0,domain_of(not_subclass_element(cross_product(x,y),z))) )
    | ~ spl0_87
    | ~ spl0_1073 ),
    inference(resolution,[],[f22118,f676]) ).

fof(f676,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
        | member(X1,domain_of(X0)) )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f675]) ).

fof(f22118,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)),unordered_pair(not_subclass_element(cross_product(x,y),z),unordered_pair(X0,X0))),X1)
        | ~ subclass(universal_class,flip(X1)) )
    | ~ spl0_1073 ),
    inference(avatar_component_clause,[],[f22117]) ).

fof(f25453,plain,
    ( spl0_1155
    | ~ spl0_1199
    | ~ spl0_65
    | ~ spl0_1073 ),
    inference(avatar_split_clause,[],[f22303,f22117,f545,f25450,f24684]) ).

fof(f24684,plain,
    ( spl0_1155
  <=> ! [X0] : domain_of(not_subclass_element(cross_product(x,y),z)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f25450,plain,
    ( spl0_1199
  <=> subclass(universal_class,flip(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f545,plain,
    ( spl0_65
  <=> ! [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_65])]) ).

fof(f22303,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(domain_relation))
        | domain_of(not_subclass_element(cross_product(x,y),z)) = X0 )
    | ~ spl0_65
    | ~ spl0_1073 ),
    inference(resolution,[],[f22118,f546]) ).

fof(f546,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f545]) ).

fof(f24947,plain,
    ( spl0_1198
    | ~ spl0_269
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f12896,f12844,f2506,f24945]) ).

fof(f24945,plain,
    ( spl0_1198
  <=> ! [X0] :
        ( ~ member(not_subclass_element(composition_function,application_function),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f12844,plain,
    ( spl0_748
  <=> not_subclass_element(composition_function,application_function) = unordered_pair(unordered_pair(first(not_subclass_element(composition_function,application_function)),first(not_subclass_element(composition_function,application_function))),unordered_pair(first(not_subclass_element(composition_function,application_function)),unordered_pair(second(not_subclass_element(composition_function,application_function)),second(not_subclass_element(composition_function,application_function))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f12896,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(composition_function,application_function),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_269
    | ~ spl0_748 ),
    inference(superposition,[],[f2507,f12846]) ).

fof(f12846,plain,
    ( not_subclass_element(composition_function,application_function) = unordered_pair(unordered_pair(first(not_subclass_element(composition_function,application_function)),first(not_subclass_element(composition_function,application_function))),unordered_pair(first(not_subclass_element(composition_function,application_function)),unordered_pair(second(not_subclass_element(composition_function,application_function)),second(not_subclass_element(composition_function,application_function)))))
    | ~ spl0_748 ),
    inference(avatar_component_clause,[],[f12844]) ).

fof(f24943,plain,
    ( spl0_1197
    | ~ spl0_68
    | ~ spl0_677 ),
    inference(avatar_split_clause,[],[f10699,f10601,f562,f24941]) ).

fof(f24941,plain,
    ( spl0_1197
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(cross_product(X0,X1)))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f562,plain,
    ( spl0_68
  <=> ! [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_68])]) ).

fof(f10601,plain,
    ( spl0_677
  <=> ! [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_677])]) ).

fof(f10699,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(cross_product(X0,X1)))
        | member(X2,X1) )
    | ~ spl0_68
    | ~ spl0_677 ),
    inference(resolution,[],[f10602,f563]) ).

fof(f563,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_68 ),
    inference(avatar_component_clause,[],[f562]) ).

fof(f10602,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_677 ),
    inference(avatar_component_clause,[],[f10601]) ).

fof(f24939,plain,
    ( spl0_1196
    | ~ spl0_68
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f10615,f10597,f562,f24937]) ).

fof(f24937,plain,
    ( spl0_1196
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f10597,plain,
    ( spl0_676
  <=> ! [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_676])]) ).

fof(f10615,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
        | member(X2,X1) )
    | ~ spl0_68
    | ~ spl0_676 ),
    inference(resolution,[],[f10598,f563]) ).

fof(f10598,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_676 ),
    inference(avatar_component_clause,[],[f10597]) ).

fof(f24935,plain,
    ( spl0_1195
    | ~ spl0_135
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5545,f5023,f1089,f24933]) ).

fof(f24933,plain,
    ( spl0_1195
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f1089,plain,
    ( spl0_135
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f5545,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_135
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5524]) ).

fof(f5524,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_135
    | ~ spl0_421 ),
    inference(resolution,[],[f5024,f1090]) ).

fof(f1090,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1089]) ).

fof(f24931,plain,
    ( spl0_1194
    | ~ spl0_136
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5543,f5023,f1093,f24929]) ).

fof(f24929,plain,
    ( spl0_1194
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f1093,plain,
    ( spl0_136
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f5543,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_136
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5526]) ).

fof(f5526,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_136
    | ~ spl0_421 ),
    inference(resolution,[],[f5024,f1094]) ).

fof(f1094,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1093]) ).

fof(f24927,plain,
    ( spl0_1193
    | ~ spl0_135
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5516,f5019,f1089,f24925]) ).

fof(f24925,plain,
    ( spl0_1193
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f5516,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_135
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5495]) ).

fof(f5495,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_135
    | ~ spl0_420 ),
    inference(resolution,[],[f5020,f1090]) ).

fof(f24923,plain,
    ( spl0_1191
    | ~ spl0_1192
    | ~ spl0_87
    | ~ spl0_1072 ),
    inference(avatar_split_clause,[],[f22159,f22113,f675,f24920,f24917]) ).

fof(f24920,plain,
    ( spl0_1192
  <=> subclass(universal_class,rotate(application_function)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

fof(f22113,plain,
    ( spl0_1072
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)),unordered_pair(not_subclass_element(cross_product(x,y),z),unordered_pair(X0,X0))),X1)
        | ~ subclass(universal_class,rotate(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f22159,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(application_function))
        | member(X0,domain_of(not_subclass_element(cross_product(x,y),z))) )
    | ~ spl0_87
    | ~ spl0_1072 ),
    inference(resolution,[],[f22114,f676]) ).

fof(f22114,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)),unordered_pair(not_subclass_element(cross_product(x,y),z),unordered_pair(X0,X0))),X1)
        | ~ subclass(universal_class,rotate(X1)) )
    | ~ spl0_1072 ),
    inference(avatar_component_clause,[],[f22113]) ).

fof(f24915,plain,
    ( spl0_1190
    | ~ spl0_136
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5514,f5019,f1093,f24913]) ).

fof(f24913,plain,
    ( spl0_1190
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f5514,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_136
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5497]) ).

fof(f5497,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_136
    | ~ spl0_420 ),
    inference(resolution,[],[f5020,f1094]) ).

fof(f24911,plain,
    ( spl0_1189
    | ~ spl0_27
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5480,f5005,f321,f24909]) ).

fof(f24909,plain,
    ( spl0_1189
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f5480,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
    | ~ spl0_27
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5427]) ).

fof(f5427,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
        | subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) )
    | ~ spl0_27
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f322]) ).

fof(f24907,plain,
    ( spl0_1188
    | ~ spl0_410
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5478,f5005,f4961,f24905]) ).

fof(f24905,plain,
    ( spl0_1188
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f4961,plain,
    ( spl0_410
  <=> ! [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_410])]) ).

fof(f5478,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
    | ~ spl0_410
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5429]) ).

fof(f5429,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) )
    | ~ spl0_410
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f4962]) ).

fof(f4962,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1)
        | subclass(intersection(X0,intersection(X1,X2)),X3) )
    | ~ spl0_410 ),
    inference(avatar_component_clause,[],[f4961]) ).

fof(f24903,plain,
    ( spl0_1187
    | ~ spl0_409
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5473,f5005,f4957,f24901]) ).

fof(f24901,plain,
    ( spl0_1187
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f4957,plain,
    ( spl0_409
  <=> ! [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_409])]) ).

fof(f5473,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
    | ~ spl0_409
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5434]) ).

fof(f5434,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) )
    | ~ spl0_409
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f4958]) ).

fof(f4958,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2)
        | subclass(intersection(X0,intersection(X1,X2)),X3) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f4957]) ).

fof(f24899,plain,
    ( spl0_1186
    | ~ spl0_408
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5416,f5001,f4953,f24897]) ).

fof(f24897,plain,
    ( spl0_1186
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f4953,plain,
    ( spl0_408
  <=> ! [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_408])]) ).

fof(f5416,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
    | ~ spl0_408
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5361]) ).

fof(f5361,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) )
    | ~ spl0_408
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f4954]) ).

fof(f4954,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0)
        | subclass(intersection(intersection(X0,X1),X2),X3) )
    | ~ spl0_408 ),
    inference(avatar_component_clause,[],[f4953]) ).

fof(f24895,plain,
    ( spl0_1185
    | ~ spl0_27
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5415,f5001,f321,f24893]) ).

fof(f24893,plain,
    ( spl0_1185
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f5415,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
    | ~ spl0_27
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5362]) ).

fof(f5362,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
        | subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) )
    | ~ spl0_27
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f322]) ).

fof(f24891,plain,
    ( spl0_1184
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5412,f5001,f4949,f24889]) ).

fof(f24889,plain,
    ( spl0_1184
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f4949,plain,
    ( spl0_407
  <=> ! [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_407])]) ).

fof(f5412,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5365]) ).

fof(f5365,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) )
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f4950]) ).

fof(f4950,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1)
        | subclass(intersection(intersection(X0,X1),X2),X3) )
    | ~ spl0_407 ),
    inference(avatar_component_clause,[],[f4949]) ).

fof(f24887,plain,
    ( spl0_1183
    | ~ spl0_315
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f5244,f4961,f3219,f24885]) ).

fof(f24885,plain,
    ( spl0_1183
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f5244,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_410 ),
    inference(duplicate_literal_removal,[],[f5204]) ).

fof(f5204,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_315
    | ~ spl0_410 ),
    inference(resolution,[],[f4962,f3220]) ).

fof(f24883,plain,
    ( spl0_1182
    | ~ spl0_315
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f5186,f4957,f3219,f24881]) ).

fof(f24881,plain,
    ( spl0_1182
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f5186,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_409 ),
    inference(duplicate_literal_removal,[],[f5146]) ).

fof(f5146,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_315
    | ~ spl0_409 ),
    inference(resolution,[],[f4958,f3220]) ).

fof(f24879,plain,
    ( spl0_1181
    | ~ spl0_315
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f5127,f4953,f3219,f24877]) ).

fof(f24877,plain,
    ( spl0_1181
  <=> ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f5127,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f5087]) ).

fof(f5087,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_315
    | ~ spl0_408 ),
    inference(resolution,[],[f4954,f3220]) ).

fof(f24875,plain,
    ( spl0_1180
    | ~ spl0_315
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5069,f4949,f3219,f24873]) ).

fof(f24873,plain,
    ( spl0_1180
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f5069,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5029]) ).

fof(f5029,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_315
    | ~ spl0_407 ),
    inference(resolution,[],[f4950,f3220]) ).

fof(f24871,plain,
    ( spl0_1179
    | ~ spl0_374
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4760,f4410,f3915,f24869]) ).

fof(f24869,plain,
    ( spl0_1179
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f4760,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2) )
    | ~ spl0_374
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4719]) ).

fof(f4719,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2)
        | subclass(intersection(complement(X1),X0),X2) )
    | ~ spl0_374
    | ~ spl0_393 ),
    inference(resolution,[],[f4411,f3916]) ).

fof(f24867,plain,
    ( spl0_1178
    | ~ spl0_375
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4659,f4402,f3919,f24865]) ).

fof(f24865,plain,
    ( spl0_1178
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f4659,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_375
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4620]) ).

fof(f4620,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_375
    | ~ spl0_391 ),
    inference(resolution,[],[f4403,f3920]) ).

fof(f24863,plain,
    ( spl0_1177
    | ~ spl0_28
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f4177,f3911,f325,f24861]) ).

fof(f24861,plain,
    ( spl0_1177
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,null_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f325,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f3911,plain,
    ( spl0_373
  <=> ! [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_373])]) ).

fof(f4177,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,null_class)
        | null_class = X1 )
    | ~ spl0_28
    | ~ spl0_373 ),
    inference(duplicate_literal_removal,[],[f4139]) ).

fof(f4139,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,null_class)
        | null_class = X1
        | subclass(X0,X1) )
    | ~ spl0_28
    | ~ spl0_373 ),
    inference(resolution,[],[f3912,f326]) ).

fof(f326,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f325]) ).

fof(f3912,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),X2)
        | subclass(X0,X1)
        | ~ subclass(X0,null_class)
        | null_class = X2 )
    | ~ spl0_373 ),
    inference(avatar_component_clause,[],[f3911]) ).

fof(f24859,plain,
    ( spl0_1176
    | ~ spl0_354
    | ~ spl0_370 ),
    inference(avatar_split_clause,[],[f4078,f3899,f3626,f24857]) ).

fof(f24857,plain,
    ( spl0_1176
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f4078,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_354
    | ~ spl0_370 ),
    inference(duplicate_literal_removal,[],[f4047]) ).

fof(f4047,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_354
    | ~ spl0_370 ),
    inference(resolution,[],[f3900,f3627]) ).

fof(f24855,plain,
    ( spl0_1175
    | ~ spl0_355
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f4010,f3891,f3630,f24853]) ).

fof(f24853,plain,
    ( spl0_1175
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f4010,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_355
    | ~ spl0_368 ),
    inference(duplicate_literal_removal,[],[f3981]) ).

fof(f3981,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1))
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_355
    | ~ spl0_368 ),
    inference(resolution,[],[f3892,f3631]) ).

fof(f24851,plain,
    ( spl0_1174
    | ~ spl0_330
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3535,f3416,f3292,f24849]) ).

fof(f24849,plain,
    ( spl0_1174
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f3292,plain,
    ( spl0_330
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f3416,plain,
    ( spl0_338
  <=> ! [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_338])]) ).

fof(f3535,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
    | ~ spl0_330
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3530]) ).

fof(f3530,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_330
    | ~ spl0_338 ),
    inference(resolution,[],[f3417,f3293]) ).

fof(f3293,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f3292]) ).

fof(f3417,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_338 ),
    inference(avatar_component_clause,[],[f3416]) ).

fof(f24847,plain,
    ( spl0_1173
    | ~ spl0_330
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f3521,f3412,f3292,f24844]) ).

fof(f24844,plain,
    ( spl0_1173
  <=> subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f3412,plain,
    ( spl0_337
  <=> ! [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_337])]) ).

fof(f3521,plain,
    ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | ~ spl0_330
    | ~ spl0_337 ),
    inference(duplicate_literal_removal,[],[f3516]) ).

fof(f3516,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_330
    | ~ spl0_337 ),
    inference(resolution,[],[f3413,f3293]) ).

fof(f3413,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_337 ),
    inference(avatar_component_clause,[],[f3412]) ).

fof(f24842,plain,
    ( spl0_1172
    | ~ spl0_330
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f3509,f3408,f3292,f24839]) ).

fof(f24839,plain,
    ( spl0_1172
  <=> subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f3408,plain,
    ( spl0_336
  <=> ! [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_336])]) ).

fof(f3509,plain,
    ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | ~ spl0_330
    | ~ spl0_336 ),
    inference(duplicate_literal_removal,[],[f3504]) ).

fof(f3504,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_330
    | ~ spl0_336 ),
    inference(resolution,[],[f3409,f3293]) ).

fof(f3409,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_336 ),
    inference(avatar_component_clause,[],[f3408]) ).

fof(f24837,plain,
    ( spl0_1171
    | ~ spl0_330
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3496,f3394,f3292,f24835]) ).

fof(f24835,plain,
    ( spl0_1171
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f3394,plain,
    ( spl0_335
  <=> ! [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_335])]) ).

fof(f3496,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
    | ~ spl0_330
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3491]) ).

fof(f3491,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_330
    | ~ spl0_335 ),
    inference(resolution,[],[f3395,f3293]) ).

fof(f3395,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f3394]) ).

fof(f24833,plain,
    ( ~ spl0_1170
    | ~ spl0_269
    | ~ spl0_1159 ),
    inference(avatar_split_clause,[],[f24774,f24766,f2506,f24830]) ).

fof(f24830,plain,
    ( spl0_1170
  <=> subclass(universal_class,complement(not_subclass_element(cross_product(x,y),z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f24766,plain,
    ( spl0_1159
  <=> member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),not_subclass_element(cross_product(x,y),z)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f24774,plain,
    ( ~ subclass(universal_class,complement(not_subclass_element(cross_product(x,y),z)))
    | ~ spl0_269
    | ~ spl0_1159 ),
    inference(resolution,[],[f24768,f2507]) ).

fof(f24768,plain,
    ( member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),not_subclass_element(cross_product(x,y),z))
    | ~ spl0_1159 ),
    inference(avatar_component_clause,[],[f24766]) ).

fof(f24828,plain,
    ( spl0_1169
    | ~ spl0_135
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3468,f3292,f1089,f24826]) ).

fof(f24826,plain,
    ( spl0_1169
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f3468,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
    | ~ spl0_135
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3435]) ).

fof(f3435,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
        | subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) )
    | ~ spl0_135
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f1090]) ).

fof(f24824,plain,
    ( spl0_1168
    | ~ spl0_136
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3467,f3292,f1093,f24822]) ).

fof(f24822,plain,
    ( spl0_1168
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f3467,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
    | ~ spl0_136
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3436]) ).

fof(f3436,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
        | subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) )
    | ~ spl0_136
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f1094]) ).

fof(f24820,plain,
    ( spl0_1167
    | ~ spl0_323
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3462,f3292,f3254,f24818]) ).

fof(f24818,plain,
    ( spl0_1167
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f3254,plain,
    ( spl0_323
  <=> ! [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_323])]) ).

fof(f3462,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
    | ~ spl0_323
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3442]) ).

fof(f3442,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_323
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f3255]) ).

fof(f3255,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f3254]) ).

fof(f24816,plain,
    ( spl0_1166
    | ~ spl0_327
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3461,f3292,f3275,f24814]) ).

fof(f24814,plain,
    ( spl0_1166
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f3275,plain,
    ( spl0_327
  <=> ! [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_327])]) ).

fof(f3461,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
    | ~ spl0_327
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3443]) ).

fof(f3443,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_327
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f3276]) ).

fof(f3276,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f3275]) ).

fof(f24812,plain,
    ( ~ spl0_1165
    | spl0_275
    | ~ spl0_276
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3033,f2878,f2544,f2540,f24809]) ).

fof(f24809,plain,
    ( spl0_1165
  <=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f2540,plain,
    ( spl0_275
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f3033,plain,
    ( null_class = subset_relation
    | ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
    | ~ spl0_276
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f2546]) ).

fof(f2546,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f2544]) ).

fof(f24807,plain,
    ( spl0_1164
    | ~ spl0_236
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2954,f2536,f2317,f24805]) ).

fof(f24805,plain,
    ( spl0_1164
  <=> ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f2536,plain,
    ( spl0_274
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f2954,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_236
    | ~ spl0_274 ),
    inference(superposition,[],[f2537,f2319]) ).

fof(f2537,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2536]) ).

fof(f24803,plain,
    ( spl0_1163
    | ~ spl0_43
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2938,f2317,f394,f24800]) ).

fof(f24800,plain,
    ( spl0_1163
  <=> singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f394,plain,
    ( spl0_43
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f2938,plain,
    ( singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation)
    | ~ spl0_43
    | ~ spl0_236 ),
    inference(superposition,[],[f396,f2319]) ).

fof(f396,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f24798,plain,
    ( spl0_1162
    | ~ spl0_39
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f2778,f2544,f378,f24796]) ).

fof(f24796,plain,
    ( spl0_1162
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f2778,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) )
    | ~ spl0_39
    | ~ spl0_276 ),
    inference(resolution,[],[f2546,f379]) ).

fof(f24794,plain,
    ( spl0_1161
    | ~ spl0_111
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2252,f2234,f825,f24792]) ).

fof(f24792,plain,
    ( spl0_1161
  <=> ! [X0] :
        ( omega = intersection(X0,omega)
        | ~ inductive(intersection(X0,omega)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f825,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f2252,plain,
    ( ! [X0] :
        ( omega = intersection(X0,omega)
        | ~ inductive(intersection(X0,omega)) )
    | ~ spl0_111
    | ~ spl0_225 ),
    inference(resolution,[],[f2235,f826]) ).

fof(f826,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f825]) ).

fof(f24790,plain,
    ( spl0_1160
    | ~ spl0_111
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2241,f2230,f825,f24788]) ).

fof(f24788,plain,
    ( spl0_1160
  <=> ! [X0] :
        ( omega = intersection(omega,X0)
        | ~ inductive(intersection(omega,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f2241,plain,
    ( ! [X0] :
        ( omega = intersection(omega,X0)
        | ~ inductive(intersection(omega,X0)) )
    | ~ spl0_111
    | ~ spl0_224 ),
    inference(resolution,[],[f2231,f826]) ).

fof(f24772,plain,
    ( ~ spl0_10
    | spl0_1158 ),
    inference(avatar_contradiction_clause,[],[f24770]) ).

fof(f24770,plain,
    ( $false
    | ~ spl0_10
    | spl0_1158 ),
    inference(resolution,[],[f24764,f247]) ).

fof(f247,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f246,plain,
    ( spl0_10
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f24764,plain,
    ( ~ member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),universal_class)
    | spl0_1158 ),
    inference(avatar_component_clause,[],[f24762]) ).

fof(f24769,plain,
    ( ~ spl0_1158
    | spl0_1159
    | ~ spl0_29
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2722,f2690,f329,f24766,f24762]) ).

fof(f329,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f2722,plain,
    ( member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),not_subclass_element(cross_product(x,y),z))
    | ~ member(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),universal_class)
    | ~ spl0_29
    | ~ spl0_278 ),
    inference(superposition,[],[f330,f2692]) ).

fof(f330,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f329]) ).

fof(f24760,plain,
    ( spl0_1157
    | ~ spl0_88
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2705,f2690,f679,f24758]) ).

fof(f24758,plain,
    ( spl0_1157
  <=> ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)))),composition_function)
        | second(not_subclass_element(cross_product(x,y),z)) = compose(X0,first(not_subclass_element(cross_product(x,y),z))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f679,plain,
    ( spl0_88
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f2705,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)))),composition_function)
        | second(not_subclass_element(cross_product(x,y),z)) = compose(X0,first(not_subclass_element(cross_product(x,y),z))) )
    | ~ spl0_88
    | ~ spl0_278 ),
    inference(superposition,[],[f680,f2692]) ).

fof(f680,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
        | compose(X0,X1) = X4 )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f679]) ).

fof(f24690,plain,
    ( spl0_1155
    | ~ spl0_1156
    | ~ spl0_65
    | ~ spl0_1072 ),
    inference(avatar_split_clause,[],[f22147,f22113,f545,f24687,f24684]) ).

fof(f24687,plain,
    ( spl0_1156
  <=> subclass(universal_class,rotate(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f22147,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(domain_relation))
        | domain_of(not_subclass_element(cross_product(x,y),z)) = X0 )
    | ~ spl0_65
    | ~ spl0_1072 ),
    inference(resolution,[],[f22114,f546]) ).

fof(f23702,plain,
    ( spl0_1154
    | ~ spl0_109
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f12889,f12844,f817,f23700]) ).

fof(f23700,plain,
    ( spl0_1154
  <=> ! [X0] :
        ( member(not_subclass_element(composition_function,application_function),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f12889,plain,
    ( ! [X0] :
        ( member(not_subclass_element(composition_function,application_function),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_748 ),
    inference(superposition,[],[f818,f12846]) ).

fof(f23698,plain,
    ( spl0_1153
    | ~ spl0_269
    | ~ spl0_677 ),
    inference(avatar_split_clause,[],[f10730,f10601,f2506,f23696]) ).

fof(f23696,plain,
    ( spl0_1153
  <=> ! [X0] :
        ( ~ subclass(universal_class,flip(X0))
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f10730,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(X0))
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_269
    | ~ spl0_677 ),
    inference(resolution,[],[f10602,f2507]) ).

fof(f23694,plain,
    ( spl0_1152
    | ~ spl0_269
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f10646,f10597,f2506,f23692]) ).

fof(f23692,plain,
    ( spl0_1152
  <=> ! [X0] :
        ( ~ subclass(universal_class,rotate(X0))
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f10646,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(X0))
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_269
    | ~ spl0_676 ),
    inference(resolution,[],[f10598,f2507]) ).

fof(f23690,plain,
    ( spl0_1151
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f4901,f4440,f2371,f2317,f23688]) ).

fof(f23688,plain,
    ( spl0_1151
  <=> ! [X0] :
        ( ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(subset_relation,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f2371,plain,
    ( spl0_245
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f4901,plain,
    ( ! [X0] :
        ( ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(subset_relation,X0)) )
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_400 ),
    inference(forward_demodulation,[],[f4900,f2319]) ).

fof(f4900,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0) )
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_400 ),
    inference(forward_demodulation,[],[f4880,f2319]) ).

fof(f4880,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0) )
    | ~ spl0_245
    | ~ spl0_400 ),
    inference(duplicate_literal_removal,[],[f4867]) ).

fof(f4867,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0)
        | subclass(identity_relation,intersection(subset_relation,X0)) )
    | ~ spl0_245
    | ~ spl0_400 ),
    inference(resolution,[],[f4441,f2372]) ).

fof(f2372,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f2371]) ).

fof(f23686,plain,
    ( spl0_1150
    | ~ spl0_27
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f4895,f4440,f321,f23684]) ).

fof(f23684,plain,
    ( spl0_1150
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f4895,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_400 ),
    inference(duplicate_literal_removal,[],[f4843]) ).

fof(f4843,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X0,X1)) )
    | ~ spl0_27
    | ~ spl0_400 ),
    inference(resolution,[],[f4441,f322]) ).

fof(f23682,plain,
    ( spl0_1122
    | ~ spl0_1149
    | ~ spl0_62
    | ~ spl0_1073 ),
    inference(avatar_split_clause,[],[f22292,f22117,f530,f23679,f23423]) ).

fof(f23423,plain,
    ( spl0_1122
  <=> ! [X0] : member(not_subclass_element(cross_product(x,y),z),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f23679,plain,
    ( spl0_1149
  <=> subclass(universal_class,flip(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f530,plain,
    ( spl0_62
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f22292,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(element_relation))
        | member(not_subclass_element(cross_product(x,y),z),X0) )
    | ~ spl0_62
    | ~ spl0_1073 ),
    inference(resolution,[],[f22118,f531]) ).

fof(f531,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f530]) ).

fof(f23677,plain,
    ( spl0_1148
    | ~ spl0_244
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f4886,f4440,f2367,f23675]) ).

fof(f23675,plain,
    ( spl0_1148
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f2367,plain,
    ( spl0_244
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f4886,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_244
    | ~ spl0_400 ),
    inference(duplicate_literal_removal,[],[f4853]) ).

fof(f4853,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(element_relation,X0)) )
    | ~ spl0_244
    | ~ spl0_400 ),
    inference(resolution,[],[f4441,f2368]) ).

fof(f2368,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2367]) ).

fof(f23673,plain,
    ( spl0_1147
    | ~ spl0_28
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4762,f4410,f325,f23671]) ).

fof(f23671,plain,
    ( spl0_1147
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f4762,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1) )
    | ~ spl0_28
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4717]) ).

fof(f4717,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1)
        | subclass(intersection(X2,X0),X1) )
    | ~ spl0_28
    | ~ spl0_393 ),
    inference(resolution,[],[f4411,f326]) ).

fof(f23669,plain,
    ( spl0_1146
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4662,f4402,f325,f23667]) ).

fof(f23667,plain,
    ( spl0_1146
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f4662,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1) )
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4617]) ).

fof(f4617,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1)
        | subclass(intersection(X0,X2),X1) )
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(resolution,[],[f4403,f326]) ).

fof(f23665,plain,
    ( spl0_1145
    | ~ spl0_354
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4605,f4398,f3626,f23663]) ).

fof(f23663,plain,
    ( spl0_1145
  <=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f4398,plain,
    ( spl0_390
  <=> ! [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_390])]) ).

fof(f4605,plain,
    ( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_354
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4575]) ).

fof(f4575,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),intersection(X0,X1))
        | null_class = intersection(complement(X0),intersection(X0,X1)) )
    | ~ spl0_354
    | ~ spl0_390 ),
    inference(resolution,[],[f4399,f3627]) ).

fof(f4399,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X1)
        | null_class = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f4398]) ).

fof(f23661,plain,
    ( spl0_1144
    | ~ spl0_354
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f4564,f4383,f3626,f23659]) ).

fof(f23659,plain,
    ( spl0_1144
  <=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f4383,plain,
    ( spl0_389
  <=> ! [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_389])]) ).

fof(f4564,plain,
    ( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_354
    | ~ spl0_389 ),
    inference(duplicate_literal_removal,[],[f4534]) ).

fof(f4534,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),intersection(X1,X0))
        | null_class = intersection(complement(X0),intersection(X1,X0)) )
    | ~ spl0_354
    | ~ spl0_389 ),
    inference(resolution,[],[f4384,f3627]) ).

fof(f4384,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X2)
        | null_class = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f4383]) ).

fof(f23657,plain,
    ( spl0_1143
    | ~ spl0_355
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4522,f4379,f3630,f23655]) ).

fof(f23655,plain,
    ( spl0_1143
  <=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f4379,plain,
    ( spl0_388
  <=> ! [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_388])]) ).

fof(f4522,plain,
    ( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_355
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4492]) ).

fof(f4492,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,X1),complement(X0))
        | null_class = intersection(intersection(X0,X1),complement(X0)) )
    | ~ spl0_355
    | ~ spl0_388 ),
    inference(resolution,[],[f4380,f3631]) ).

fof(f4380,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X0)
        | null_class = intersection(intersection(X0,X1),X2) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f4379]) ).

fof(f23653,plain,
    ( spl0_1142
    | ~ spl0_355
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4483,f4375,f3630,f23651]) ).

fof(f23651,plain,
    ( spl0_1142
  <=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f4375,plain,
    ( spl0_387
  <=> ! [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_387])]) ).

fof(f4483,plain,
    ( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_355
    | ~ spl0_387 ),
    inference(duplicate_literal_removal,[],[f4453]) ).

fof(f4453,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,X1),complement(X1))
        | null_class = intersection(intersection(X0,X1),complement(X1)) )
    | ~ spl0_355
    | ~ spl0_387 ),
    inference(resolution,[],[f4376,f3631]) ).

fof(f4376,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X1)
        | null_class = intersection(intersection(X0,X1),X2) )
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f4375]) ).

fof(f23649,plain,
    ( spl0_1141
    | ~ spl0_131
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3466,f3292,f1018,f23647]) ).

fof(f23647,plain,
    ( spl0_1141
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f3466,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3437]) ).

fof(f3437,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_131
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f1019]) ).

fof(f23645,plain,
    ( spl0_1140
    | ~ spl0_306
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3463,f3292,f3008,f23643]) ).

fof(f23643,plain,
    ( spl0_1140
  <=> ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f3463,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_306
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3441]) ).

fof(f3441,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_306
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f3009]) ).

fof(f23641,plain,
    ( spl0_1139
    | ~ spl0_313
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3459,f3292,f3179,f23639]) ).

fof(f23639,plain,
    ( spl0_1139
  <=> ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f3459,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3452]) ).

fof(f3452,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f3180]) ).

fof(f23637,plain,
    ( spl0_1138
    | ~ spl0_313
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3317,f3219,f3179,f23635]) ).

fof(f23635,plain,
    ( spl0_1138
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f3317,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3308]) ).

fof(f3308,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_315 ),
    inference(resolution,[],[f3220,f3180]) ).

fof(f23633,plain,
    ( spl0_1137
    | ~ spl0_131
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3313,f3219,f1018,f23631]) ).

fof(f3313,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_131
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3312]) ).

fof(f3312,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_131
    | ~ spl0_315 ),
    inference(resolution,[],[f3220,f1019]) ).

fof(f23620,plain,
    ( ~ spl0_611
    | spl0_1136
    | ~ spl0_145
    | ~ spl0_236
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f3171,f3133,f2317,f1173,f23617,f9414]) ).

fof(f9414,plain,
    ( spl0_611
  <=> member(regular(singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f23617,plain,
    ( spl0_1136
  <=> member(regular(singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f1173,plain,
    ( spl0_145
  <=> ! [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_145])]) ).

fof(f3133,plain,
    ( spl0_312
  <=> member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f3171,plain,
    ( member(regular(singleton_relation),singleton_relation)
    | ~ member(regular(singleton_relation),subset_relation)
    | ~ spl0_145
    | ~ spl0_236
    | ~ spl0_312 ),
    inference(forward_demodulation,[],[f3167,f2319]) ).

fof(f3167,plain,
    ( ~ member(regular(singleton_relation),subset_relation)
    | member(regular(singleton_relation),identity_relation)
    | ~ spl0_145
    | ~ spl0_312 ),
    inference(resolution,[],[f3135,f1174]) ).

fof(f1174,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1173]) ).

fof(f3135,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f3133]) ).

fof(f23615,plain,
    ( spl0_1135
    | ~ spl0_38
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2984,f2510,f365,f23613]) ).

fof(f23613,plain,
    ( spl0_1135
  <=> ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f365,plain,
    ( spl0_38
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f2510,plain,
    ( spl0_270
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f2984,plain,
    ( ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_38
    | ~ spl0_270 ),
    inference(resolution,[],[f2511,f366]) ).

fof(f366,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f365]) ).

fof(f2511,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f2510]) ).

fof(f23611,plain,
    ( spl0_1134
    | ~ spl0_236
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2950,f2371,f2317,f23609]) ).

fof(f23609,plain,
    ( spl0_1134
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),subset_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f2950,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),subset_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_236
    | ~ spl0_245 ),
    inference(superposition,[],[f2372,f2319]) ).

fof(f23607,plain,
    ( ~ spl0_1132
    | spl0_1133
    | ~ spl0_113
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2839,f2788,f890,f23604,f23600]) ).

fof(f23600,plain,
    ( spl0_1132
  <=> subclass(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f23604,plain,
    ( spl0_1133
  <=> null_class = complement(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f890,plain,
    ( spl0_113
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f2839,plain,
    ( null_class = complement(element_relation)
    | ~ subclass(complement(element_relation),singleton_relation)
    | ~ spl0_113
    | ~ spl0_287 ),
    inference(duplicate_literal_removal,[],[f2831]) ).

fof(f2831,plain,
    ( null_class = complement(element_relation)
    | ~ subclass(complement(element_relation),singleton_relation)
    | null_class = complement(element_relation)
    | ~ spl0_113
    | ~ spl0_287 ),
    inference(resolution,[],[f2789,f891]) ).

fof(f891,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f890]) ).

fof(f23598,plain,
    ( ~ spl0_1131
    | ~ spl0_236
    | spl0_1129 ),
    inference(avatar_split_clause,[],[f23593,f23585,f2317,f23595]) ).

fof(f23595,plain,
    ( spl0_1131
  <=> subclass(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f23585,plain,
    ( spl0_1129
  <=> subclass(complement(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f23593,plain,
    ( ~ subclass(complement(subset_relation),singleton_relation)
    | ~ spl0_236
    | spl0_1129 ),
    inference(forward_demodulation,[],[f23587,f2319]) ).

fof(f23587,plain,
    ( ~ subclass(complement(subset_relation),identity_relation)
    | spl0_1129 ),
    inference(avatar_component_clause,[],[f23585]) ).

fof(f23592,plain,
    ( ~ spl0_1129
    | spl0_1130
    | ~ spl0_113
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2830,f2784,f890,f23589,f23585]) ).

fof(f23589,plain,
    ( spl0_1130
  <=> null_class = complement(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f2830,plain,
    ( null_class = complement(subset_relation)
    | ~ subclass(complement(subset_relation),identity_relation)
    | ~ spl0_113
    | ~ spl0_286 ),
    inference(duplicate_literal_removal,[],[f2822]) ).

fof(f2822,plain,
    ( null_class = complement(subset_relation)
    | ~ subclass(complement(subset_relation),identity_relation)
    | null_class = complement(subset_relation)
    | ~ spl0_113
    | ~ spl0_286 ),
    inference(resolution,[],[f2785,f891]) ).

fof(f23478,plain,
    ( ~ spl0_276
    | ~ spl0_1128 ),
    inference(avatar_contradiction_clause,[],[f23462]) ).

fof(f23462,plain,
    ( $false
    | ~ spl0_276
    | ~ spl0_1128 ),
    inference(resolution,[],[f23454,f2546]) ).

fof(f23454,plain,
    ( ! [X0] : ~ member(regular(subset_relation),X0)
    | ~ spl0_1128 ),
    inference(avatar_component_clause,[],[f23453]) ).

fof(f23453,plain,
    ( spl0_1128
  <=> ! [X0] : ~ member(regular(subset_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f23477,plain,
    ( ~ spl0_467
    | ~ spl0_1128 ),
    inference(avatar_contradiction_clause,[],[f23465]) ).

fof(f23465,plain,
    ( $false
    | ~ spl0_467
    | ~ spl0_1128 ),
    inference(resolution,[],[f23454,f6372]) ).

fof(f23455,plain,
    ( spl0_1127
    | spl0_1128
    | ~ spl0_276
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f2776,f2563,f2544,f23453,f23449]) ).

fof(f23449,plain,
    ( spl0_1127
  <=> member(regular(subset_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f2563,plain,
    ( spl0_277
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f2776,plain,
    ( ! [X0] :
        ( ~ member(regular(subset_relation),X0)
        | member(regular(subset_relation),universal_class) )
    | ~ spl0_276
    | ~ spl0_277 ),
    inference(resolution,[],[f2546,f2564]) ).

fof(f2564,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,universal_class) )
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f2563]) ).

fof(f23443,plain,
    ( spl0_1126
    | ~ spl0_236
    | ~ spl0_1125 ),
    inference(avatar_split_clause,[],[f23438,f23435,f2317,f23441]) ).

fof(f23441,plain,
    ( spl0_1126
  <=> ! [X0] : ~ member(regular(singleton_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f23435,plain,
    ( spl0_1125
  <=> ! [X0] : ~ member(regular(identity_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f23438,plain,
    ( ! [X0] : ~ member(regular(singleton_relation),X0)
    | ~ spl0_236
    | ~ spl0_1125 ),
    inference(forward_demodulation,[],[f23436,f2319]) ).

fof(f23436,plain,
    ( ! [X0] : ~ member(regular(identity_relation),X0)
    | ~ spl0_1125 ),
    inference(avatar_component_clause,[],[f23435]) ).

fof(f23437,plain,
    ( spl0_1124
    | spl0_1125
    | ~ spl0_235
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f2676,f2563,f2311,f23435,f23431]) ).

fof(f23431,plain,
    ( spl0_1124
  <=> member(regular(identity_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

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

fof(f2676,plain,
    ( ! [X0] :
        ( ~ member(regular(identity_relation),X0)
        | member(regular(identity_relation),universal_class) )
    | ~ spl0_235
    | ~ spl0_277 ),
    inference(resolution,[],[f2564,f2313]) ).

fof(f2313,plain,
    ( member(regular(identity_relation),subset_relation)
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2311]) ).

fof(f23429,plain,
    ( spl0_1122
    | ~ spl0_1123
    | ~ spl0_62
    | ~ spl0_1072 ),
    inference(avatar_split_clause,[],[f22136,f22113,f530,f23426,f23423]) ).

fof(f23426,plain,
    ( spl0_1123
  <=> subclass(universal_class,rotate(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f22136,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(element_relation))
        | member(not_subclass_element(cross_product(x,y),z),X0) )
    | ~ spl0_62
    | ~ spl0_1072 ),
    inference(resolution,[],[f22114,f531]) ).

fof(f22852,plain,
    ( ~ spl0_1121
    | ~ spl0_579
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f20719,f20614,f8915,f22849]) ).

fof(f22849,plain,
    ( spl0_1121
  <=> subclass(universal_class,complement(intersection(cross_product(x,y),cross_product(x,y)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f8915,plain,
    ( spl0_579
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(cross_product(x,y),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f20719,plain,
    ( ~ subclass(universal_class,complement(intersection(cross_product(x,y),cross_product(x,y))))
    | ~ spl0_579
    | ~ spl0_1048 ),
    inference(resolution,[],[f20615,f8916]) ).

fof(f8916,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(x,y),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f8915]) ).

fof(f22647,plain,
    ( spl0_923
    | spl0_1120
    | ~ spl0_148
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f12344,f3016,f1231,f22644,f17297]) ).

fof(f17297,plain,
    ( spl0_923
  <=> null_class = composition_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f22644,plain,
    ( spl0_1120
  <=> member(regular(composition_function),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f1231,plain,
    ( spl0_148
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f3016,plain,
    ( spl0_308
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f12344,plain,
    ( member(regular(composition_function),universal_class)
    | null_class = composition_function
    | ~ spl0_148
    | ~ spl0_308 ),
    inference(superposition,[],[f3017,f1233]) ).

fof(f1233,plain,
    ( composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_148 ),
    inference(avatar_component_clause,[],[f1231]) ).

fof(f3017,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_308 ),
    inference(avatar_component_clause,[],[f3016]) ).

fof(f22642,plain,
    ( spl0_1119
    | ~ spl0_10
    | ~ spl0_681 ),
    inference(avatar_split_clause,[],[f10975,f10791,f246,f22639]) ).

fof(f22639,plain,
    ( spl0_1119
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f10975,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class)
    | ~ spl0_10
    | ~ spl0_681 ),
    inference(superposition,[],[f247,f10793]) ).

fof(f22637,plain,
    ( spl0_1118
    | ~ spl0_10
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10901,f10786,f246,f22634]) ).

fof(f22634,plain,
    ( spl0_1118
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f10901,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class)
    | ~ spl0_10
    | ~ spl0_680 ),
    inference(superposition,[],[f247,f10788]) ).

fof(f22632,plain,
    ( spl0_1117
    | ~ spl0_10
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f10827,f10781,f246,f22629]) ).

fof(f22629,plain,
    ( spl0_1117
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f10827,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class)
    | ~ spl0_10
    | ~ spl0_679 ),
    inference(superposition,[],[f247,f10783]) ).

fof(f22627,plain,
    ( spl0_1114
    | ~ spl0_1116
    | ~ spl0_365
    | ~ spl0_677 ),
    inference(avatar_split_clause,[],[f10711,f10601,f3873,f22624,f22616]) ).

fof(f22616,plain,
    ( spl0_1114
  <=> ! [X0] : member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f22624,plain,
    ( spl0_1116
  <=> subclass(universal_class,flip(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f3873,plain,
    ( spl0_365
  <=> ! [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_365])]) ).

fof(f10711,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(subset_relation))
        | member(X0,universal_class) )
    | ~ spl0_365
    | ~ spl0_677 ),
    inference(resolution,[],[f10602,f3874]) ).

fof(f3874,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_365 ),
    inference(avatar_component_clause,[],[f3873]) ).

fof(f22622,plain,
    ( spl0_1114
    | ~ spl0_1115
    | ~ spl0_365
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f10627,f10597,f3873,f22619,f22616]) ).

fof(f22619,plain,
    ( spl0_1115
  <=> subclass(universal_class,rotate(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f10627,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(subset_relation))
        | member(X0,universal_class) )
    | ~ spl0_365
    | ~ spl0_676 ),
    inference(resolution,[],[f10598,f3874]) ).

fof(f22614,plain,
    ( spl0_1
    | ~ spl0_1113
    | ~ spl0_131
    | spl0_1056 ),
    inference(avatar_split_clause,[],[f20796,f20791,f1018,f22611,f205]) ).

fof(f22611,plain,
    ( spl0_1113
  <=> subclass(cross_product(x,y),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f20791,plain,
    ( spl0_1056
  <=> member(not_subclass_element(cross_product(x,y),z),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f20796,plain,
    ( ~ subclass(cross_product(x,y),domain_relation)
    | subclass(cross_product(x,y),z)
    | ~ spl0_131
    | spl0_1056 ),
    inference(resolution,[],[f20793,f1019]) ).

fof(f20793,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),domain_relation)
    | spl0_1056 ),
    inference(avatar_component_clause,[],[f20791]) ).

fof(f22609,plain,
    ( ~ spl0_1112
    | spl0_913
    | ~ spl0_67
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f6951,f6616,f558,f16898,f22606]) ).

fof(f22606,plain,
    ( spl0_1112
  <=> subclass(domain_relation,complement(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f558,plain,
    ( spl0_67
  <=> ! [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_67])]) ).

fof(f6951,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(domain_relation)) )
    | ~ spl0_67
    | ~ spl0_485 ),
    inference(duplicate_literal_removal,[],[f6950]) ).

fof(f6950,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(domain_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_67
    | ~ spl0_485 ),
    inference(resolution,[],[f6617,f559]) ).

fof(f559,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_67 ),
    inference(avatar_component_clause,[],[f558]) ).

fof(f22604,plain,
    ( spl0_1111
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5482,f5005,f1089,f22602]) ).

fof(f22602,plain,
    ( spl0_1111
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f5482,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0))
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5425]) ).

fof(f5425,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X0))
        | subclass(intersection(X0,X1),intersection(X0,X0)) )
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f1090]) ).

fof(f22600,plain,
    ( spl0_1110
    | ~ spl0_136
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5479,f5005,f1093,f22598]) ).

fof(f22598,plain,
    ( spl0_1110
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f5479,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0))
    | ~ spl0_136
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5428]) ).

fof(f5428,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X0))
        | subclass(intersection(X0,X1),intersection(X1,X0)) )
    | ~ spl0_136
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f1094]) ).

fof(f22596,plain,
    ( spl0_1109
    | ~ spl0_323
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5470,f5005,f3254,f22594]) ).

fof(f22594,plain,
    ( spl0_1109
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f5470,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
    | ~ spl0_323
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5438]) ).

fof(f5438,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) )
    | ~ spl0_323
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f3255]) ).

fof(f22592,plain,
    ( spl0_1108
    | ~ spl0_327
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5469,f5005,f3275,f22590]) ).

fof(f22590,plain,
    ( spl0_1108
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f5469,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
    | ~ spl0_327
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5439]) ).

fof(f5439,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) )
    | ~ spl0_327
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f3276]) ).

fof(f22588,plain,
    ( spl0_1107
    | ~ spl0_335
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5467,f5005,f3394,f22586]) ).

fof(f22586,plain,
    ( spl0_1107
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f5467,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
    | ~ spl0_335
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5450]) ).

fof(f5450,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) )
    | ~ spl0_335
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f3395]) ).

fof(f22584,plain,
    ( spl0_1106
    | ~ spl0_338
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5466,f5005,f3416,f22582]) ).

fof(f22582,plain,
    ( spl0_1106
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f5466,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
    | ~ spl0_338
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5451]) ).

fof(f5451,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) )
    | ~ spl0_338
    | ~ spl0_419 ),
    inference(resolution,[],[f5006,f3417]) ).

fof(f22580,plain,
    ( spl0_1105
    | ~ spl0_136
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5414,f5001,f1093,f22578]) ).

fof(f22578,plain,
    ( spl0_1105
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f5414,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
    | ~ spl0_136
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5363]) ).

fof(f5363,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X1))
        | subclass(intersection(X0,X1),intersection(X1,X1)) )
    | ~ spl0_136
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f1094]) ).

fof(f22576,plain,
    ( spl0_1104
    | ~ spl0_323
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5405,f5001,f3254,f22574]) ).

fof(f22574,plain,
    ( spl0_1104
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f5405,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
    | ~ spl0_323
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5373]) ).

fof(f5373,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) )
    | ~ spl0_323
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f3255]) ).

fof(f22572,plain,
    ( spl0_1103
    | ~ spl0_327
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5404,f5001,f3275,f22570]) ).

fof(f22570,plain,
    ( spl0_1103
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f5404,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
    | ~ spl0_327
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5374]) ).

fof(f5374,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) )
    | ~ spl0_327
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f3276]) ).

fof(f22568,plain,
    ( spl0_1102
    | ~ spl0_335
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5402,f5001,f3394,f22566]) ).

fof(f22566,plain,
    ( spl0_1102
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f5402,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
    | ~ spl0_335
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5385]) ).

fof(f5385,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) )
    | ~ spl0_335
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f3395]) ).

fof(f22564,plain,
    ( spl0_1101
    | ~ spl0_338
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5401,f5001,f3416,f22562]) ).

fof(f22562,plain,
    ( spl0_1101
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f5401,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
    | ~ spl0_338
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5386]) ).

fof(f5386,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) )
    | ~ spl0_338
    | ~ spl0_418 ),
    inference(resolution,[],[f5002,f3417]) ).

fof(f22560,plain,
    ( spl0_1100
    | ~ spl0_28
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f5247,f4961,f325,f22558]) ).

fof(f22558,plain,
    ( spl0_1100
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f5247,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1)
    | ~ spl0_28
    | ~ spl0_410 ),
    inference(duplicate_literal_removal,[],[f5201]) ).

fof(f5201,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X1)
        | subclass(intersection(X0,intersection(X1,X2)),X1) )
    | ~ spl0_28
    | ~ spl0_410 ),
    inference(resolution,[],[f4962,f326]) ).

fof(f22556,plain,
    ( spl0_1099
    | ~ spl0_28
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f5189,f4957,f325,f22554]) ).

fof(f22554,plain,
    ( spl0_1099
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f5189,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2)
    | ~ spl0_28
    | ~ spl0_409 ),
    inference(duplicate_literal_removal,[],[f5143]) ).

fof(f5143,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X2)
        | subclass(intersection(X0,intersection(X1,X2)),X2) )
    | ~ spl0_28
    | ~ spl0_409 ),
    inference(resolution,[],[f4958,f326]) ).

fof(f22552,plain,
    ( spl0_1098
    | ~ spl0_28
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f5130,f4953,f325,f22550]) ).

fof(f22550,plain,
    ( spl0_1098
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f5130,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0)
    | ~ spl0_28
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f5084]) ).

fof(f5084,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X0)
        | subclass(intersection(intersection(X0,X1),X2),X0) )
    | ~ spl0_28
    | ~ spl0_408 ),
    inference(resolution,[],[f4954,f326]) ).

fof(f22548,plain,
    ( spl0_1097
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f5072,f4949,f325,f22546]) ).

fof(f22546,plain,
    ( spl0_1097
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f5072,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1)
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f5026]) ).

fof(f5026,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X1)
        | subclass(intersection(intersection(X0,X1),X2),X1) )
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(resolution,[],[f4950,f326]) ).

fof(f22544,plain,
    ( spl0_1096
    | ~ spl0_315
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3537,f3416,f3219,f22542]) ).

fof(f22542,plain,
    ( spl0_1096
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f3537,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3528]) ).

fof(f3528,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_315
    | ~ spl0_338 ),
    inference(resolution,[],[f3417,f3220]) ).

fof(f22540,plain,
    ( spl0_1095
    | ~ spl0_28
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f3524,f3412,f325,f22537]) ).

fof(f22537,plain,
    ( spl0_1095
  <=> subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f3524,plain,
    ( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_28
    | ~ spl0_337 ),
    inference(duplicate_literal_removal,[],[f3513]) ).

fof(f3513,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_337 ),
    inference(resolution,[],[f3413,f326]) ).

fof(f22535,plain,
    ( spl0_1094
    | ~ spl0_28
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f3512,f3408,f325,f22532]) ).

fof(f22532,plain,
    ( spl0_1094
  <=> subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f3512,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_28
    | ~ spl0_336 ),
    inference(duplicate_literal_removal,[],[f3501]) ).

fof(f3501,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_28
    | ~ spl0_336 ),
    inference(resolution,[],[f3409,f326]) ).

fof(f22530,plain,
    ( spl0_1075
    | ~ spl0_1093
    | ~ spl0_743
    | ~ spl0_1073 ),
    inference(avatar_split_clause,[],[f22301,f22117,f12630,f22527,f22437]) ).

fof(f22437,plain,
    ( spl0_1075
  <=> ! [X0] : member(X0,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f22527,plain,
    ( spl0_1093
  <=> subclass(universal_class,flip(composition_function)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f12630,plain,
    ( spl0_743
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | member(X1,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f22301,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(composition_function))
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_743
    | ~ spl0_1073 ),
    inference(resolution,[],[f22118,f12631]) ).

fof(f12631,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | member(X1,cross_product(universal_class,universal_class)) )
    | ~ spl0_743 ),
    inference(avatar_component_clause,[],[f12630]) ).

fof(f22525,plain,
    ( spl0_1092
    | ~ spl0_315
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3498,f3394,f3219,f22523]) ).

fof(f22523,plain,
    ( spl0_1092
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f3498,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3489]) ).

fof(f3489,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_315
    | ~ spl0_335 ),
    inference(resolution,[],[f3395,f3220]) ).

fof(f22521,plain,
    ( spl0_1091
    | ~ spl0_15
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f3479,f3296,f268,f22519]) ).

fof(f22519,plain,
    ( spl0_1091
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f268,plain,
    ( spl0_15
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f3296,plain,
    ( spl0_331
  <=> ! [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_331])]) ).

fof(f3479,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(X0),universal_class) )
    | ~ spl0_15
    | ~ spl0_331 ),
    inference(resolution,[],[f3297,f270]) ).

fof(f270,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f268]) ).

fof(f3297,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f3296]) ).

fof(f22517,plain,
    ( spl0_1090
    | ~ spl0_51
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3470,f3292,f2792,f458,f22514]) ).

fof(f22514,plain,
    ( spl0_1090
  <=> subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f458,plain,
    ( spl0_51
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f3470,plain,
    ( subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class)))
    | ~ spl0_51
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3465,f459]) ).

fof(f459,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f458]) ).

fof(f3465,plain,
    ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3438]) ).

fof(f3438,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_288
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f2793]) ).

fof(f22512,plain,
    ( spl0_1089
    | ~ spl0_27
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3383,f3236,f321,f22510]) ).

fof(f22510,plain,
    ( spl0_1089
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f3383,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_319 ),
    inference(duplicate_literal_removal,[],[f3352]) ).

fof(f3352,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0))
        | subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_319 ),
    inference(resolution,[],[f3237,f322]) ).

fof(f22508,plain,
    ( spl0_1088
    | ~ spl0_135
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3315,f3219,f1089,f22506]) ).

fof(f22506,plain,
    ( spl0_1088
  <=> ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f3315,plain,
    ( ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
    | ~ spl0_135
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3310]) ).

fof(f3310,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_135
    | ~ spl0_315 ),
    inference(resolution,[],[f3220,f1090]) ).

fof(f22504,plain,
    ( spl0_1087
    | ~ spl0_136
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3314,f3219,f1093,f22502]) ).

fof(f22502,plain,
    ( spl0_1087
  <=> ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f3314,plain,
    ( ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_136
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3311]) ).

fof(f3311,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_136
    | ~ spl0_315 ),
    inference(resolution,[],[f3220,f1094]) ).

fof(f22500,plain,
    ( ~ spl0_1086
    | ~ spl0_21
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f3138,f3128,f293,f22497]) ).

fof(f22497,plain,
    ( spl0_1086
  <=> member(regular(singleton_relation),compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f293,plain,
    ( spl0_21
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f3128,plain,
    ( spl0_311
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f3138,plain,
    ( ~ member(regular(singleton_relation),compose(element_relation,complement(singleton_relation)))
    | ~ spl0_21
    | ~ spl0_311 ),
    inference(resolution,[],[f3130,f294]) ).

fof(f294,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f293]) ).

fof(f3130,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_311 ),
    inference(avatar_component_clause,[],[f3128]) ).

fof(f22495,plain,
    ( spl0_232
    | ~ spl0_1085
    | ~ spl0_235
    | ~ spl0_236
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3111,f2878,f2317,f2311,f22492,f2289]) ).

fof(f2289,plain,
    ( spl0_232
  <=> null_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f22492,plain,
    ( spl0_1085
  <=> subclass(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f3111,plain,
    ( ~ subclass(singleton_relation,complement(subset_relation))
    | null_class = singleton_relation
    | ~ spl0_235
    | ~ spl0_236
    | ~ spl0_294 ),
    inference(forward_demodulation,[],[f3077,f2319]) ).

fof(f3077,plain,
    ( null_class = singleton_relation
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_235
    | ~ spl0_236
    | ~ spl0_294 ),
    inference(forward_demodulation,[],[f3044,f2319]) ).

fof(f3044,plain,
    ( null_class = identity_relation
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_235
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f2313]) ).

fof(f22490,plain,
    ( spl0_1084
    | ~ spl0_24
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3055,f2878,f305,f22488]) ).

fof(f22488,plain,
    ( spl0_1084
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f305,plain,
    ( spl0_24
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f3055,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_24
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f3027]) ).

fof(f3027,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0))
        | null_class = X0 )
    | ~ spl0_24
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f306]) ).

fof(f306,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f22486,plain,
    ( ~ spl0_1083
    | spl0_232
    | ~ spl0_233
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3035,f2878,f2293,f2289,f22483]) ).

fof(f22483,plain,
    ( spl0_1083
  <=> subclass(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f2293,plain,
    ( spl0_233
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f3035,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(element_relation))
    | ~ spl0_233
    | ~ spl0_294 ),
    inference(resolution,[],[f2879,f2295]) ).

fof(f2295,plain,
    ( member(regular(singleton_relation),element_relation)
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2293]) ).

fof(f22481,plain,
    ( spl0_913
    | ~ spl0_1082
    | ~ spl0_67
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2589,f2506,f558,f22478,f16898]) ).

fof(f22478,plain,
    ( spl0_1082
  <=> subclass(universal_class,complement(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f2589,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(domain_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_67
    | ~ spl0_269 ),
    inference(resolution,[],[f2507,f559]) ).

fof(f22476,plain,
    ( spl0_1081
    | ~ spl0_109
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2567,f2506,f817,f22474]) ).

fof(f22474,plain,
    ( spl0_1081
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f2567,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_269 ),
    inference(resolution,[],[f2507,f818]) ).

fof(f22471,plain,
    ( spl0_1080
    | ~ spl0_39
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2444,f2311,f378,f22469]) ).

fof(f22469,plain,
    ( spl0_1080
  <=> ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f2444,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) )
    | ~ spl0_39
    | ~ spl0_235 ),
    inference(resolution,[],[f2313,f379]) ).

fof(f22467,plain,
    ( spl0_1079
    | ~ spl0_39
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2334,f2293,f378,f22465]) ).

fof(f22465,plain,
    ( spl0_1079
  <=> ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f2334,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_39
    | ~ spl0_233 ),
    inference(resolution,[],[f2295,f379]) ).

fof(f22462,plain,
    ( spl0_1078
    | ~ spl0_44
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2247,f2230,f399,f22459]) ).

fof(f22459,plain,
    ( spl0_1078
  <=> subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f399,plain,
    ( spl0_44
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f2247,plain,
    ( subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_44
    | ~ spl0_224 ),
    inference(superposition,[],[f2231,f401]) ).

fof(f401,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f399]) ).

fof(f22456,plain,
    ( spl0_1077
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2246,f2230,f394,f22453]) ).

fof(f22453,plain,
    ( spl0_1077
  <=> subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f2246,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(superposition,[],[f2231,f396]) ).

fof(f22443,plain,
    ( spl0_1075
    | ~ spl0_1076
    | ~ spl0_743
    | ~ spl0_1072 ),
    inference(avatar_split_clause,[],[f22145,f22113,f12630,f22440,f22437]) ).

fof(f22440,plain,
    ( spl0_1076
  <=> subclass(universal_class,rotate(composition_function)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f22145,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(composition_function))
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_743
    | ~ spl0_1072 ),
    inference(resolution,[],[f22114,f12631]) ).

fof(f22435,plain,
    ( spl0_1074
    | ~ spl0_87
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2704,f2690,f675,f22433]) ).

fof(f22433,plain,
    ( spl0_1074
  <=> ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)))),application_function)
        | member(first(not_subclass_element(cross_product(x,y),z)),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f2704,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)))),application_function)
        | member(first(not_subclass_element(cross_product(x,y),z)),domain_of(X0)) )
    | ~ spl0_87
    | ~ spl0_278 ),
    inference(superposition,[],[f676,f2692]) ).

fof(f22119,plain,
    ( spl0_1073
    | ~ spl0_278
    | ~ spl0_677 ),
    inference(avatar_split_clause,[],[f10770,f10601,f2690,f22117]) ).

fof(f10770,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)),unordered_pair(not_subclass_element(cross_product(x,y),z),unordered_pair(X0,X0))),X1)
        | ~ subclass(universal_class,flip(X1)) )
    | ~ spl0_278
    | ~ spl0_677 ),
    inference(superposition,[],[f10602,f2692]) ).

fof(f22115,plain,
    ( spl0_1072
    | ~ spl0_278
    | ~ spl0_676 ),
    inference(avatar_split_clause,[],[f10686,f10597,f2690,f22113]) ).

fof(f10686,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(not_subclass_element(cross_product(x,y),z),not_subclass_element(cross_product(x,y),z)),unordered_pair(not_subclass_element(cross_product(x,y),z),unordered_pair(X0,X0))),X1)
        | ~ subclass(universal_class,rotate(X1)) )
    | ~ spl0_278
    | ~ spl0_676 ),
    inference(superposition,[],[f10598,f2692]) ).

fof(f22100,plain,
    ( spl0_1071
    | ~ spl0_78
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2701,f2690,f619,f22098]) ).

fof(f22098,plain,
    ( spl0_1071
  <=> ! [X0,X1] :
        ( member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | ~ member(second(not_subclass_element(cross_product(x,y),z)),X1)
        | ~ member(first(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f619,plain,
    ( spl0_78
  <=> ! [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_78])]) ).

fof(f2701,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | ~ member(second(not_subclass_element(cross_product(x,y),z)),X1)
        | ~ member(first(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_78
    | ~ spl0_278 ),
    inference(superposition,[],[f620,f2692]) ).

fof(f620,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_78 ),
    inference(avatar_component_clause,[],[f619]) ).

fof(f20878,plain,
    ( spl0_913
    | ~ spl0_1070
    | ~ spl0_5
    | ~ spl0_10
    | ~ spl0_263
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f6954,f6616,f2459,f246,f225,f20875,f16898]) ).

fof(f20875,plain,
    ( spl0_1070
  <=> subclass(domain_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f2459,plain,
    ( spl0_263
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f6954,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_5
    | ~ spl0_10
    | ~ spl0_263
    | ~ spl0_485 ),
    inference(forward_demodulation,[],[f6931,f2491]) ).

fof(f2491,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_5
    | ~ spl0_263 ),
    inference(resolution,[],[f2460,f226]) ).

fof(f2460,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2459]) ).

fof(f6931,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(universal_class)) )
    | ~ spl0_10
    | ~ spl0_485 ),
    inference(resolution,[],[f6617,f247]) ).

fof(f20873,plain,
    ( spl0_1
    | ~ spl0_1069
    | ~ spl0_131
    | spl0_1040 ),
    inference(avatar_split_clause,[],[f20574,f20568,f1018,f20870,f205]) ).

fof(f20870,plain,
    ( spl0_1069
  <=> subclass(cross_product(x,y),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f20568,plain,
    ( spl0_1040
  <=> member(not_subclass_element(cross_product(x,y),z),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f20574,plain,
    ( ~ subclass(cross_product(x,y),element_relation)
    | subclass(cross_product(x,y),z)
    | ~ spl0_131
    | spl0_1040 ),
    inference(resolution,[],[f20570,f1019]) ).

fof(f20570,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),element_relation)
    | spl0_1040 ),
    inference(avatar_component_clause,[],[f20568]) ).

fof(f20868,plain,
    ( spl0_1068
    | ~ spl0_5
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f3858,f3731,f225,f20866]) ).

fof(f20866,plain,
    ( spl0_1068
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f3731,plain,
    ( spl0_361
  <=> ! [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_361])]) ).

fof(f3858,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) )
    | ~ spl0_5
    | ~ spl0_361 ),
    inference(resolution,[],[f3732,f226]) ).

fof(f3732,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_361 ),
    inference(avatar_component_clause,[],[f3731]) ).

fof(f20864,plain,
    ( spl0_1067
    | ~ spl0_236
    | ~ spl0_295
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3796,f3630,f2882,f2317,f20861]) ).

fof(f20861,plain,
    ( spl0_1067
  <=> null_class = intersection(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f2882,plain,
    ( spl0_295
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f3796,plain,
    ( null_class = intersection(singleton_relation,complement(subset_relation))
    | ~ spl0_236
    | ~ spl0_295
    | ~ spl0_355 ),
    inference(forward_demodulation,[],[f3786,f2319]) ).

fof(f3786,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_295
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3782]) ).

fof(f3782,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_295
    | ~ spl0_355 ),
    inference(resolution,[],[f3631,f2883]) ).

fof(f2883,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f2882]) ).

fof(f20859,plain,
    ( spl0_1066
    | ~ spl0_129
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3791,f3630,f1010,f20857]) ).

fof(f20857,plain,
    ( spl0_1066
  <=> ! [X0] : null_class = intersection(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f1010,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f3791,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_129
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3769]) ).

fof(f3769,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(X0))
        | null_class = intersection(X0,complement(X0)) )
    | ~ spl0_129
    | ~ spl0_355 ),
    inference(resolution,[],[f3631,f1011]) ).

fof(f1011,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1010]) ).

fof(f20855,plain,
    ( spl0_1065
    | ~ spl0_296
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3788,f3630,f2886,f20852]) ).

fof(f20852,plain,
    ( spl0_1065
  <=> null_class = intersection(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f2886,plain,
    ( spl0_296
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f3788,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_296
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3773]) ).

fof(f3773,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_296
    | ~ spl0_355 ),
    inference(resolution,[],[f3631,f2887]) ).

fof(f2887,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_296 ),
    inference(avatar_component_clause,[],[f2886]) ).

fof(f20850,plain,
    ( spl0_1064
    | ~ spl0_130
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3762,f3626,f1014,f20848]) ).

fof(f20848,plain,
    ( spl0_1064
  <=> ! [X0] : null_class = intersection(complement(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f1014,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f3762,plain,
    ( ! [X0] : null_class = intersection(complement(X0),X0)
    | ~ spl0_130
    | ~ spl0_354 ),
    inference(duplicate_literal_removal,[],[f3738]) ).

fof(f3738,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(X0),X0)
        | null_class = intersection(complement(X0),X0) )
    | ~ spl0_130
    | ~ spl0_354 ),
    inference(resolution,[],[f3627,f1015]) ).

fof(f1015,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1014]) ).

fof(f20846,plain,
    ( spl0_1063
    | ~ spl0_304
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3759,f3626,f2998,f20843]) ).

fof(f20843,plain,
    ( spl0_1063
  <=> null_class = intersection(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f2998,plain,
    ( spl0_304
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f3759,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_304
    | ~ spl0_354 ),
    inference(duplicate_literal_removal,[],[f3742]) ).

fof(f3742,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_304
    | ~ spl0_354 ),
    inference(resolution,[],[f3627,f2999]) ).

fof(f2999,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_304 ),
    inference(avatar_component_clause,[],[f2998]) ).

fof(f20841,plain,
    ( spl0_1062
    | ~ spl0_314
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3757,f3626,f3200,f20838]) ).

fof(f20838,plain,
    ( spl0_1062
  <=> null_class = intersection(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f3200,plain,
    ( spl0_314
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f3757,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_314
    | ~ spl0_354 ),
    inference(duplicate_literal_removal,[],[f3751]) ).

fof(f3751,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_314
    | ~ spl0_354 ),
    inference(resolution,[],[f3627,f3201]) ).

fof(f3201,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f3200]) ).

fof(f20836,plain,
    ( spl0_1061
    | ~ spl0_28
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3211,f3179,f325,f20834]) ).

fof(f20834,plain,
    ( spl0_1061
  <=> ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f3211,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3203]) ).

fof(f3203,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,subset_relation) )
    | ~ spl0_28
    | ~ spl0_313 ),
    inference(resolution,[],[f3180,f326]) ).

fof(f20832,plain,
    ( spl0_1060
    | ~ spl0_28
    | ~ spl0_306 ),
    inference(avatar_split_clause,[],[f3190,f3008,f325,f20830]) ).

fof(f20830,plain,
    ( spl0_1060
  <=> ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f3190,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_306 ),
    inference(duplicate_literal_removal,[],[f3182]) ).

fof(f3182,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,element_relation) )
    | ~ spl0_28
    | ~ spl0_306 ),
    inference(resolution,[],[f3009,f326]) ).

fof(f20828,plain,
    ( spl0_1059
    | ~ spl0_5
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f3024,f2874,f225,f20826]) ).

fof(f20826,plain,
    ( spl0_1059
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f2874,plain,
    ( spl0_293
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f3024,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_5
    | ~ spl0_293 ),
    inference(resolution,[],[f2875,f226]) ).

fof(f2875,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f2874]) ).

fof(f20806,plain,
    ( spl0_1058
    | ~ spl0_103
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2943,f2317,f763,f20804]) ).

fof(f20804,plain,
    ( spl0_1058
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f2943,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) )
    | ~ spl0_103
    | ~ spl0_236 ),
    inference(superposition,[],[f764,f2319]) ).

fof(f20800,plain,
    ( spl0_1057
    | ~ spl0_73
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2700,f2690,f590,f20798]) ).

fof(f20798,plain,
    ( spl0_1057
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),compose_class(X0))
        | second(not_subclass_element(cross_product(x,y),z)) = compose(X0,first(not_subclass_element(cross_product(x,y),z))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f590,plain,
    ( spl0_73
  <=> ! [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_73])]) ).

fof(f2700,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),compose_class(X0))
        | second(not_subclass_element(cross_product(x,y),z)) = compose(X0,first(not_subclass_element(cross_product(x,y),z))) )
    | ~ spl0_73
    | ~ spl0_278 ),
    inference(superposition,[],[f591,f2692]) ).

fof(f591,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_73 ),
    inference(avatar_component_clause,[],[f590]) ).

fof(f20794,plain,
    ( spl0_1055
    | ~ spl0_1056
    | ~ spl0_65
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2697,f2690,f545,f20791,f20787]) ).

fof(f20787,plain,
    ( spl0_1055
  <=> second(not_subclass_element(cross_product(x,y),z)) = domain_of(first(not_subclass_element(cross_product(x,y),z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f2697,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),domain_relation)
    | second(not_subclass_element(cross_product(x,y),z)) = domain_of(first(not_subclass_element(cross_product(x,y),z)))
    | ~ spl0_65
    | ~ spl0_278 ),
    inference(superposition,[],[f546,f2692]) ).

fof(f20753,plain,
    ( spl0_1054
    | ~ spl0_994
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f20704,f20614,f19494,f20750]) ).

fof(f20750,plain,
    ( spl0_1054
  <=> member(second(not_subclass_element(cross_product(x,y),z)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f19494,plain,
    ( spl0_994
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f20704,plain,
    ( member(second(not_subclass_element(cross_product(x,y),z)),universal_class)
    | ~ spl0_994
    | ~ spl0_1048 ),
    inference(resolution,[],[f20615,f19495]) ).

fof(f19495,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_994 ),
    inference(avatar_component_clause,[],[f19494]) ).

fof(f20640,plain,
    ( ~ spl0_1053
    | spl0_801
    | ~ spl0_864 ),
    inference(avatar_split_clause,[],[f16046,f16036,f14588,f20637]) ).

fof(f20637,plain,
    ( spl0_1053
  <=> null_class = cross_product(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f14588,plain,
    ( spl0_801
  <=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f16036,plain,
    ( spl0_864
  <=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f16046,plain,
    ( null_class != cross_product(null_class,universal_class)
    | spl0_801
    | ~ spl0_864 ),
    inference(superposition,[],[f14589,f16038]) ).

fof(f16038,plain,
    ( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
    | ~ spl0_864 ),
    inference(avatar_component_clause,[],[f16036]) ).

fof(f14589,plain,
    ( null_class != cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | spl0_801 ),
    inference(avatar_component_clause,[],[f14588]) ).

fof(f20635,plain,
    ( spl0_1052
    | ~ spl0_10
    | ~ spl0_748 ),
    inference(avatar_split_clause,[],[f12885,f12844,f246,f20632]) ).

fof(f20632,plain,
    ( spl0_1052
  <=> member(not_subclass_element(composition_function,application_function),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f12885,plain,
    ( member(not_subclass_element(composition_function,application_function),universal_class)
    | ~ spl0_10
    | ~ spl0_748 ),
    inference(superposition,[],[f247,f12846]) ).

fof(f20630,plain,
    ( spl0_1051
    | ~ spl0_28
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3539,f3416,f325,f20628]) ).

fof(f20628,plain,
    ( spl0_1051
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f3539,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation)
    | ~ spl0_28
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3526]) ).

fof(f3526,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),subset_relation)
        | subclass(intersection(X0,singleton_relation),subset_relation) )
    | ~ spl0_28
    | ~ spl0_338 ),
    inference(resolution,[],[f3417,f326]) ).

fof(f20625,plain,
    ( spl0_1050
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3500,f3394,f325,f20623]) ).

fof(f20623,plain,
    ( spl0_1050
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f3500,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation)
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3487]) ).

fof(f3487,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),subset_relation)
        | subclass(intersection(singleton_relation,X0),subset_relation) )
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(resolution,[],[f3395,f326]) ).

fof(f20621,plain,
    ( spl0_1049
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3475,f3292,f2371,f2317,f20618]) ).

fof(f20618,plain,
    ( spl0_1049
  <=> subclass(singleton_relation,intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f3475,plain,
    ( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3460,f2319]) ).

fof(f3460,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3451]) ).

fof(f3451,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f2372]) ).

fof(f20616,plain,
    ( spl0_1048
    | ~ spl0_27
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3469,f3292,f321,f20614]) ).

fof(f3469,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_27
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3434]) ).

fof(f3434,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(X0,X0))
        | subclass(X0,intersection(X0,X0)) )
    | ~ spl0_27
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f322]) ).

fof(f20612,plain,
    ( spl0_1047
    | ~ spl0_244
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3464,f3292,f2367,f20609]) ).

fof(f20609,plain,
    ( spl0_1047
  <=> subclass(singleton_relation,intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f3464,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_244
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3440]) ).

fof(f3440,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_244
    | ~ spl0_330 ),
    inference(resolution,[],[f3293,f2368]) ).

fof(f20607,plain,
    ( spl0_1046
    | ~ spl0_28
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3428,f3275,f325,f20605]) ).

fof(f20605,plain,
    ( spl0_1046
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f3428,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),element_relation)
    | ~ spl0_28
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3419]) ).

fof(f3419,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),element_relation)
        | subclass(intersection(X0,singleton_relation),element_relation) )
    | ~ spl0_28
    | ~ spl0_327 ),
    inference(resolution,[],[f3276,f326]) ).

fof(f20603,plain,
    ( spl0_1045
    | ~ spl0_28
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3406,f3254,f325,f20601]) ).

fof(f20601,plain,
    ( spl0_1045
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f3406,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),element_relation)
    | ~ spl0_28
    | ~ spl0_323 ),
    inference(duplicate_literal_removal,[],[f3397]) ).

fof(f3397,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),element_relation)
        | subclass(intersection(singleton_relation,X0),element_relation) )
    | ~ spl0_28
    | ~ spl0_323 ),
    inference(resolution,[],[f3255,f326]) ).

fof(f20599,plain,
    ( spl0_1044
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3319,f3219,f2371,f2317,f20596]) ).

fof(f20596,plain,
    ( spl0_1044
  <=> subclass(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f3319,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_236
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(forward_demodulation,[],[f3318,f2319]) ).

fof(f3318,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3307]) ).

fof(f3307,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(resolution,[],[f3220,f2372]) ).

fof(f20594,plain,
    ( ~ spl0_1043
    | ~ spl0_183
    | spl0_192
    | ~ spl0_13
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1569,f1562,f260,f1607,f1544,f20591]) ).

fof(f20591,plain,
    ( spl0_1043
  <=> 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_1043])]) ).

fof(f1544,plain,
    ( spl0_183
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f1607,plain,
    ( spl0_192
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f260,plain,
    ( spl0_13
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f1569,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_13
    | ~ spl0_186 ),
    inference(resolution,[],[f1563,f261]) ).

fof(f261,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f260]) ).

fof(f20585,plain,
    ( spl0_1
    | ~ spl0_1042
    | ~ spl0_131
    | spl0_1032 ),
    inference(avatar_split_clause,[],[f20510,f20332,f1018,f20582,f205]) ).

fof(f20582,plain,
    ( spl0_1042
  <=> subclass(cross_product(x,y),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f20332,plain,
    ( spl0_1032
  <=> member(not_subclass_element(cross_product(x,y),z),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f20510,plain,
    ( ~ subclass(cross_product(x,y),composition_function)
    | subclass(cross_product(x,y),z)
    | ~ spl0_131
    | spl0_1032 ),
    inference(resolution,[],[f20334,f1019]) ).

fof(f20334,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),composition_function)
    | spl0_1032 ),
    inference(avatar_component_clause,[],[f20332]) ).

fof(f20580,plain,
    ( spl0_183
    | ~ spl0_7
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f2518,f2486,f234,f1544]) ).

fof(f2486,plain,
    ( spl0_266
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f2518,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_7
    | ~ spl0_266 ),
    inference(resolution,[],[f2487,f235]) ).

fof(f2487,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f2486]) ).

fof(f20579,plain,
    ( spl0_1041
    | ~ spl0_77
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2245,f2230,f614,f20576]) ).

fof(f20576,plain,
    ( spl0_1041
  <=> subclass(subset_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

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

fof(f2245,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_77
    | ~ spl0_224 ),
    inference(superposition,[],[f2231,f616]) ).

fof(f616,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_77 ),
    inference(avatar_component_clause,[],[f614]) ).

fof(f20571,plain,
    ( spl0_1039
    | ~ spl0_1040
    | ~ spl0_62
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2696,f2690,f530,f20568,f20564]) ).

fof(f20564,plain,
    ( spl0_1039
  <=> member(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f2696,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),element_relation)
    | member(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z)))
    | ~ spl0_62
    | ~ spl0_278 ),
    inference(superposition,[],[f531,f2692]) ).

fof(f20514,plain,
    ( spl0_1038
    | ~ spl0_91
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1849,f1819,f692,f20512]) ).

fof(f20512,plain,
    ( spl0_1038
  <=> ! [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_1038])]) ).

fof(f692,plain,
    ( spl0_91
  <=> ! [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_91])]) ).

fof(f1819,plain,
    ( spl0_205
  <=> ! [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_205])]) ).

fof(f1849,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_91
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f693]) ).

fof(f693,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_91 ),
    inference(avatar_component_clause,[],[f692]) ).

fof(f1820,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_205 ),
    inference(avatar_component_clause,[],[f1819]) ).

fof(f20508,plain,
    ( spl0_1037
    | ~ spl0_91
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1823,f1815,f692,f20506]) ).

fof(f20506,plain,
    ( spl0_1037
  <=> ! [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_1037])]) ).

fof(f1815,plain,
    ( spl0_204
  <=> ! [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_204])]) ).

fof(f1823,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_91
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f693]) ).

fof(f1816,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_204 ),
    inference(avatar_component_clause,[],[f1815]) ).

fof(f20464,plain,
    ( spl0_1036
    | ~ spl0_112
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2135,f2131,f829,f20462]) ).

fof(f20462,plain,
    ( spl0_1036
  <=> ! [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_1036])]) ).

fof(f829,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2131,plain,
    ( spl0_222
  <=> ! [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_222])]) ).

fof(f2135,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_112
    | ~ spl0_222 ),
    inference(resolution,[],[f2132,f830]) ).

fof(f830,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f829]) ).

fof(f2132,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_222 ),
    inference(avatar_component_clause,[],[f2131]) ).

fof(f20430,plain,
    ( spl0_1035
    | ~ spl0_102
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1886,f1875,f756,f20428]) ).

fof(f20428,plain,
    ( spl0_1035
  <=> ! [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_1035])]) ).

fof(f756,plain,
    ( spl0_102
  <=> ! [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_102])]) ).

fof(f1875,plain,
    ( spl0_206
  <=> ! [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_206])]) ).

fof(f1886,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_102
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f757]) ).

fof(f757,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_102 ),
    inference(avatar_component_clause,[],[f756]) ).

fof(f1876,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_206 ),
    inference(avatar_component_clause,[],[f1875]) ).

fof(f20400,plain,
    ( spl0_1034
    | ~ spl0_198
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2023,f2001,f1711,f20398]) ).

fof(f20398,plain,
    ( spl0_1034
  <=> ! [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_1034])]) ).

fof(f1711,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

fof(f2001,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))),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_212])]) ).

fof(f2023,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_198
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1712]) ).

fof(f1712,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_198 ),
    inference(avatar_component_clause,[],[f1711]) ).

fof(f2002,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_212 ),
    inference(avatar_component_clause,[],[f2001]) ).

fof(f20354,plain,
    ( spl0_1033
    | ~ spl0_78
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2134,f2131,f619,f20352]) ).

fof(f20352,plain,
    ( spl0_1033
  <=> ! [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_1033])]) ).

fof(f2134,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_78
    | ~ spl0_222 ),
    inference(resolution,[],[f2132,f620]) ).

fof(f20335,plain,
    ( spl0_1031
    | ~ spl0_1032
    | ~ spl0_278
    | ~ spl0_741 ),
    inference(avatar_split_clause,[],[f12624,f12606,f2690,f20332,f20328]) ).

fof(f20328,plain,
    ( spl0_1031
  <=> member(first(not_subclass_element(cross_product(x,y),z)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f12606,plain,
    ( spl0_741
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f12624,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),composition_function)
    | member(first(not_subclass_element(cross_product(x,y),z)),universal_class)
    | ~ spl0_278
    | ~ spl0_741 ),
    inference(superposition,[],[f12607,f2692]) ).

fof(f12607,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | member(X0,universal_class) )
    | ~ spl0_741 ),
    inference(avatar_component_clause,[],[f12606]) ).

fof(f20326,plain,
    ( spl0_1030
    | ~ spl0_864
    | ~ spl0_1029 ),
    inference(avatar_split_clause,[],[f20322,f20315,f16036,f20324]) ).

fof(f20324,plain,
    ( spl0_1030
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f20315,plain,
    ( spl0_1029
  <=> ! [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_1029])]) ).

fof(f20322,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_1029 ),
    inference(forward_demodulation,[],[f20321,f16038]) ).

fof(f20321,plain,
    ( ! [X2,X3,X0,X1] :
        ( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_1029 ),
    inference(forward_demodulation,[],[f20320,f16038]) ).

fof(f20320,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_1029 ),
    inference(forward_demodulation,[],[f20319,f16038]) ).

fof(f20319,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,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_864
    | ~ spl0_1029 ),
    inference(forward_demodulation,[],[f20318,f16038]) ).

fof(f20318,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X2),universal_class))),X3))))))),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_864
    | ~ spl0_1029 ),
    inference(forward_demodulation,[],[f20316,f16038]) ).

fof(f20316,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_1029 ),
    inference(avatar_component_clause,[],[f20315]) ).

fof(f20317,plain,
    ( spl0_1029
    | ~ spl0_42
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2138,f2131,f390,f20315]) ).

fof(f390,plain,
    ( spl0_42
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f2138,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_42
    | ~ spl0_222 ),
    inference(superposition,[],[f2132,f391]) ).

fof(f391,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f390]) ).

fof(f20287,plain,
    ( spl0_1028
    | ~ spl0_206
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2009,f2001,f1875,f20285]) ).

fof(f20285,plain,
    ( spl0_1028
  <=> ! [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_1028])]) ).

fof(f2009,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_206
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1876]) ).

fof(f20257,plain,
    ( spl0_1027
    | ~ spl0_93
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2028,f2001,f702,f20255]) ).

fof(f20255,plain,
    ( spl0_1027
  <=> ! [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_1027])]) ).

fof(f702,plain,
    ( spl0_93
  <=> ! [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_93])]) ).

fof(f2028,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_93
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f703]) ).

fof(f703,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_93 ),
    inference(avatar_component_clause,[],[f702]) ).

fof(f20240,plain,
    ( spl0_1026
    | ~ spl0_102
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1758,f1751,f756,f20238]) ).

fof(f20238,plain,
    ( spl0_1026
  <=> ! [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_1026])]) ).

fof(f1751,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

fof(f1758,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_102
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f757]) ).

fof(f1752,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_200 ),
    inference(avatar_component_clause,[],[f1751]) ).

fof(f20229,plain,
    ( spl0_1025
    | ~ spl0_199
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2125,f2117,f1717,f20227]) ).

fof(f20227,plain,
    ( spl0_1025
  <=> ! [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_1025])]) ).

fof(f1717,plain,
    ( spl0_199
  <=> ! [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_199])]) ).

fof(f2117,plain,
    ( spl0_220
  <=> ! [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_220])]) ).

fof(f2125,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_199
    | ~ spl0_220 ),
    inference(superposition,[],[f2118,f1718]) ).

fof(f1718,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_199 ),
    inference(avatar_component_clause,[],[f1717]) ).

fof(f2118,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_220 ),
    inference(avatar_component_clause,[],[f2117]) ).

fof(f20205,plain,
    ( spl0_1024
    | ~ spl0_102
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1737,f1717,f756,f20203]) ).

fof(f20203,plain,
    ( spl0_1024
  <=> ! [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_1024])]) ).

fof(f1737,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_102
    | ~ spl0_199 ),
    inference(superposition,[],[f757,f1718]) ).

fof(f20035,plain,
    ( spl0_1023
    | ~ spl0_196
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1862,f1819,f1662,f20033]) ).

fof(f20033,plain,
    ( spl0_1023
  <=> ! [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_1023])]) ).

fof(f1662,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))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f1862,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_196
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1663]) ).

fof(f1663,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_196 ),
    inference(avatar_component_clause,[],[f1662]) ).

fof(f20031,plain,
    ( spl0_1022
    | ~ spl0_197
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1854,f1819,f1666,f20029]) ).

fof(f20029,plain,
    ( spl0_1022
  <=> ! [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_1022])]) ).

fof(f1666,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

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(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_197
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1667]) ).

fof(f1667,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_197 ),
    inference(avatar_component_clause,[],[f1666]) ).

fof(f20027,plain,
    ( spl0_1021
    | ~ spl0_39
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f17819,f17629,f378,f20025]) ).

fof(f20025,plain,
    ( spl0_1021
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f17629,plain,
    ( spl0_937
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f17819,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_39
    | ~ spl0_937 ),
    inference(resolution,[],[f17630,f379]) ).

fof(f17630,plain,
    ( ! [X0] :
        ( member(second(not_subclass_element(cross_product(x,y),z)),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_937 ),
    inference(avatar_component_clause,[],[f17629]) ).

fof(f20023,plain,
    ( spl0_1020
    | ~ spl0_196
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1836,f1815,f1662,f20021]) ).

fof(f20021,plain,
    ( spl0_1020
  <=> ! [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_1020])]) ).

fof(f1836,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_196
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1663]) ).

fof(f20019,plain,
    ( spl0_1019
    | ~ spl0_197
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1828,f1815,f1666,f20017]) ).

fof(f20017,plain,
    ( spl0_1019
  <=> ! [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_1019])]) ).

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(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_197
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1667]) ).

fof(f20015,plain,
    ( spl0_1018
    | ~ spl0_94
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1699,f1666,f708,f20013]) ).

fof(f20013,plain,
    ( spl0_1018
  <=> ! [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_1018])]) ).

fof(f708,plain,
    ( spl0_94
  <=> ! [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_94])]) ).

fof(f1699,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_94
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f709]) ).

fof(f709,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_94 ),
    inference(avatar_component_clause,[],[f708]) ).

fof(f20011,plain,
    ( spl0_1017
    | ~ spl0_94
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1678,f1662,f708,f20009]) ).

fof(f20009,plain,
    ( spl0_1017
  <=> ! [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_1017])]) ).

fof(f1678,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_94
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f709]) ).

fof(f20007,plain,
    ( spl0_1016
    | ~ spl0_10
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2120,f2117,f246,f20005]) ).

fof(f20005,plain,
    ( spl0_1016
  <=> ! [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_1016])]) ).

fof(f2120,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_10
    | ~ spl0_220 ),
    inference(resolution,[],[f2118,f247]) ).

fof(f20003,plain,
    ( spl0_1015
    | ~ spl0_102
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1419,f1375,f756,f20001]) ).

fof(f20001,plain,
    ( spl0_1015
  <=> ! [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_1015])]) ).

fof(f1419,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_102
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f757]) ).

fof(f19971,plain,
    ( spl0_1014
    | ~ spl0_236
    | ~ spl0_1013 ),
    inference(avatar_split_clause,[],[f19957,f19954,f2317,f19969]) ).

fof(f19969,plain,
    ( spl0_1014
  <=> ! [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_1014])]) ).

fof(f19954,plain,
    ( spl0_1013
  <=> ! [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_1013])]) ).

fof(f19957,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_236
    | ~ spl0_1013 ),
    inference(forward_demodulation,[],[f19955,f2319]) ).

fof(f19955,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_1013 ),
    inference(avatar_component_clause,[],[f19954]) ).

fof(f19956,plain,
    ( spl0_1013
    | ~ spl0_51
    | ~ spl0_102
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1008,f965,f756,f458,f19954]) ).

fof(f965,plain,
    ( spl0_126
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1008,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_51
    | ~ spl0_102
    | ~ spl0_126 ),
    inference(forward_demodulation,[],[f1006,f459]) ).

fof(f1006,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_102
    | ~ spl0_126 ),
    inference(resolution,[],[f966,f757]) ).

fof(f966,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f965]) ).

fof(f19912,plain,
    ( spl0_1012
    | ~ spl0_85
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1853,f1819,f660,f19910]) ).

fof(f19910,plain,
    ( spl0_1012
  <=> ! [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_1012])]) ).

fof(f660,plain,
    ( spl0_85
  <=> ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1853,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_85
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f661]) ).

fof(f661,plain,
    ( ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f660]) ).

fof(f19908,plain,
    ( spl0_1011
    | ~ spl0_85
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1827,f1815,f660,f19906]) ).

fof(f19906,plain,
    ( spl0_1011
  <=> ! [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_1011])]) ).

fof(f1827,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_85
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f661]) ).

fof(f19868,plain,
    ( spl0_1010
    | ~ spl0_112
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2108,f2104,f829,f19866]) ).

fof(f19866,plain,
    ( spl0_1010
  <=> ! [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_1010])]) ).

fof(f2104,plain,
    ( spl0_219
  <=> ! [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_219])]) ).

fof(f2108,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_112
    | ~ spl0_219 ),
    inference(resolution,[],[f2105,f830]) ).

fof(f2105,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_219 ),
    inference(avatar_component_clause,[],[f2104]) ).

fof(f19864,plain,
    ( spl0_1009
    | ~ spl0_102
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f836,f817,f756,f19862]) ).

fof(f19862,plain,
    ( spl0_1009
  <=> ! [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_1009])]) ).

fof(f836,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_102
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f757]) ).

fof(f19850,plain,
    ( ~ spl0_1007
    | spl0_1008
    | ~ spl0_42
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2141,f2131,f390,f19848,f19844]) ).

fof(f19844,plain,
    ( spl0_1007
  <=> operation(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f19848,plain,
    ( spl0_1008
  <=> ! [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_1008])]) ).

fof(f2141,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_42
    | ~ spl0_222 ),
    inference(superposition,[],[f2132,f391]) ).

fof(f19825,plain,
    ( spl0_1006
    | ~ spl0_864
    | ~ spl0_1005 ),
    inference(avatar_split_clause,[],[f19821,f19815,f16036,f19823]) ).

fof(f19823,plain,
    ( spl0_1006
  <=> ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f19815,plain,
    ( spl0_1005
  <=> ! [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_1005])]) ).

fof(f19821,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_1005 ),
    inference(forward_demodulation,[],[f19820,f16038]) ).

fof(f19820,plain,
    ( ! [X0,X1] :
        ( ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),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_864
    | ~ spl0_1005 ),
    inference(forward_demodulation,[],[f19819,f16038]) ).

fof(f19819,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,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_864
    | ~ spl0_1005 ),
    inference(forward_demodulation,[],[f19818,f16038]) ).

fof(f19818,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),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_864
    | ~ spl0_1005 ),
    inference(forward_demodulation,[],[f19816,f16038]) ).

fof(f19816,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_1005 ),
    inference(avatar_component_clause,[],[f19815]) ).

fof(f19817,plain,
    ( spl0_1005
    | ~ spl0_42
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2111,f2104,f390,f19815]) ).

fof(f2111,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_42
    | ~ spl0_219 ),
    inference(superposition,[],[f2105,f391]) ).

fof(f19667,plain,
    ( spl0_1004
    | ~ spl0_96
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1891,f1875,f729,f19665]) ).

fof(f19665,plain,
    ( spl0_1004
  <=> ! [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_1004])]) ).

fof(f729,plain,
    ( spl0_96
  <=> ! [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_96])]) ).

fof(f1891,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_96
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f730]) ).

fof(f730,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_96 ),
    inference(avatar_component_clause,[],[f729]) ).

fof(f19625,plain,
    ( spl0_1003
    | ~ spl0_78
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2107,f2104,f619,f19623]) ).

fof(f19623,plain,
    ( spl0_1003
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(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_1003])]) ).

fof(f2107,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_78
    | ~ spl0_219 ),
    inference(resolution,[],[f2105,f620]) ).

fof(f19621,plain,
    ( spl0_1001
    | ~ spl0_1002
    | ~ spl0_100
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1893,f1875,f745,f19618,f19615]) ).

fof(f19615,plain,
    ( spl0_1001
  <=> ! [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_1001])]) ).

fof(f19618,plain,
    ( spl0_1002
  <=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f745,plain,
    ( spl0_100
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1893,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_100
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f746]) ).

fof(f746,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f745]) ).

fof(f19613,plain,
    ( spl0_1000
    | ~ spl0_32
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f17836,f17629,f341,f19611]) ).

fof(f19611,plain,
    ( spl0_1000
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f341,plain,
    ( spl0_32
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f17836,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_32
    | ~ spl0_937 ),
    inference(resolution,[],[f17630,f342]) ).

fof(f342,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f19583,plain,
    ( spl0_999
    | ~ spl0_187
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2027,f2001,f1584,f19581]) ).

fof(f19581,plain,
    ( spl0_999
  <=> ! [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_999])]) ).

fof(f1584,plain,
    ( spl0_187
  <=> ! [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_187])]) ).

fof(f2027,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_187
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1585]) ).

fof(f1585,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_187 ),
    inference(avatar_component_clause,[],[f1584]) ).

fof(f19558,plain,
    ( spl0_998
    | ~ spl0_205
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1906,f1875,f1819,f19556]) ).

fof(f19556,plain,
    ( spl0_998
  <=> ! [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_998])]) ).

fof(f1906,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_205
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1820]) ).

fof(f19554,plain,
    ( spl0_997
    | ~ spl0_204
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1905,f1875,f1815,f19552]) ).

fof(f19552,plain,
    ( spl0_997
  <=> ! [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_997])]) ).

fof(f1905,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_204
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1816]) ).

fof(f19550,plain,
    ( spl0_996
    | ~ spl0_94
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1904,f1875,f708,f19548]) ).

fof(f19548,plain,
    ( spl0_996
  <=> ! [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_996])]) ).

fof(f1904,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_94
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f709]) ).

fof(f19545,plain,
    ( spl0_995
    | ~ spl0_101
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1736,f1717,f751,f19543]) ).

fof(f19543,plain,
    ( spl0_995
  <=> ! [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_995])]) ).

fof(f751,plain,
    ( spl0_101
  <=> ! [X4,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1736,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_101
    | ~ spl0_199 ),
    inference(superposition,[],[f752,f1718]) ).

fof(f752,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f751]) ).

fof(f19496,plain,
    ( spl0_994
    | ~ spl0_33
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f17835,f17629,f345,f19494]) ).

fof(f345,plain,
    ( spl0_33
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f17835,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_33
    | ~ spl0_937 ),
    inference(resolution,[],[f17630,f346]) ).

fof(f346,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f19492,plain,
    ( spl0_993
    | ~ spl0_206
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2037,f2005,f1875,f19490]) ).

fof(f19490,plain,
    ( spl0_993
  <=> ! [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_993])]) ).

fof(f2005,plain,
    ( spl0_213
  <=> ! [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_213])]) ).

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(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_206
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1876]) ).

fof(f2006,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_213 ),
    inference(avatar_component_clause,[],[f2005]) ).

fof(f19451,plain,
    ( spl0_992
    | ~ spl0_166
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2008,f2001,f1375,f19449]) ).

fof(f19449,plain,
    ( spl0_992
  <=> ! [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_992])]) ).

fof(f2008,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_166
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1376]) ).

fof(f19447,plain,
    ( spl0_991
    | ~ spl0_80
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1692,f1666,f634,f19445]) ).

fof(f19445,plain,
    ( spl0_991
  <=> ! [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_991])]) ).

fof(f634,plain,
    ( spl0_80
  <=> ! [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_80])]) ).

fof(f1692,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_80
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f635]) ).

fof(f635,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_80 ),
    inference(avatar_component_clause,[],[f634]) ).

fof(f19443,plain,
    ( spl0_990
    | ~ spl0_80
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1671,f1662,f634,f19441]) ).

fof(f19441,plain,
    ( spl0_990
  <=> ! [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_990])]) ).

fof(f1671,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_80
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f635]) ).

fof(f19394,plain,
    ( spl0_989
    | ~ spl0_93
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2056,f2005,f702,f19392]) ).

fof(f19392,plain,
    ( spl0_989
  <=> ! [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_989])]) ).

fof(f2056,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_93
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f703]) ).

fof(f19346,plain,
    ( spl0_988
    | ~ spl0_199
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2072,f2063,f1717,f19344]) ).

fof(f19344,plain,
    ( spl0_988
  <=> ! [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_988])]) ).

fof(f2063,plain,
    ( spl0_215
  <=> ! [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_215])]) ).

fof(f2072,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_199
    | ~ spl0_215 ),
    inference(superposition,[],[f2064,f1718]) ).

fof(f2064,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_215 ),
    inference(avatar_component_clause,[],[f2063]) ).

fof(f19342,plain,
    ( spl0_987
    | ~ spl0_67
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2029,f2001,f558,f19340]) ).

fof(f19340,plain,
    ( spl0_987
  <=> ! [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_987])]) ).

fof(f2029,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_67
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f559]) ).

fof(f19265,plain,
    ( spl0_986
    | ~ spl0_200
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2071,f2063,f1751,f19263]) ).

fof(f19263,plain,
    ( spl0_986
  <=> ! [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_986])]) ).

fof(f2071,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_200
    | ~ spl0_215 ),
    inference(resolution,[],[f2064,f1752]) ).

fof(f19260,plain,
    ( spl0_985
    | ~ spl0_210
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2053,f2005,f1942,f19258]) ).

fof(f19258,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))),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_985])]) ).

fof(f1942,plain,
    ( spl0_210
  <=> ! [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_210])]) ).

fof(f2053,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_210
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1943]) ).

fof(f1943,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_210 ),
    inference(avatar_component_clause,[],[f1942]) ).

fof(f19256,plain,
    ( spl0_984
    | ~ spl0_72
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2049,f2005,f579,f19254]) ).

fof(f19254,plain,
    ( spl0_984
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_984])]) ).

fof(f579,plain,
    ( spl0_72
  <=> ! [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_72])]) ).

fof(f2049,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_72
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f580]) ).

fof(f580,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_72 ),
    inference(avatar_component_clause,[],[f579]) ).

fof(f19200,plain,
    ( spl0_983
    | ~ spl0_685
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f18780,f18534,f11030,f19198]) ).

fof(f19198,plain,
    ( spl0_983
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).

fof(f11030,plain,
    ( spl0_685
  <=> ! [X0] :
        ( ~ subclass(y,X0)
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f18534,plain,
    ( spl0_961
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(second(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f18780,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(y,X0) )
    | ~ spl0_685
    | ~ spl0_961 ),
    inference(resolution,[],[f18535,f11031]) ).

fof(f11031,plain,
    ( ! [X0] :
        ( member(second(not_subclass_element(cross_product(x,y),z)),X0)
        | ~ subclass(y,X0) )
    | ~ spl0_685 ),
    inference(avatar_component_clause,[],[f11030]) ).

fof(f18535,plain,
    ( ! [X0] :
        ( ~ member(second(not_subclass_element(cross_product(x,y),z)),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_961 ),
    inference(avatar_component_clause,[],[f18534]) ).

fof(f19196,plain,
    ( spl0_982
    | ~ spl0_864
    | ~ spl0_981 ),
    inference(avatar_split_clause,[],[f19192,f19189,f16036,f19194]) ).

fof(f19194,plain,
    ( spl0_982
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,null_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f19189,plain,
    ( spl0_981
  <=> ! [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_981])]) ).

fof(f19192,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,null_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_864
    | ~ spl0_981 ),
    inference(forward_demodulation,[],[f19190,f16038]) ).

fof(f19190,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_981 ),
    inference(avatar_component_clause,[],[f19189]) ).

fof(f19191,plain,
    ( spl0_981
    | ~ spl0_210
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2025,f2001,f1942,f19189]) ).

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(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_210
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1943]) ).

fof(f19187,plain,
    ( spl0_980
    | ~ spl0_72
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2021,f2001,f579,f19185]) ).

fof(f19185,plain,
    ( spl0_980
  <=> ! [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_980])]) ).

fof(f2021,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_72
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f580]) ).

fof(f19161,plain,
    ( spl0_979
    | ~ spl0_199
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2058,f2005,f1717,f19159]) ).

fof(f19159,plain,
    ( spl0_979
  <=> ! [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_979])]) ).

fof(f2058,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_199
    | ~ spl0_213 ),
    inference(superposition,[],[f2006,f1718]) ).

fof(f19157,plain,
    ( spl0_978
    | ~ spl0_159
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1908,f1875,f1300,f19155]) ).

fof(f19155,plain,
    ( spl0_978
  <=> ! [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_978])]) ).

fof(f1300,plain,
    ( spl0_159
  <=> ! [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_159])]) ).

fof(f1908,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_159
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1301]) ).

fof(f1301,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_159 ),
    inference(avatar_component_clause,[],[f1300]) ).

fof(f19112,plain,
    ( spl0_977
    | ~ spl0_198
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2060,f2005,f1711,f19110]) ).

fof(f19110,plain,
    ( spl0_977
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_977])]) ).

fof(f2060,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_198
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f2051]) ).

fof(f2051,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_198
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1712]) ).

fof(f19087,plain,
    ( spl0_976
    | ~ spl0_200
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1868,f1819,f1751,f19085]) ).

fof(f19085,plain,
    ( spl0_976
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f1868,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_200
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1752]) ).

fof(f19083,plain,
    ( spl0_975
    | ~ spl0_200
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1842,f1815,f1751,f19081]) ).

fof(f19081,plain,
    ( spl0_975
  <=> ! [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_975])]) ).

fof(f1842,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_200
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1752]) ).

fof(f19079,plain,
    ( spl0_974
    | ~ spl0_94
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1772,f1751,f708,f19077]) ).

fof(f19077,plain,
    ( spl0_974
  <=> ! [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_974])]) ).

fof(f1772,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_94
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f709]) ).

fof(f19029,plain,
    ( spl0_973
    | ~ spl0_864
    | ~ spl0_972 ),
    inference(avatar_split_clause,[],[f19025,f19022,f16036,f19027]) ).

fof(f19027,plain,
    ( spl0_973
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f19022,plain,
    ( spl0_972
  <=> ! [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_972])]) ).

fof(f19025,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_864
    | ~ spl0_972 ),
    inference(forward_demodulation,[],[f19023,f16038]) ).

fof(f19023,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_972 ),
    inference(avatar_component_clause,[],[f19022]) ).

fof(f19024,plain,
    ( spl0_972
    | ~ spl0_207
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2052,f2005,f1913,f19022]) ).

fof(f1913,plain,
    ( spl0_207
  <=> ! [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_207])]) ).

fof(f2052,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_207
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1914]) ).

fof(f1914,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_207 ),
    inference(avatar_component_clause,[],[f1913]) ).

fof(f18974,plain,
    ( spl0_971
    | ~ spl0_864
    | ~ spl0_969 ),
    inference(avatar_split_clause,[],[f18965,f18962,f16036,f18972]) ).

fof(f18972,plain,
    ( spl0_971
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f18962,plain,
    ( spl0_969
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_969])]) ).

fof(f18965,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_864
    | ~ spl0_969 ),
    inference(forward_demodulation,[],[f18963,f16038]) ).

fof(f18963,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_969 ),
    inference(avatar_component_clause,[],[f18962]) ).

fof(f18970,plain,
    ( ~ spl0_970
    | ~ spl0_672
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f18797,f18534,f10551,f18967]) ).

fof(f18967,plain,
    ( spl0_970
  <=> subclass(universal_class,complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f10551,plain,
    ( spl0_672
  <=> member(second(not_subclass_element(cross_product(x,y),z)),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f18797,plain,
    ( ~ subclass(universal_class,complement(y))
    | ~ spl0_672
    | ~ spl0_961 ),
    inference(resolution,[],[f18535,f10553]) ).

fof(f10553,plain,
    ( member(second(not_subclass_element(cross_product(x,y),z)),y)
    | ~ spl0_672 ),
    inference(avatar_component_clause,[],[f10551]) ).

fof(f18964,plain,
    ( spl0_969
    | ~ spl0_207
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2024,f2001,f1913,f18962]) ).

fof(f2024,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_207
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1914]) ).

fof(f18810,plain,
    ( spl0_968
    | ~ spl0_136
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1857,f1819,f1093,f18808]) ).

fof(f18808,plain,
    ( spl0_968
  <=> ! [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_968])]) ).

fof(f1857,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_136
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1094]) ).

fof(f18806,plain,
    ( spl0_967
    | ~ spl0_135
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1851,f1819,f1089,f18804]) ).

fof(f18804,plain,
    ( spl0_967
  <=> ! [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_967])]) ).

fof(f1851,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_135
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1090]) ).

fof(f18802,plain,
    ( spl0_966
    | ~ spl0_136
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1831,f1815,f1093,f18800]) ).

fof(f18800,plain,
    ( spl0_966
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(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_966])]) ).

fof(f1831,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_136
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1094]) ).

fof(f18778,plain,
    ( spl0_965
    | ~ spl0_135
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1825,f1815,f1089,f18776]) ).

fof(f18776,plain,
    ( spl0_965
  <=> ! [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_965])]) ).

fof(f1825,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_135
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1090]) ).

fof(f18774,plain,
    ( spl0_964
    | ~ spl0_94
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1143,f1093,f708,f18772]) ).

fof(f18772,plain,
    ( spl0_964
  <=> ! [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_964])]) ).

fof(f1143,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_94
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f709]) ).

fof(f18770,plain,
    ( spl0_963
    | ~ spl0_94
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1125,f1089,f708,f18768]) ).

fof(f18768,plain,
    ( spl0_963
  <=> ! [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_963])]) ).

fof(f1125,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_94
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f709]) ).

fof(f18687,plain,
    ( spl0_962
    | ~ spl0_100
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1735,f1717,f745,f18685]) ).

fof(f18685,plain,
    ( spl0_962
  <=> ! [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_962])]) ).

fof(f1735,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_100
    | ~ spl0_199 ),
    inference(superposition,[],[f746,f1718]) ).

fof(f18536,plain,
    ( spl0_961
    | ~ spl0_21
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f17839,f17629,f293,f18534]) ).

fof(f17839,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_21
    | ~ spl0_937 ),
    inference(resolution,[],[f17630,f294]) ).

fof(f18505,plain,
    ( spl0_960
    | ~ spl0_130
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1864,f1819,f1014,f18503]) ).

fof(f18503,plain,
    ( spl0_960
  <=> ! [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_960])]) ).

fof(f1864,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_130
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1015]) ).

fof(f18501,plain,
    ( spl0_959
    | ~ spl0_129
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1856,f1819,f1010,f18499]) ).

fof(f18499,plain,
    ( spl0_959
  <=> ! [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_959])]) ).

fof(f1856,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_129
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1011]) ).

fof(f18497,plain,
    ( spl0_958
    | ~ spl0_130
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1838,f1815,f1014,f18495]) ).

fof(f18495,plain,
    ( spl0_958
  <=> ! [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_958])]) ).

fof(f1838,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_130
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1015]) ).

fof(f18493,plain,
    ( spl0_957
    | ~ spl0_129
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1830,f1815,f1010,f18491]) ).

fof(f18491,plain,
    ( spl0_957
  <=> ! [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_957])]) ).

fof(f1830,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_129
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1011]) ).

fof(f18489,plain,
    ( spl0_956
    | ~ spl0_94
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1056,f1014,f708,f18487]) ).

fof(f18487,plain,
    ( spl0_956
  <=> ! [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_956])]) ).

fof(f1056,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_94
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f709]) ).

fof(f18485,plain,
    ( spl0_955
    | ~ spl0_94
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1040,f1010,f708,f18483]) ).

fof(f18483,plain,
    ( spl0_955
  <=> ! [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_955])]) ).

fof(f1040,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_94
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f709]) ).

fof(f18435,plain,
    ( spl0_954
    | ~ spl0_27
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1850,f1819,f321,f18433]) ).

fof(f18433,plain,
    ( spl0_954
  <=> ! [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_954])]) ).

fof(f1850,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_205 ),
    inference(resolution,[],[f1820,f322]) ).

fof(f18430,plain,
    ( spl0_953
    | ~ spl0_27
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1824,f1815,f321,f18428]) ).

fof(f18428,plain,
    ( spl0_953
  <=> ! [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_953])]) ).

fof(f1824,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(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_204 ),
    inference(resolution,[],[f1816,f322]) ).

fof(f18393,plain,
    ( spl0_952
    | ~ spl0_112
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2091,f2087,f829,f18391]) ).

fof(f18391,plain,
    ( spl0_952
  <=> ! [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_952])]) ).

fof(f2087,plain,
    ( spl0_217
  <=> ! [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_217])]) ).

fof(f2091,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_112
    | ~ spl0_217 ),
    inference(resolution,[],[f2088,f830]) ).

fof(f2088,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_217 ),
    inference(avatar_component_clause,[],[f2087]) ).

fof(f18352,plain,
    ( spl0_951
    | ~ spl0_24
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1855,f1819,f305,f18350]) ).

fof(f18350,plain,
    ( spl0_951
  <=> ! [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_951])]) ).

fof(f1855,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_24
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f306]) ).

fof(f18348,plain,
    ( spl0_950
    | ~ spl0_24
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1829,f1815,f305,f18346]) ).

fof(f18346,plain,
    ( spl0_950
  <=> ! [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_950])]) ).

fof(f1829,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_24
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f306]) ).

fof(f18205,plain,
    ( spl0_949
    | ~ spl0_97
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1892,f1875,f733,f18203]) ).

fof(f18203,plain,
    ( spl0_949
  <=> ! [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_949])]) ).

fof(f733,plain,
    ( spl0_97
  <=> ! [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_97])]) ).

fof(f1892,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_97
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f734]) ).

fof(f734,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_97 ),
    inference(avatar_component_clause,[],[f733]) ).

fof(f18170,plain,
    ( spl0_948
    | ~ spl0_731
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f17812,f17629,f11962,f18168]) ).

fof(f18168,plain,
    ( spl0_948
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(y,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f11962,plain,
    ( spl0_731
  <=> ! [X0] :
        ( ~ subclass(y,complement(X0))
        | ~ member(second(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f17812,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(y,complement(X0)) )
    | ~ spl0_731
    | ~ spl0_937 ),
    inference(resolution,[],[f17630,f11963]) ).

fof(f11963,plain,
    ( ! [X0] :
        ( ~ member(second(not_subclass_element(cross_product(x,y),z)),X0)
        | ~ subclass(y,complement(X0)) )
    | ~ spl0_731 ),
    inference(avatar_component_clause,[],[f11962]) ).

fof(f18166,plain,
    ( spl0_947
    | ~ spl0_112
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2078,f2074,f829,f18164]) ).

fof(f18164,plain,
    ( spl0_947
  <=> ! [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_947])]) ).

fof(f2074,plain,
    ( spl0_216
  <=> ! [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_216])]) ).

fof(f2078,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_112
    | ~ spl0_216 ),
    inference(resolution,[],[f2075,f830]) ).

fof(f2075,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_216 ),
    inference(avatar_component_clause,[],[f2074]) ).

fof(f18110,plain,
    ( spl0_946
    | ~ spl0_99
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1734,f1717,f741,f18108]) ).

fof(f18108,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))),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_946])]) ).

fof(f741,plain,
    ( spl0_99
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1734,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_99
    | ~ spl0_199 ),
    inference(superposition,[],[f742,f1718]) ).

fof(f742,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f18106,plain,
    ( spl0_944
    | ~ spl0_945
    | ~ spl0_100
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1426,f1375,f745,f18103,f18100]) ).

fof(f18100,plain,
    ( spl0_944
  <=> ! [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_944])]) ).

fof(f18103,plain,
    ( spl0_945
  <=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f1426,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_100
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f746]) ).

fof(f17902,plain,
    ( spl0_943
    | ~ spl0_50
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2045,f2005,f454,f17900]) ).

fof(f17900,plain,
    ( spl0_943
  <=> ! [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_943])]) ).

fof(f454,plain,
    ( spl0_50
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f2045,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_50
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f455]) ).

fof(f455,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f454]) ).

fof(f17898,plain,
    ( spl0_942
    | ~ spl0_50
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2017,f2001,f454,f17896]) ).

fof(f17896,plain,
    ( spl0_942
  <=> ! [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_942])]) ).

fof(f2017,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_50
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f455]) ).

fof(f17761,plain,
    ( spl0_941
    | ~ spl0_45
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2047,f2005,f430,f17759]) ).

fof(f17759,plain,
    ( spl0_941
  <=> ! [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_941])]) ).

fof(f430,plain,
    ( spl0_45
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f2047,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_45
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f431]) ).

fof(f431,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f430]) ).

fof(f17757,plain,
    ( spl0_940
    | ~ spl0_45
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2019,f2001,f430,f17755]) ).

fof(f17755,plain,
    ( spl0_940
  <=> ! [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_940])]) ).

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(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_45
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f431]) ).

fof(f17753,plain,
    ( spl0_939
    | ~ spl0_80
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1631,f1626,f634,f17751]) ).

fof(f17751,plain,
    ( spl0_939
  <=> ! [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_939])]) ).

fof(f1626,plain,
    ( spl0_194
  <=> ! [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_194])]) ).

fof(f1631,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_80
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f635]) ).

fof(f1627,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_194 ),
    inference(avatar_component_clause,[],[f1626]) ).

fof(f17727,plain,
    ( spl0_938
    | ~ spl0_101
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12322,f1231,f751,f17725]) ).

fof(f17725,plain,
    ( spl0_938
  <=> ! [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(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))),composition_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(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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f12322,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(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))),composition_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(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_101
    | ~ spl0_148 ),
    inference(superposition,[],[f752,f1233]) ).

fof(f17631,plain,
    ( spl0_937
    | ~ spl0_5
    | ~ spl0_901 ),
    inference(avatar_split_clause,[],[f17381,f16801,f225,f17629]) ).

fof(f16801,plain,
    ( spl0_901
  <=> ! [X0,X1] :
        ( ~ subclass(y,X0)
        | ~ subclass(X0,X1)
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f17381,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_5
    | ~ spl0_901 ),
    inference(resolution,[],[f16802,f226]) ).

fof(f16802,plain,
    ( ! [X0,X1] :
        ( ~ subclass(y,X0)
        | ~ subclass(X0,X1)
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_901 ),
    inference(avatar_component_clause,[],[f16801]) ).

fof(f17407,plain,
    ( spl0_936
    | ~ spl0_30
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2041,f2005,f333,f17405]) ).

fof(f17405,plain,
    ( spl0_936
  <=> ! [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_936])]) ).

fof(f333,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

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(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_213 ),
    inference(resolution,[],[f2006,f334]) ).

fof(f334,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f333]) ).

fof(f17403,plain,
    ( spl0_935
    | ~ spl0_29
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2040,f2005,f329,f17401]) ).

fof(f17401,plain,
    ( spl0_935
  <=> ! [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_935])]) ).

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(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_213 ),
    inference(resolution,[],[f2006,f330]) ).

fof(f17399,plain,
    ( spl0_934
    | ~ spl0_199
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2030,f2001,f1717,f17397]) ).

fof(f17397,plain,
    ( spl0_934
  <=> ! [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_934])]) ).

fof(f2030,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_199
    | ~ spl0_212 ),
    inference(superposition,[],[f2002,f1718]) ).

fof(f17395,plain,
    ( spl0_933
    | ~ spl0_30
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2013,f2001,f333,f17393]) ).

fof(f17393,plain,
    ( spl0_933
  <=> ! [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_933])]) ).

fof(f2013,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_212 ),
    inference(resolution,[],[f2002,f334]) ).

fof(f17391,plain,
    ( spl0_932
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2012,f2001,f329,f17389]) ).

fof(f17389,plain,
    ( spl0_932
  <=> ! [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_932])]) ).

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(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_212 ),
    inference(resolution,[],[f2002,f330]) ).

fof(f17387,plain,
    ( spl0_931
    | ~ spl0_159
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1774,f1751,f1300,f17385]) ).

fof(f17385,plain,
    ( spl0_931
  <=> ! [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_931])]) ).

fof(f1774,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_159
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f1301]) ).

fof(f17379,plain,
    ( spl0_930
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1733,f1717,f733,f17377]) ).

fof(f17377,plain,
    ( spl0_930
  <=> ! [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_930])]) ).

fof(f1733,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_97
    | ~ spl0_199 ),
    inference(superposition,[],[f734,f1718]) ).

fof(f17328,plain,
    ( spl0_929
    | ~ spl0_864
    | ~ spl0_928 ),
    inference(avatar_split_clause,[],[f17324,f17319,f16036,f17326]) ).

fof(f17326,plain,
    ( spl0_929
  <=> ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f17319,plain,
    ( spl0_928
  <=> ! [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_928])]) ).

fof(f17324,plain,
    ( ! [X2,X0,X1] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_928 ),
    inference(forward_demodulation,[],[f17323,f16038]) ).

fof(f17323,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_928 ),
    inference(forward_demodulation,[],[f17322,f16038]) ).

fof(f17322,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_928 ),
    inference(forward_demodulation,[],[f17320,f16038]) ).

fof(f17320,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_928 ),
    inference(avatar_component_clause,[],[f17319]) ).

fof(f17321,plain,
    ( spl0_928
    | ~ spl0_42
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2094,f2087,f390,f17319]) ).

fof(f2094,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_42
    | ~ spl0_217 ),
    inference(superposition,[],[f2088,f391]) ).

fof(f17317,plain,
    ( spl0_927
    | ~ spl0_194
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1861,f1819,f1626,f17315]) ).

fof(f17315,plain,
    ( spl0_927
  <=> ! [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_927])]) ).

fof(f1861,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_194
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1627]) ).

fof(f17313,plain,
    ( spl0_926
    | ~ spl0_194
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1835,f1815,f1626,f17311]) ).

fof(f17311,plain,
    ( spl0_926
  <=> ! [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_926])]) ).

fof(f1835,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_194
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1627]) ).

fof(f17309,plain,
    ( spl0_925
    | ~ spl0_94
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1638,f1626,f708,f17307]) ).

fof(f17307,plain,
    ( spl0_925
  <=> ! [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_925])]) ).

fof(f1638,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_94
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f709]) ).

fof(f17304,plain,
    ( spl0_922
    | spl0_923
    | ~ spl0_924
    | ~ spl0_148
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f12340,f2100,f1231,f17301,f17297,f17293]) ).

fof(f17293,plain,
    ( spl0_922
  <=> domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),universal_class)),universal_class))))))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f17301,plain,
    ( spl0_924
  <=> member(composition_function,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f2100,plain,
    ( spl0_218
  <=> ! [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_218])]) ).

fof(f12340,plain,
    ( ~ member(composition_function,universal_class)
    | null_class = composition_function
    | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),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(composition_function,composition_function),universal_class)),universal_class)))))))))))
    | ~ spl0_148
    | ~ spl0_218 ),
    inference(superposition,[],[f2101,f1233]) ).

fof(f2101,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_218 ),
    inference(avatar_component_clause,[],[f2100]) ).

fof(f17279,plain,
    ( spl0_921
    | ~ spl0_864
    | ~ spl0_920 ),
    inference(avatar_split_clause,[],[f17275,f17270,f16036,f17277]) ).

fof(f17277,plain,
    ( spl0_921
  <=> ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f17270,plain,
    ( spl0_920
  <=> ! [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_920])]) ).

fof(f17275,plain,
    ( ! [X0,X1] :
        ( null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_920 ),
    inference(forward_demodulation,[],[f17274,f16038]) ).

fof(f17274,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_920 ),
    inference(forward_demodulation,[],[f17273,f16038]) ).

fof(f17273,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(null_class,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_864
    | ~ spl0_920 ),
    inference(forward_demodulation,[],[f17271,f16038]) ).

fof(f17271,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_920 ),
    inference(avatar_component_clause,[],[f17270]) ).

fof(f17272,plain,
    ( spl0_920
    | ~ spl0_42
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2081,f2074,f390,f17270]) ).

fof(f2081,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_42
    | ~ spl0_216 ),
    inference(superposition,[],[f2075,f391]) ).

fof(f17255,plain,
    ( spl0_919
    | ~ spl0_25
    | ~ spl0_101
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1881,f1875,f751,f309,f17253]) ).

fof(f17253,plain,
    ( spl0_919
  <=> ! [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_919])]) ).

fof(f309,plain,
    ( spl0_25
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1881,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_101
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f752]) ).

fof(f17225,plain,
    ( spl0_918
    | ~ spl0_112
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2067,f2063,f829,f17223]) ).

fof(f17223,plain,
    ( spl0_918
  <=> ! [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_918])]) ).

fof(f2067,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_112
    | ~ spl0_215 ),
    inference(resolution,[],[f2064,f830]) ).

fof(f17189,plain,
    ( spl0_917
    | ~ spl0_78
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2090,f2087,f619,f17187]) ).

fof(f17187,plain,
    ( spl0_917
  <=> ! [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_917])]) ).

fof(f2090,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_78
    | ~ spl0_217 ),
    inference(resolution,[],[f2088,f620]) ).

fof(f17056,plain,
    ( spl0_916
    | ~ spl0_78
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2077,f2074,f619,f17054]) ).

fof(f17054,plain,
    ( spl0_916
  <=> ! [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_916])]) ).

fof(f2077,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_78
    | ~ spl0_216 ),
    inference(resolution,[],[f2075,f620]) ).

fof(f17052,plain,
    ( spl0_915
    | ~ spl0_96
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1732,f1717,f729,f17050]) ).

fof(f17050,plain,
    ( spl0_915
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),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_915])]) ).

fof(f1732,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_96
    | ~ spl0_199 ),
    inference(superposition,[],[f730,f1718]) ).

fof(f16903,plain,
    ( spl0_913
    | spl0_914
    | ~ spl0_78
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2066,f2063,f619,f16901,f16898]) ).

fof(f16901,plain,
    ( spl0_914
  <=> ! [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_914])]) ).

fof(f2066,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_78
    | ~ spl0_215 ),
    inference(resolution,[],[f2064,f620]) ).

fof(f16896,plain,
    ( ~ spl0_911
    | ~ spl0_912
    | ~ spl0_236
    | ~ spl0_274
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11461,f11030,f2536,f2317,f16893,f16889]) ).

fof(f16889,plain,
    ( spl0_911
  <=> member(second(not_subclass_element(cross_product(x,y),z)),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f16893,plain,
    ( spl0_912
  <=> subclass(y,compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f11461,plain,
    ( ~ subclass(y,compose(element_relation,complement(singleton_relation)))
    | ~ member(second(not_subclass_element(cross_product(x,y),z)),singleton_relation)
    | ~ spl0_236
    | ~ spl0_274
    | ~ spl0_685 ),
    inference(forward_demodulation,[],[f11452,f2319]) ).

fof(f11452,plain,
    ( ~ subclass(y,compose(element_relation,complement(identity_relation)))
    | ~ member(second(not_subclass_element(cross_product(x,y),z)),singleton_relation)
    | ~ spl0_274
    | ~ spl0_685 ),
    inference(resolution,[],[f11031,f2537]) ).

fof(f16887,plain,
    ( spl0_910
    | ~ spl0_96
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1424,f1375,f729,f16885]) ).

fof(f16885,plain,
    ( spl0_910
  <=> ! [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_910])]) ).

fof(f1424,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_96
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f730]) ).

fof(f16883,plain,
    ( ~ spl0_908
    | spl0_909
    | ~ spl0_91
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1211,f1173,f692,f16881,f16877]) ).

fof(f16877,plain,
    ( spl0_908
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f16881,plain,
    ( spl0_909
  <=> ! [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_909])]) ).

fof(f1211,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_91
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f693]) ).

fof(f16874,plain,
    ( spl0_906
    | ~ spl0_907
    | ~ spl0_101
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f844,f817,f751,f16871,f16868]) ).

fof(f16868,plain,
    ( spl0_906
  <=> ! [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_906])]) ).

fof(f16871,plain,
    ( spl0_907
  <=> subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f844,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) )
    | ~ spl0_101
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f752]) ).

fof(f16866,plain,
    ( spl0_904
    | ~ spl0_905
    | ~ spl0_186
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1900,f1875,f1562,f16863,f16860]) ).

fof(f16860,plain,
    ( spl0_904
  <=> ! [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_904])]) ).

fof(f16863,plain,
    ( spl0_905
  <=> 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_905])]) ).

fof(f1900,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_186
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1563]) ).

fof(f16811,plain,
    ( spl0_903
    | ~ spl0_163
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2046,f2005,f1357,f16809]) ).

fof(f16809,plain,
    ( spl0_903
  <=> ! [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_903])]) ).

fof(f1357,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

fof(f2046,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_163
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1358]) ).

fof(f1358,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_163 ),
    inference(avatar_component_clause,[],[f1357]) ).

fof(f16807,plain,
    ( spl0_902
    | ~ spl0_163
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2018,f2001,f1357,f16805]) ).

fof(f16805,plain,
    ( spl0_902
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_902])]) ).

fof(f2018,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_163
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1358]) ).

fof(f16803,plain,
    ( spl0_901
    | ~ spl0_39
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11422,f11030,f378,f16801]) ).

fof(f11422,plain,
    ( ! [X0,X1] :
        ( ~ subclass(y,X0)
        | ~ subclass(X0,X1)
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_39
    | ~ spl0_685 ),
    inference(resolution,[],[f11031,f379]) ).

fof(f16781,plain,
    ( spl0_900
    | ~ spl0_172
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1859,f1819,f1462,f16779]) ).

fof(f16779,plain,
    ( spl0_900
  <=> ! [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_900])]) ).

fof(f1462,plain,
    ( spl0_172
  <=> ! [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_172])]) ).

fof(f1859,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_172
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1463]) ).

fof(f1463,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_172 ),
    inference(avatar_component_clause,[],[f1462]) ).

fof(f16777,plain,
    ( spl0_899
    | ~ spl0_172
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1833,f1815,f1462,f16775]) ).

fof(f16775,plain,
    ( spl0_899
  <=> ! [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_899])]) ).

fof(f1833,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_172
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1463]) ).

fof(f16773,plain,
    ( spl0_898
    | ~ spl0_94
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1512,f1462,f708,f16771]) ).

fof(f16771,plain,
    ( spl0_898
  <=> ! [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_898])]) ).

fof(f1512,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_94
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f709]) ).

fof(f16732,plain,
    ( spl0_897
    | ~ spl0_187
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2059,f2005,f1584,f16730]) ).

fof(f16730,plain,
    ( spl0_897
  <=> ! [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_897])]) ).

fof(f2059,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_187
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f2055]) ).

fof(f2055,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_187
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1585]) ).

fof(f16687,plain,
    ( spl0_896
    | ~ spl0_166
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2036,f2005,f1375,f16685]) ).

fof(f16685,plain,
    ( spl0_896
  <=> ! [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_896])]) ).

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(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_166
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1376]) ).

fof(f16681,plain,
    ( ~ spl0_81
    | spl0_180
    | ~ spl0_864 ),
    inference(avatar_split_clause,[],[f16043,f16036,f1528,f638]) ).

fof(f638,plain,
    ( spl0_81
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1528,plain,
    ( spl0_180
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f16043,plain,
    ( ~ member(null_class,universal_class)
    | spl0_180
    | ~ spl0_864 ),
    inference(superposition,[],[f1529,f16038]) ).

fof(f1529,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | spl0_180 ),
    inference(avatar_component_clause,[],[f1528]) ).

fof(f16639,plain,
    ( spl0_895
    | ~ spl0_42
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2097,f2087,f390,f16637]) ).

fof(f16637,plain,
    ( spl0_895
  <=> ! [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_895])]) ).

fof(f2097,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_42
    | ~ spl0_217 ),
    inference(superposition,[],[f2088,f391]) ).

fof(f16635,plain,
    ( spl0_894
    | ~ spl0_200
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1938,f1930,f1751,f16633]) ).

fof(f16633,plain,
    ( spl0_894
  <=> ! [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_894])]) ).

fof(f1930,plain,
    ( spl0_209
  <=> ! [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_209])]) ).

fof(f1938,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_200
    | ~ spl0_209 ),
    inference(resolution,[],[f1931,f1752]) ).

fof(f1931,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_209 ),
    inference(avatar_component_clause,[],[f1930]) ).

fof(f16631,plain,
    ( spl0_893
    | ~ spl0_166
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1858,f1819,f1375,f16629]) ).

fof(f16629,plain,
    ( spl0_893
  <=> ! [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_893])]) ).

fof(f1858,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_166
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1376]) ).

fof(f16627,plain,
    ( spl0_892
    | ~ spl0_166
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1832,f1815,f1375,f16625]) ).

fof(f16625,plain,
    ( spl0_892
  <=> ! [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_892])]) ).

fof(f1832,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_166
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1376]) ).

fof(f16623,plain,
    ( spl0_891
    | ~ spl0_94
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1436,f1375,f708,f16621]) ).

fof(f16621,plain,
    ( spl0_891
  <=> ! [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_891])]) ).

fof(f1436,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_94
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f709]) ).

fof(f16499,plain,
    ( spl0_890
    | ~ spl0_236
    | ~ spl0_884 ),
    inference(avatar_split_clause,[],[f16452,f16449,f2317,f16497]) ).

fof(f16497,plain,
    ( spl0_890
  <=> ! [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_890])]) ).

fof(f16449,plain,
    ( spl0_884
  <=> ! [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_884])]) ).

fof(f16452,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_236
    | ~ spl0_884 ),
    inference(forward_demodulation,[],[f16450,f2319]) ).

fof(f16450,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_884 ),
    inference(avatar_component_clause,[],[f16449]) ).

fof(f16495,plain,
    ( spl0_889
    | ~ spl0_236
    | ~ spl0_883 ),
    inference(avatar_split_clause,[],[f16447,f16444,f2317,f16493]) ).

fof(f16493,plain,
    ( spl0_889
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_889])]) ).

fof(f16444,plain,
    ( spl0_883
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_883])]) ).

fof(f16447,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_236
    | ~ spl0_883 ),
    inference(forward_demodulation,[],[f16445,f2319]) ).

fof(f16445,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_883 ),
    inference(avatar_component_clause,[],[f16444]) ).

fof(f16469,plain,
    ( spl0_888
    | ~ spl0_236
    | ~ spl0_881 ),
    inference(avatar_split_clause,[],[f16438,f16435,f2317,f16467]) ).

fof(f16467,plain,
    ( spl0_888
  <=> ! [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_888])]) ).

fof(f16435,plain,
    ( spl0_881
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_881])]) ).

fof(f16438,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_236
    | ~ spl0_881 ),
    inference(forward_demodulation,[],[f16436,f2319]) ).

fof(f16436,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_881 ),
    inference(avatar_component_clause,[],[f16435]) ).

fof(f16465,plain,
    ( spl0_887
    | ~ spl0_236
    | ~ spl0_880 ),
    inference(avatar_split_clause,[],[f16433,f16430,f2317,f16463]) ).

fof(f16463,plain,
    ( spl0_887
  <=> ! [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_887])]) ).

fof(f16430,plain,
    ( spl0_880
  <=> ! [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_880])]) ).

fof(f16433,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_236
    | ~ spl0_880 ),
    inference(forward_demodulation,[],[f16431,f2319]) ).

fof(f16431,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_880 ),
    inference(avatar_component_clause,[],[f16430]) ).

fof(f16461,plain,
    ( spl0_886
    | ~ spl0_124
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2054,f2005,f957,f16459]) ).

fof(f16459,plain,
    ( spl0_886
  <=> ! [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_886])]) ).

fof(f957,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f2054,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_124
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f958]) ).

fof(f958,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,null_class)
        | null_class = X0 )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f957]) ).

fof(f16457,plain,
    ( ~ spl0_885
    | ~ spl0_112
    | spl0_839 ),
    inference(avatar_split_clause,[],[f15771,f15544,f829,f16454]) ).

fof(f16454,plain,
    ( spl0_885
  <=> member(second(not_subclass_element(cross_product(x,y),z)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f15544,plain,
    ( spl0_839
  <=> member(second(not_subclass_element(cross_product(x,y),z)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f15771,plain,
    ( ~ member(second(not_subclass_element(cross_product(x,y),z)),subset_relation)
    | ~ spl0_112
    | spl0_839 ),
    inference(resolution,[],[f15545,f830]) ).

fof(f15545,plain,
    ( ~ member(second(not_subclass_element(cross_product(x,y),z)),cross_product(universal_class,universal_class))
    | spl0_839 ),
    inference(avatar_component_clause,[],[f15544]) ).

fof(f16451,plain,
    ( spl0_884
    | ~ spl0_126
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2050,f2005,f965,f16449]) ).

fof(f2050,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_126
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f966]) ).

fof(f16446,plain,
    ( spl0_883
    | ~ spl0_125
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2048,f2005,f961,f16444]) ).

fof(f2048,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_125
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f962]) ).

fof(f16442,plain,
    ( spl0_882
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2026,f2001,f957,f16440]) ).

fof(f16440,plain,
    ( spl0_882
  <=> ! [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_882])]) ).

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))),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_124
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f958]) ).

fof(f16437,plain,
    ( spl0_881
    | ~ spl0_126
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2022,f2001,f965,f16435]) ).

fof(f2022,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_126
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f966]) ).

fof(f16432,plain,
    ( spl0_880
    | ~ spl0_125
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2020,f2001,f961,f16430]) ).

fof(f2020,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_125
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f962]) ).

fof(f16304,plain,
    ( spl0_879
    | ~ spl0_67
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2057,f2005,f558,f16302]) ).

fof(f16302,plain,
    ( spl0_879
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_879])]) ).

fof(f2057,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_67
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f559]) ).

fof(f16300,plain,
    ( spl0_878
    | ~ spl0_143
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1910,f1875,f1165,f16298]) ).

fof(f16298,plain,
    ( spl0_878
  <=> ! [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_878])]) ).

fof(f1165,plain,
    ( spl0_143
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1910,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_143
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1166]) ).

fof(f1166,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,null_class)
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1165]) ).

fof(f16295,plain,
    ( spl0_876
    | ~ spl0_877
    | ~ spl0_145
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1907,f1875,f1173,f16292,f16289]) ).

fof(f16289,plain,
    ( spl0_876
  <=> ! [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_876])]) ).

fof(f16292,plain,
    ( spl0_877
  <=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f1907,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_145
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1174]) ).

fof(f16287,plain,
    ( ~ spl0_875
    | ~ spl0_236
    | spl0_874 ),
    inference(avatar_split_clause,[],[f16282,f16278,f2317,f16284]) ).

fof(f16284,plain,
    ( spl0_875
  <=> subclass(composition_function,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f16278,plain,
    ( spl0_874
  <=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f16282,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_236
    | spl0_874 ),
    inference(forward_demodulation,[],[f16280,f2319]) ).

fof(f16280,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
    | spl0_874 ),
    inference(avatar_component_clause,[],[f16278]) ).

fof(f16281,plain,
    ( spl0_873
    | ~ spl0_874
    | ~ spl0_144
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1902,f1875,f1169,f16278,f16275]) ).

fof(f16275,plain,
    ( spl0_873
  <=> ! [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_873])]) ).

fof(f1169,plain,
    ( spl0_144
  <=> ! [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_144])]) ).

fof(f1902,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_144
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1170]) ).

fof(f1170,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1169]) ).

fof(f16273,plain,
    ( spl0_872
    | ~ spl0_171
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1867,f1819,f1458,f16271]) ).

fof(f16271,plain,
    ( spl0_872
  <=> ! [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_872])]) ).

fof(f1458,plain,
    ( spl0_171
  <=> ! [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_171])]) ).

fof(f1867,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_171
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1459]) ).

fof(f1459,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_171 ),
    inference(avatar_component_clause,[],[f1458]) ).

fof(f16269,plain,
    ( spl0_871
    | ~ spl0_171
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1841,f1815,f1458,f16267]) ).

fof(f16267,plain,
    ( spl0_871
  <=> ! [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_871])]) ).

fof(f1841,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_171
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1459]) ).

fof(f16197,plain,
    ( ~ spl0_870
    | ~ spl0_23
    | spl0_859 ),
    inference(avatar_split_clause,[],[f16030,f15888,f301,f16194]) ).

fof(f16194,plain,
    ( spl0_870
  <=> function(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f301,plain,
    ( spl0_23
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f15888,plain,
    ( spl0_859
  <=> subclass(y,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f16030,plain,
    ( ~ function(y)
    | ~ spl0_23
    | spl0_859 ),
    inference(resolution,[],[f15890,f302]) ).

fof(f302,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f15890,plain,
    ( ~ subclass(y,cross_product(universal_class,universal_class))
    | spl0_859 ),
    inference(avatar_component_clause,[],[f15888]) ).

fof(f16192,plain,
    ( spl0_869
    | spl0_627
    | ~ spl0_80
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1506,f1462,f634,f9692,f16190]) ).

fof(f16190,plain,
    ( spl0_869
  <=> ! [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_869])]) ).

fof(f9692,plain,
    ( spl0_627
  <=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f1506,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_80
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f635]) ).

fof(f16188,plain,
    ( spl0_868
    | ~ spl0_94
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1494,f1458,f708,f16186]) ).

fof(f16186,plain,
    ( spl0_868
  <=> ! [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_868])]) ).

fof(f1494,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_94
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f709]) ).

fof(f16137,plain,
    ( spl0_867
    | ~ spl0_112
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2043,f2005,f829,f16135]) ).

fof(f16135,plain,
    ( spl0_867
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_867])]) ).

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(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_112
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f830]) ).

fof(f16133,plain,
    ( spl0_866
    | ~ spl0_112
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2015,f2001,f829,f16131]) ).

fof(f16131,plain,
    ( spl0_866
  <=> ! [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_866])]) ).

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(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_112
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f830]) ).

fof(f16042,plain,
    ( spl0_864
    | spl0_865
    | ~ spl0_42
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2084,f2074,f390,f16040,f16036]) ).

fof(f16040,plain,
    ( spl0_865
  <=> ! [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_865])]) ).

fof(f2084,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_42
    | ~ spl0_216 ),
    inference(superposition,[],[f2075,f391]) ).

fof(f16034,plain,
    ( spl0_863
    | ~ spl0_49
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1896,f1875,f450,f16032]) ).

fof(f16032,plain,
    ( spl0_863
  <=> ! [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_863])]) ).

fof(f450,plain,
    ( spl0_49
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f1896,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_49
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f451]) ).

fof(f451,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f450]) ).

fof(f16012,plain,
    ( spl0_862
    | ~ spl0_159
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1640,f1626,f1300,f16010]) ).

fof(f16010,plain,
    ( spl0_862
  <=> ! [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_862])]) ).

fof(f1640,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_159
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f1301]) ).

fof(f15995,plain,
    ( spl0_861
    | ~ spl0_186
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1768,f1751,f1562,f15993]) ).

fof(f15993,plain,
    ( spl0_861
  <=> ! [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_861])]) ).

fof(f1768,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_186
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f1563]) ).

fof(f15991,plain,
    ( spl0_860
    | ~ spl0_51
    | ~ spl0_72
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1660,f1645,f579,f458,f15989]) ).

fof(f15989,plain,
    ( spl0_860
  <=> ! [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_860])]) ).

fof(f1645,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

fof(f1660,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_51
    | ~ spl0_72
    | ~ spl0_195 ),
    inference(forward_demodulation,[],[f1656,f459]) ).

fof(f1656,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_72
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f580]) ).

fof(f1646,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_195 ),
    inference(avatar_component_clause,[],[f1645]) ).

fof(f15891,plain,
    ( ~ spl0_859
    | ~ spl0_685
    | spl0_839 ),
    inference(avatar_split_clause,[],[f15772,f15544,f11030,f15888]) ).

fof(f15772,plain,
    ( ~ subclass(y,cross_product(universal_class,universal_class))
    | ~ spl0_685
    | spl0_839 ),
    inference(resolution,[],[f15545,f11031]) ).

fof(f15886,plain,
    ( spl0_858
    | ~ spl0_236
    | ~ spl0_854 ),
    inference(avatar_split_clause,[],[f15870,f15867,f2317,f15884]) ).

fof(f15884,plain,
    ( spl0_858
  <=> ! [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_858])]) ).

fof(f15867,plain,
    ( spl0_854
  <=> ! [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_854])]) ).

fof(f15870,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_236
    | ~ spl0_854 ),
    inference(forward_demodulation,[],[f15868,f2319]) ).

fof(f15868,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_854 ),
    inference(avatar_component_clause,[],[f15867]) ).

fof(f15882,plain,
    ( spl0_857
    | ~ spl0_236
    | ~ spl0_853 ),
    inference(avatar_split_clause,[],[f15865,f15859,f2317,f15880]) ).

fof(f15880,plain,
    ( spl0_857
  <=> ! [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_857])]) ).

fof(f15859,plain,
    ( spl0_853
  <=> ! [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_853])]) ).

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(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_236
    | ~ spl0_853 ),
    inference(forward_demodulation,[],[f15864,f2319]) ).

fof(f15864,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_236
    | ~ spl0_853 ),
    inference(forward_demodulation,[],[f15863,f2319]) ).

fof(f15863,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_236
    | ~ spl0_853 ),
    inference(forward_demodulation,[],[f15862,f2319]) ).

fof(f15862,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_236
    | ~ spl0_853 ),
    inference(forward_demodulation,[],[f15860,f2319]) ).

fof(f15860,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_853 ),
    inference(avatar_component_clause,[],[f15859]) ).

fof(f15878,plain,
    ( spl0_856
    | ~ spl0_236
    | ~ spl0_852 ),
    inference(avatar_split_clause,[],[f15857,f15854,f2317,f15876]) ).

fof(f15876,plain,
    ( spl0_856
  <=> ! [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_856])]) ).

fof(f15854,plain,
    ( spl0_852
  <=> ! [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_852])]) ).

fof(f15857,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_236
    | ~ spl0_852 ),
    inference(forward_demodulation,[],[f15855,f2319]) ).

fof(f15855,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_852 ),
    inference(avatar_component_clause,[],[f15854]) ).

fof(f15874,plain,
    ( spl0_855
    | ~ spl0_236
    | ~ spl0_851 ),
    inference(avatar_split_clause,[],[f15852,f15846,f2317,f15872]) ).

fof(f15872,plain,
    ( spl0_855
  <=> ! [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_855])]) ).

fof(f15846,plain,
    ( spl0_851
  <=> ! [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_851])]) ).

fof(f15852,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_236
    | ~ spl0_851 ),
    inference(forward_demodulation,[],[f15851,f2319]) ).

fof(f15851,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_236
    | ~ spl0_851 ),
    inference(forward_demodulation,[],[f15850,f2319]) ).

fof(f15850,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_236
    | ~ spl0_851 ),
    inference(forward_demodulation,[],[f15849,f2319]) ).

fof(f15849,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_236
    | ~ spl0_851 ),
    inference(forward_demodulation,[],[f15847,f2319]) ).

fof(f15847,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_851 ),
    inference(avatar_component_clause,[],[f15846]) ).

fof(f15869,plain,
    ( spl0_854
    | ~ spl0_145
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1700,f1666,f1173,f15867]) ).

fof(f1700,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_145
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f1174]) ).

fof(f15861,plain,
    ( spl0_853
    | ~ spl0_144
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1697,f1666,f1169,f15859]) ).

fof(f1697,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_144
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f1170]) ).

fof(f15856,plain,
    ( spl0_852
    | ~ spl0_145
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1679,f1662,f1173,f15854]) ).

fof(f1679,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_145
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f1174]) ).

fof(f15848,plain,
    ( spl0_851
    | ~ spl0_144
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1676,f1662,f1169,f15846]) ).

fof(f1676,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_144
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f1170]) ).

fof(f15776,plain,
    ( spl0_627
    | spl0_850
    | ~ spl0_80
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1488,f1458,f634,f15774,f9692]) ).

fof(f15774,plain,
    ( spl0_850
  <=> ! [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_850])]) ).

fof(f1488,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_80
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f635]) ).

fof(f15758,plain,
    ( spl0_849
    | ~ spl0_199
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1947,f1942,f1717,f15756]) ).

fof(f15756,plain,
    ( spl0_849
  <=> ! [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_849])]) ).

fof(f1947,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_199
    | ~ spl0_210 ),
    inference(superposition,[],[f1943,f1718]) ).

fof(f15754,plain,
    ( spl0_847
    | ~ spl0_848
    | ~ spl0_100
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f849,f817,f745,f15751,f15748]) ).

fof(f15748,plain,
    ( spl0_847
  <=> ! [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_847])]) ).

fof(f15751,plain,
    ( spl0_848
  <=> subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f849,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_100
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f746]) ).

fof(f15720,plain,
    ( spl0_846
    | ~ spl0_177
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2016,f2001,f1483,f15718]) ).

fof(f15718,plain,
    ( spl0_846
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_846])]) ).

fof(f1483,plain,
    ( spl0_177
  <=> ! [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_177])]) ).

fof(f2016,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_177
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1484]) ).

fof(f1484,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_177 ),
    inference(avatar_component_clause,[],[f1483]) ).

fof(f15713,plain,
    ( ~ spl0_844
    | ~ spl0_845
    | spl0_628
    | ~ spl0_163
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1653,f1645,f1357,f9767,f15710,f15706]) ).

fof(f15706,plain,
    ( spl0_844
  <=> 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_844])]) ).

fof(f15710,plain,
    ( spl0_845
  <=> 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_845])]) ).

fof(f9767,plain,
    ( spl0_628
  <=> 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_628])]) ).

fof(f1653,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_163
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f1358]) ).

fof(f15653,plain,
    ( spl0_843
    | ~ spl0_177
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2061,f2005,f1483,f15651]) ).

fof(f15651,plain,
    ( spl0_843
  <=> ! [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_843])]) ).

fof(f2061,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_177
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f2044]) ).

fof(f2044,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_177
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1484]) ).

fof(f15649,plain,
    ( spl0_842
    | ~ spl0_90
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1945,f1942,f688,f15647]) ).

fof(f15647,plain,
    ( spl0_842
  <=> ! [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_842])]) ).

fof(f688,plain,
    ( spl0_90
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f1945,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_90
    | ~ spl0_210 ),
    inference(resolution,[],[f1943,f689]) ).

fof(f689,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f688]) ).

fof(f15555,plain,
    ( spl0_841
    | ~ spl0_236
    | ~ spl0_833 ),
    inference(avatar_split_clause,[],[f15513,f15510,f2317,f15553]) ).

fof(f15553,plain,
    ( spl0_841
  <=> ! [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_841])]) ).

fof(f15510,plain,
    ( spl0_833
  <=> ! [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_833])]) ).

fof(f15513,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_236
    | ~ spl0_833 ),
    inference(forward_demodulation,[],[f15511,f2319]) ).

fof(f15511,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_833 ),
    inference(avatar_component_clause,[],[f15510]) ).

fof(f15551,plain,
    ( spl0_839
    | ~ spl0_840
    | ~ spl0_77
    | ~ spl0_805 ),
    inference(avatar_split_clause,[],[f15202,f14722,f614,f15548,f15544]) ).

fof(f15548,plain,
    ( spl0_840
  <=> subclass(y,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f14722,plain,
    ( spl0_805
  <=> ! [X0,X1] :
        ( ~ subclass(y,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f15202,plain,
    ( ~ subclass(y,subset_relation)
    | member(second(not_subclass_element(cross_product(x,y),z)),cross_product(universal_class,universal_class))
    | ~ spl0_77
    | ~ spl0_805 ),
    inference(superposition,[],[f14723,f616]) ).

fof(f14723,plain,
    ( ! [X0,X1] :
        ( ~ subclass(y,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_805 ),
    inference(avatar_component_clause,[],[f14722]) ).

fof(f15542,plain,
    ( spl0_838
    | ~ spl0_236
    | ~ spl0_832 ),
    inference(avatar_split_clause,[],[f15508,f15505,f2317,f15540]) ).

fof(f15540,plain,
    ( spl0_838
  <=> ! [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_838])]) ).

fof(f15505,plain,
    ( spl0_832
  <=> ! [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_832])]) ).

fof(f15508,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_236
    | ~ spl0_832 ),
    inference(forward_demodulation,[],[f15506,f2319]) ).

fof(f15506,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_832 ),
    inference(avatar_component_clause,[],[f15505]) ).

fof(f15529,plain,
    ( spl0_837
    | ~ spl0_199
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1939,f1930,f1717,f15527]) ).

fof(f15527,plain,
    ( spl0_837
  <=> ! [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_837])]) ).

fof(f1939,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_199
    | ~ spl0_209 ),
    inference(superposition,[],[f1931,f1718]) ).

fof(f15525,plain,
    ( spl0_836
    | ~ spl0_153
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1860,f1819,f1253,f15523]) ).

fof(f15523,plain,
    ( spl0_836
  <=> ! [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_836])]) ).

fof(f1253,plain,
    ( spl0_153
  <=> ! [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_153])]) ).

fof(f1860,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_153
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1254]) ).

fof(f1254,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1253]) ).

fof(f15521,plain,
    ( spl0_835
    | ~ spl0_153
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1834,f1815,f1253,f15519]) ).

fof(f15519,plain,
    ( spl0_835
  <=> ! [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_835])]) ).

fof(f1834,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_153
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1254]) ).

fof(f15517,plain,
    ( spl0_834
    | ~ spl0_143
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1776,f1751,f1165,f15515]) ).

fof(f15515,plain,
    ( spl0_834
  <=> ! [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_834])]) ).

fof(f1776,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_143
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f1166]) ).

fof(f15512,plain,
    ( spl0_833
    | ~ spl0_145
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1773,f1751,f1173,f15510]) ).

fof(f1773,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_145
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f1174]) ).

fof(f15507,plain,
    ( spl0_832
    | ~ spl0_144
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1770,f1751,f1169,f15505]) ).

fof(f1770,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_144
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f1170]) ).

fof(f15503,plain,
    ( spl0_831
    | ~ spl0_94
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1273,f1253,f708,f15501]) ).

fof(f15501,plain,
    ( spl0_831
  <=> ! [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_831])]) ).

fof(f1273,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_94
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f709]) ).

fof(f15475,plain,
    ( spl0_830
    | ~ spl0_199
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1918,f1913,f1717,f15473]) ).

fof(f15473,plain,
    ( spl0_830
  <=> ! [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_830])]) ).

fof(f1918,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_199
    | ~ spl0_207 ),
    inference(superposition,[],[f1914,f1718]) ).

fof(f15471,plain,
    ( spl0_829
    | ~ spl0_49
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1764,f1751,f450,f15469]) ).

fof(f15469,plain,
    ( spl0_829
  <=> ! [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_829])]) ).

fof(f1764,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_49
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f451]) ).

fof(f15264,plain,
    ( spl0_828
    | ~ spl0_78
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2042,f2005,f619,f15262]) ).

fof(f15262,plain,
    ( spl0_828
  <=> ! [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_828])]) ).

fof(f2042,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_78
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f620]) ).

fof(f15260,plain,
    ( spl0_827
    | ~ spl0_78
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2014,f2001,f619,f15258]) ).

fof(f15258,plain,
    ( spl0_827
  <=> ! [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_827])]) ).

fof(f2014,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_78
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f620]) ).

fof(f15256,plain,
    ( ~ spl0_826
    | ~ spl0_23
    | spl0_825 ),
    inference(avatar_split_clause,[],[f15251,f15247,f301,f15253]) ).

fof(f15253,plain,
    ( spl0_826
  <=> function(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f15251,plain,
    ( ~ function(composition_function)
    | ~ spl0_23
    | spl0_825 ),
    inference(resolution,[],[f15249,f302]) ).

fof(f15250,plain,
    ( spl0_824
    | ~ spl0_825
    | ~ spl0_86
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1884,f1875,f670,f15247,f15244]) ).

fof(f15244,plain,
    ( spl0_824
  <=> ! [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_824])]) ).

fof(f670,plain,
    ( spl0_86
  <=> ! [X0,X1] :
        ( ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1884,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_86
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f671]) ).

fof(f671,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f670]) ).

fof(f15242,plain,
    ( spl0_823
    | ~ spl0_49
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1691,f1666,f450,f15240]) ).

fof(f15240,plain,
    ( spl0_823
  <=> ! [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_823])]) ).

fof(f1691,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_49
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f451]) ).

fof(f15238,plain,
    ( spl0_822
    | ~ spl0_49
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1670,f1662,f450,f15236]) ).

fof(f15236,plain,
    ( spl0_822
  <=> ! [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_822])]) ).

fof(f1670,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_49
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f451]) ).

fof(f15234,plain,
    ( spl0_821
    | ~ spl0_97
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1425,f1375,f733,f15232]) ).

fof(f15232,plain,
    ( spl0_821
  <=> ! [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_821])]) ).

fof(f1425,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_97
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f734]) ).

fof(f15228,plain,
    ( ~ spl0_820
    | ~ spl0_236
    | spl0_818 ),
    inference(avatar_split_clause,[],[f15220,f15212,f2317,f15225]) ).

fof(f15225,plain,
    ( spl0_820
  <=> 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_820])]) ).

fof(f15212,plain,
    ( spl0_818
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_818])]) ).

fof(f15220,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_236
    | spl0_818 ),
    inference(forward_demodulation,[],[f15213,f2319]) ).

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(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_818 ),
    inference(avatar_component_clause,[],[f15212]) ).

fof(f15219,plain,
    ( spl0_526
    | ~ spl0_817
    | spl0_818
    | ~ spl0_819
    | ~ spl0_85
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1215,f1173,f660,f15216,f15212,f15208,f7551]) ).

fof(f7551,plain,
    ( spl0_526
  <=> null_class = domain_of(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f15208,plain,
    ( spl0_817
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f15216,plain,
    ( spl0_819
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_819])]) ).

fof(f1215,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
    | ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_85
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f661]) ).

fof(f15190,plain,
    ( ~ spl0_816
    | ~ spl0_236
    | spl0_812 ),
    inference(avatar_split_clause,[],[f15174,f15165,f2317,f15187]) ).

fof(f15187,plain,
    ( spl0_816
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f15165,plain,
    ( spl0_812
  <=> 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_812])]) ).

fof(f15174,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_236
    | spl0_812 ),
    inference(forward_demodulation,[],[f15166,f2319]) ).

fof(f15166,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_812 ),
    inference(avatar_component_clause,[],[f15165]) ).

fof(f15185,plain,
    ( ~ spl0_815
    | ~ spl0_236
    | spl0_813 ),
    inference(avatar_split_clause,[],[f15173,f15169,f2317,f15182]) ).

fof(f15182,plain,
    ( spl0_815
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f15169,plain,
    ( spl0_813
  <=> 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_813])]) ).

fof(f15173,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_236
    | spl0_813 ),
    inference(forward_demodulation,[],[f15171,f2319]) ).

fof(f15171,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_813 ),
    inference(avatar_component_clause,[],[f15169]) ).

fof(f15180,plain,
    ( ~ spl0_814
    | ~ spl0_236
    | spl0_811 ),
    inference(avatar_split_clause,[],[f15175,f15161,f2317,f15177]) ).

fof(f15177,plain,
    ( spl0_814
  <=> member(complement(compose(element_relation,complement(singleton_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f15161,plain,
    ( spl0_811
  <=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f15175,plain,
    ( ~ member(complement(compose(element_relation,complement(singleton_relation))),universal_class)
    | ~ spl0_236
    | spl0_811 ),
    inference(forward_demodulation,[],[f15163,f2319]) ).

fof(f15163,plain,
    ( ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | spl0_811 ),
    inference(avatar_component_clause,[],[f15161]) ).

fof(f15172,plain,
    ( spl0_519
    | ~ spl0_811
    | spl0_812
    | ~ spl0_813
    | ~ spl0_85
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1201,f1169,f660,f15169,f15165,f15161,f7512]) ).

fof(f7512,plain,
    ( spl0_519
  <=> null_class = complement(compose(element_relation,complement(identity_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f1201,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_85
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f661]) ).

fof(f15150,plain,
    ( spl0_810
    | ~ spl0_39
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1946,f1942,f378,f15148]) ).

fof(f15148,plain,
    ( spl0_810
  <=> ! [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_810])]) ).

fof(f1946,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_39
    | ~ spl0_210 ),
    inference(resolution,[],[f1943,f379]) ).

fof(f14949,plain,
    ( spl0_809
    | ~ spl0_157
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1786,f1779,f1292,f14947]) ).

fof(f14947,plain,
    ( spl0_809
  <=> ! [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_809])]) ).

fof(f1292,plain,
    ( spl0_157
  <=> ! [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_157])]) ).

fof(f1779,plain,
    ( spl0_201
  <=> ! [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_201])]) ).

fof(f1786,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_157
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1293]) ).

fof(f1293,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_157 ),
    inference(avatar_component_clause,[],[f1292]) ).

fof(f1780,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_201 ),
    inference(avatar_component_clause,[],[f1779]) ).

fof(f14945,plain,
    ( spl0_808
    | ~ spl0_156
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1785,f1779,f1288,f14943]) ).

fof(f14943,plain,
    ( spl0_808
  <=> ! [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_808])]) ).

fof(f1288,plain,
    ( spl0_156
  <=> ! [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_156])]) ).

fof(f1785,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_156
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1289]) ).

fof(f1289,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_156 ),
    inference(avatar_component_clause,[],[f1288]) ).

fof(f14733,plain,
    ( spl0_807
    | ~ spl0_801
    | ~ spl0_806 ),
    inference(avatar_split_clause,[],[f14729,f14726,f14588,f14731]) ).

fof(f14731,plain,
    ( spl0_807
  <=> ! [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_807])]) ).

fof(f14726,plain,
    ( spl0_806
  <=> ! [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_806])]) ).

fof(f14729,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_801
    | ~ spl0_806 ),
    inference(forward_demodulation,[],[f14727,f14590]) ).

fof(f14590,plain,
    ( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_801 ),
    inference(avatar_component_clause,[],[f14588]) ).

fof(f14727,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_806 ),
    inference(avatar_component_clause,[],[f14726]) ).

fof(f14728,plain,
    ( spl0_806
    | ~ spl0_90
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1916,f1913,f688,f14726]) ).

fof(f1916,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_90
    | ~ spl0_207 ),
    inference(resolution,[],[f1914,f689]) ).

fof(f14724,plain,
    ( spl0_805
    | ~ spl0_32
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11436,f11030,f341,f14722]) ).

fof(f11436,plain,
    ( ! [X0,X1] :
        ( ~ subclass(y,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_32
    | ~ spl0_685 ),
    inference(resolution,[],[f11031,f342]) ).

fof(f14720,plain,
    ( spl0_804
    | ~ spl0_143
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1702,f1666,f1165,f14718]) ).

fof(f14718,plain,
    ( spl0_804
  <=> ! [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_804])]) ).

fof(f1702,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_143
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f1166]) ).

fof(f14716,plain,
    ( spl0_803
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1681,f1662,f1165,f14714]) ).

fof(f14714,plain,
    ( spl0_803
  <=> ! [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_803])]) ).

fof(f1681,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_143
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f1166]) ).

fof(f14594,plain,
    ( spl0_801
    | spl0_802
    | ~ spl0_42
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1949,f1942,f390,f14592,f14588]) ).

fof(f14592,plain,
    ( spl0_802
  <=> ! [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_802])]) ).

fof(f1949,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_42
    | ~ spl0_210 ),
    inference(superposition,[],[f1943,f391]) ).

fof(f14586,plain,
    ( spl0_800
    | ~ spl0_42
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1846,f1815,f390,f14584]) ).

fof(f14584,plain,
    ( spl0_800
  <=> ! [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_800])]) ).

fof(f1846,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_42
    | ~ spl0_204 ),
    inference(superposition,[],[f1816,f391]) ).

fof(f14579,plain,
    ( spl0_798
    | ~ spl0_799
    | ~ spl0_42
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1812,f1800,f390,f14576,f14573]) ).

fof(f14573,plain,
    ( spl0_798
  <=> ! [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_798])]) ).

fof(f14576,plain,
    ( spl0_799
  <=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f1800,plain,
    ( spl0_202
  <=> ! [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_202])]) ).

fof(f1812,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_42
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f391]) ).

fof(f1801,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_202 ),
    inference(avatar_component_clause,[],[f1800]) ).

fof(f14571,plain,
    ( spl0_797
    | ~ spl0_159
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1514,f1462,f1300,f14569]) ).

fof(f14569,plain,
    ( spl0_797
  <=> ! [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_797])]) ).

fof(f1514,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_159
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f1301]) ).

fof(f14567,plain,
    ( spl0_796
    | ~ spl0_33
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11435,f11030,f345,f14565]) ).

fof(f14565,plain,
    ( spl0_796
  <=> ! [X0,X1] :
        ( ~ subclass(y,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f11435,plain,
    ( ! [X0,X1] :
        ( ~ subclass(y,intersection(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_33
    | ~ spl0_685 ),
    inference(resolution,[],[f11031,f346]) ).

fof(f14521,plain,
    ( spl0_795
    | ~ spl0_50
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1652,f1645,f454,f14519]) ).

fof(f14519,plain,
    ( spl0_795
  <=> ! [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_795])]) ).

fof(f1652,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_50
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f455]) ).

fof(f14487,plain,
    ( spl0_794
    | ~ spl0_186
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1634,f1626,f1562,f14485]) ).

fof(f14485,plain,
    ( spl0_794
  <=> ! [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_794])]) ).

fof(f1634,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_186
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f1563]) ).

fof(f14404,plain,
    ( spl0_793
    | ~ spl0_131
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1866,f1819,f1018,f14402]) ).

fof(f14402,plain,
    ( spl0_793
  <=> ! [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_793])]) ).

fof(f1866,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_131
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1019]) ).

fof(f14400,plain,
    ( spl0_792
    | ~ spl0_131
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1840,f1815,f1018,f14398]) ).

fof(f14398,plain,
    ( spl0_792
  <=> ! [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_792])]) ).

fof(f1840,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_131
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1019]) ).

fof(f14396,plain,
    ( spl0_791
    | ~ spl0_115
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1796,f1779,f898,f14394]) ).

fof(f14394,plain,
    ( spl0_791
  <=> ! [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_791])]) ).

fof(f898,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1796,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_115
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f899]) ).

fof(f899,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f898]) ).

fof(f14392,plain,
    ( spl0_790
    | ~ spl0_94
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1074,f1018,f708,f14390]) ).

fof(f14390,plain,
    ( spl0_790
  <=> ! [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_790])]) ).

fof(f1074,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_94
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f709]) ).

fof(f14218,plain,
    ( spl0_789
    | ~ spl0_147
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1788,f1779,f1227,f14216]) ).

fof(f14216,plain,
    ( spl0_789
  <=> ! [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_789])]) ).

fof(f1227,plain,
    ( spl0_147
  <=> ! [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_147])]) ).

fof(f1788,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_147
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1228]) ).

fof(f1228,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1227]) ).

fof(f14214,plain,
    ( spl0_788
    | ~ spl0_159
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1438,f1375,f1300,f14212]) ).

fof(f14212,plain,
    ( spl0_788
  <=> ! [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_788])]) ).

fof(f1438,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_159
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f1301]) ).

fof(f14210,plain,
    ( spl0_787
    | ~ spl0_80
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1138,f1093,f634,f14208]) ).

fof(f14208,plain,
    ( spl0_787
  <=> ! [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_787])]) ).

fof(f1138,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_80
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f635]) ).

fof(f14206,plain,
    ( spl0_786
    | ~ spl0_80
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1120,f1089,f634,f14204]) ).

fof(f14204,plain,
    ( spl0_786
  <=> ! [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_786])]) ).

fof(f1120,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_80
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f635]) ).

fof(f14202,plain,
    ( ~ spl0_5
    | spl0_782 ),
    inference(avatar_contradiction_clause,[],[f14201]) ).

fof(f14201,plain,
    ( $false
    | ~ spl0_5
    | spl0_782 ),
    inference(resolution,[],[f13887,f226]) ).

fof(f13887,plain,
    ( ~ subclass(y,universal_class)
    | spl0_782 ),
    inference(avatar_component_clause,[],[f13885]) ).

fof(f13885,plain,
    ( spl0_782
  <=> subclass(y,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f14137,plain,
    ( spl0_785
    | ~ spl0_39
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1917,f1913,f378,f14135]) ).

fof(f14135,plain,
    ( spl0_785
  <=> ! [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_785])]) ).

fof(f1917,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_39
    | ~ spl0_207 ),
    inference(resolution,[],[f1914,f379]) ).

fof(f13896,plain,
    ( spl0_784
    | ~ spl0_109
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1865,f1819,f817,f13894]) ).

fof(f13894,plain,
    ( spl0_784
  <=> ! [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_784])]) ).

fof(f1865,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_109
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f818]) ).

fof(f13892,plain,
    ( ~ spl0_782
    | ~ spl0_783
    | ~ spl0_607
    | ~ spl0_770 ),
    inference(avatar_split_clause,[],[f13795,f13655,f9294,f13889,f13885]) ).

fof(f13889,plain,
    ( spl0_783
  <=> subclass(y,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f9294,plain,
    ( spl0_607
  <=> null_class = complement(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f13655,plain,
    ( spl0_770
  <=> ! [X0] :
        ( ~ subclass(y,complement(X0))
        | ~ subclass(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f13795,plain,
    ( ~ subclass(y,null_class)
    | ~ subclass(y,universal_class)
    | ~ spl0_607
    | ~ spl0_770 ),
    inference(superposition,[],[f13656,f9296]) ).

fof(f9296,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_607 ),
    inference(avatar_component_clause,[],[f9294]) ).

fof(f13656,plain,
    ( ! [X0] :
        ( ~ subclass(y,complement(X0))
        | ~ subclass(y,X0) )
    | ~ spl0_770 ),
    inference(avatar_component_clause,[],[f13655]) ).

fof(f13883,plain,
    ( spl0_781
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1848,f1819,f579,f13881]) ).

fof(f13881,plain,
    ( spl0_781
  <=> ! [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_781])]) ).

fof(f1848,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_72
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f580]) ).

fof(f13879,plain,
    ( spl0_780
    | ~ spl0_109
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1839,f1815,f817,f13877]) ).

fof(f13877,plain,
    ( spl0_780
  <=> ! [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_780])]) ).

fof(f1839,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_109
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f818]) ).

fof(f13875,plain,
    ( spl0_779
    | ~ spl0_72
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1822,f1815,f579,f13873]) ).

fof(f13873,plain,
    ( spl0_779
  <=> ! [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_779])]) ).

fof(f1822,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_72
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f580]) ).

fof(f13871,plain,
    ( spl0_778
    | ~ spl0_185
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1783,f1779,f1555,f13869]) ).

fof(f13869,plain,
    ( spl0_778
  <=> ! [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_778])]) ).

fof(f1555,plain,
    ( spl0_185
  <=> ! [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_185])]) ).

fof(f1783,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_185
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1556]) ).

fof(f1556,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_185 ),
    inference(avatar_component_clause,[],[f1555]) ).

fof(f13867,plain,
    ( spl0_777
    | ~ spl0_159
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1496,f1458,f1300,f13865]) ).

fof(f13865,plain,
    ( spl0_777
  <=> ! [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_777])]) ).

fof(f1496,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_159
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f1301]) ).

fof(f13863,plain,
    ( spl0_776
    | ~ spl0_94
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f857,f817,f708,f13861]) ).

fof(f13861,plain,
    ( spl0_776
  <=> ! [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_776])]) ).

fof(f857,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_94
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f709]) ).

fof(f13770,plain,
    ( spl0_775
    | ~ spl0_117
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1863,f1819,f925,f13768]) ).

fof(f13768,plain,
    ( spl0_775
  <=> ! [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_775])]) ).

fof(f1863,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_117
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f926]) ).

fof(f13766,plain,
    ( spl0_774
    | ~ spl0_117
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1837,f1815,f925,f13764]) ).

fof(f13764,plain,
    ( spl0_774
  <=> ! [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_774])]) ).

fof(f1837,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_117
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f926]) ).

fof(f13762,plain,
    ( spl0_773
    | ~ spl0_45
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1654,f1645,f430,f13760]) ).

fof(f13760,plain,
    ( spl0_773
  <=> ! [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_773])]) ).

fof(f1654,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_45
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f431]) ).

fof(f13758,plain,
    ( spl0_772
    | ~ spl0_164
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1623,f1620,f1367,f13756]) ).

fof(f13756,plain,
    ( spl0_772
  <=> ! [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_772])]) ).

fof(f1367,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

fof(f1620,plain,
    ( spl0_193
  <=> ! [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_193])]) ).

fof(f1623,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_164
    | ~ spl0_193 ),
    inference(resolution,[],[f1621,f1368]) ).

fof(f1368,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_164 ),
    inference(avatar_component_clause,[],[f1367]) ).

fof(f1621,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_193 ),
    inference(avatar_component_clause,[],[f1620]) ).

fof(f13754,plain,
    ( spl0_771
    | ~ spl0_94
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f990,f925,f708,f13752]) ).

fof(f13752,plain,
    ( spl0_771
  <=> ! [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_771])]) ).

fof(f990,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_94
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f709]) ).

fof(f13657,plain,
    ( spl0_770
    | ~ spl0_685
    | ~ spl0_731 ),
    inference(avatar_split_clause,[],[f13100,f11962,f11030,f13655]) ).

fof(f13100,plain,
    ( ! [X0] :
        ( ~ subclass(y,complement(X0))
        | ~ subclass(y,X0) )
    | ~ spl0_685
    | ~ spl0_731 ),
    inference(resolution,[],[f11963,f11031]) ).

fof(f13615,plain,
    ( spl0_769
    | ~ spl0_109
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2038,f2005,f817,f13613]) ).

fof(f13613,plain,
    ( spl0_769
  <=> ! [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_769])]) ).

fof(f2038,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_109
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f818]) ).

fof(f13611,plain,
    ( spl0_768
    | ~ spl0_109
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2010,f2001,f817,f13609]) ).

fof(f13609,plain,
    ( spl0_768
  <=> ! [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_768])]) ).

fof(f2010,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_109
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f818]) ).

fof(f13607,plain,
    ( spl0_767
    | ~ spl0_112
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1934,f1930,f829,f13605]) ).

fof(f13605,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(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_767])]) ).

fof(f1934,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_209 ),
    inference(resolution,[],[f1931,f830]) ).

fof(f13603,plain,
    ( spl0_766
    | ~ spl0_42
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1870,f1819,f390,f13601]) ).

fof(f13601,plain,
    ( spl0_766
  <=> ! [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_766])]) ).

fof(f1870,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_42
    | ~ spl0_205 ),
    inference(superposition,[],[f1820,f391]) ).

fof(f13599,plain,
    ( spl0_765
    | ~ spl0_163
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1398,f1371,f1357,f13597]) ).

fof(f13597,plain,
    ( spl0_765
  <=> ! [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_765])]) ).

fof(f1371,plain,
    ( spl0_165
  <=> ! [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_165])]) ).

fof(f1398,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_163
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f1358]) ).

fof(f1372,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_165 ),
    inference(avatar_component_clause,[],[f1371]) ).

fof(f13567,plain,
    ( spl0_764
    | ~ spl0_39
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1895,f1875,f378,f13565]) ).

fof(f13565,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f1895,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_39
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f379]) ).

fof(f13563,plain,
    ( spl0_763
    | ~ spl0_42
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1809,f1800,f390,f13561]) ).

fof(f13561,plain,
    ( spl0_763
  <=> ! [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_763])]) ).

fof(f1809,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_42
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f391]) ).

fof(f13492,plain,
    ( spl0_762
    | spl0_627
    | ~ spl0_80
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1267,f1253,f634,f9692,f13490]) ).

fof(f13490,plain,
    ( spl0_762
  <=> ! [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_762])]) ).

fof(f1267,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_80
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f635]) ).

fof(f13253,plain,
    ( ~ spl0_761
    | ~ spl0_672
    | ~ spl0_731 ),
    inference(avatar_split_clause,[],[f13117,f11962,f10551,f13250]) ).

fof(f13250,plain,
    ( spl0_761
  <=> subclass(y,complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f13117,plain,
    ( ~ subclass(y,complement(y))
    | ~ spl0_672
    | ~ spl0_731 ),
    inference(resolution,[],[f11963,f10553]) ).

fof(f13155,plain,
    ( spl0_760
    | ~ spl0_32
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1899,f1875,f341,f13153]) ).

fof(f13153,plain,
    ( spl0_760
  <=> ! [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_760])]) ).

fof(f1899,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_32
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f342]) ).

fof(f13151,plain,
    ( spl0_759
    | ~ spl0_33
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1898,f1875,f345,f13149]) ).

fof(f13149,plain,
    ( spl0_759
  <=> ! [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_759])]) ).

fof(f1898,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_33
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f346]) ).

fof(f13147,plain,
    ( spl0_758
    | ~ spl0_90
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1888,f1875,f688,f13145]) ).

fof(f13145,plain,
    ( spl0_758
  <=> ! [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_758])]) ).

fof(f1888,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,compose(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_90
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f689]) ).

fof(f13143,plain,
    ( spl0_757
    | ~ spl0_86
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1756,f1751,f670,f13141]) ).

fof(f13141,plain,
    ( spl0_757
  <=> ! [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_757])]) ).

fof(f1756,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_86
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f671]) ).

fof(f13139,plain,
    ( spl0_756
    | ~ spl0_164
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1749,f1717,f1367,f13137]) ).

fof(f13137,plain,
    ( spl0_756
  <=> ! [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_756])]) ).

fof(f1749,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_164
    | ~ spl0_199 ),
    inference(superposition,[],[f1368,f1718]) ).

fof(f13135,plain,
    ( spl0_755
    | ~ spl0_92
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1731,f1717,f698,f13133]) ).

fof(f13133,plain,
    ( spl0_755
  <=> ! [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_755])]) ).

fof(f698,plain,
    ( spl0_92
  <=> ! [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_92])]) ).

fof(f1731,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_92
    | ~ spl0_199 ),
    inference(superposition,[],[f699,f1718]) ).

fof(f699,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_92 ),
    inference(avatar_component_clause,[],[f698]) ).

fof(f13131,plain,
    ( spl0_754
    | ~ spl0_85
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1187,f1165,f660,f13129]) ).

fof(f13129,plain,
    ( spl0_754
  <=> ! [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_754])]) ).

fof(f1187,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
        | null_class = X0
        | ~ member(regular(X0),universal_class)
        | null_class = regular(X0) )
    | ~ spl0_85
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f661]) ).

fof(f13127,plain,
    ( spl0_753
    | ~ spl0_80
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1051,f1014,f634,f13125]) ).

fof(f13125,plain,
    ( spl0_753
  <=> ! [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_753])]) ).

fof(f1051,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_80
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f635]) ).

fof(f13123,plain,
    ( spl0_752
    | ~ spl0_80
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1035,f1010,f634,f13121]) ).

fof(f13121,plain,
    ( spl0_752
  <=> ! [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_752])]) ).

fof(f1035,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_80
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f635]) ).

fof(f12942,plain,
    ( spl0_751
    | ~ spl0_10
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2039,f2005,f246,f12940]) ).

fof(f12940,plain,
    ( spl0_751
  <=> ! [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_751])]) ).

fof(f2039,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_10
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f247]) ).

fof(f12938,plain,
    ( spl0_750
    | ~ spl0_10
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2011,f2001,f246,f12936]) ).

fof(f12936,plain,
    ( spl0_750
  <=> ! [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_750])]) ).

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(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_10
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f247]) ).

fof(f12934,plain,
    ( spl0_749
    | ~ spl0_21
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1901,f1875,f293,f12932]) ).

fof(f12932,plain,
    ( spl0_749
  <=> ! [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_749])]) ).

fof(f1901,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_21
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f294]) ).

fof(f12847,plain,
    ( spl0_748
    | ~ spl0_148
    | ~ spl0_747 ),
    inference(avatar_split_clause,[],[f12841,f12837,f1231,f12844]) ).

fof(f12837,plain,
    ( spl0_747
  <=> 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_747])]) ).

fof(f12841,plain,
    ( not_subclass_element(composition_function,application_function) = unordered_pair(unordered_pair(first(not_subclass_element(composition_function,application_function)),first(not_subclass_element(composition_function,application_function))),unordered_pair(first(not_subclass_element(composition_function,application_function)),unordered_pair(second(not_subclass_element(composition_function,application_function)),second(not_subclass_element(composition_function,application_function)))))
    | ~ spl0_148
    | ~ spl0_747 ),
    inference(forward_demodulation,[],[f12839,f1233]) ).

fof(f12839,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_747 ),
    inference(avatar_component_clause,[],[f12837]) ).

fof(f12840,plain,
    ( spl0_747
    | spl0_151
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1792,f1779,f1244,f12837]) ).

fof(f1244,plain,
    ( spl0_151
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1792,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_151
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1246]) ).

fof(f1246,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | spl0_151 ),
    inference(avatar_component_clause,[],[f1244]) ).

fof(f12738,plain,
    ( spl0_746
    | ~ spl0_148
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f12337,f1555,f1231,f12736]) ).

fof(f12736,plain,
    ( spl0_746
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(X1,universal_class)
        | ~ member(X2,cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f12337,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(X1,universal_class)
        | ~ member(X2,cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0) )
    | ~ spl0_148
    | ~ spl0_185 ),
    inference(superposition,[],[f1556,f1233]) ).

fof(f12655,plain,
    ( spl0_745
    | ~ spl0_80
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12335,f1231,f634,f12653]) ).

fof(f12653,plain,
    ( spl0_745
  <=> ! [X0] :
        ( ~ member(X0,composition_function)
        | 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_745])]) ).

fof(f12335,plain,
    ( ! [X0] :
        ( ~ member(X0,composition_function)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
    | ~ spl0_80
    | ~ spl0_148 ),
    inference(superposition,[],[f635,f1233]) ).

fof(f12651,plain,
    ( spl0_744
    | ~ spl0_78
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12334,f1231,f619,f12649]) ).

fof(f12649,plain,
    ( spl0_744
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f12334,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_148 ),
    inference(superposition,[],[f620,f1233]) ).

fof(f12632,plain,
    ( spl0_743
    | ~ spl0_68
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12332,f1231,f562,f12630]) ).

fof(f12332,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | member(X1,cross_product(universal_class,universal_class)) )
    | ~ spl0_68
    | ~ spl0_148 ),
    inference(superposition,[],[f563,f1233]) ).

fof(f12613,plain,
    ( ~ spl0_742
    | ~ spl0_148
    | spl0_272 ),
    inference(avatar_split_clause,[],[f12325,f2525,f1231,f12610]) ).

fof(f12610,plain,
    ( spl0_742
  <=> member(null_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f2525,plain,
    ( spl0_272
  <=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f12325,plain,
    ( ~ member(null_class,composition_function)
    | ~ spl0_148
    | spl0_272 ),
    inference(superposition,[],[f2526,f1233]) ).

fof(f2526,plain,
    ( ~ member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | spl0_272 ),
    inference(avatar_component_clause,[],[f2525]) ).

fof(f12608,plain,
    ( spl0_741
    | ~ spl0_69
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12333,f1231,f566,f12606]) ).

fof(f566,plain,
    ( spl0_69
  <=> ! [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_69])]) ).

fof(f12333,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),composition_function)
        | member(X0,universal_class) )
    | ~ spl0_69
    | ~ spl0_148 ),
    inference(superposition,[],[f567,f1233]) ).

fof(f567,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_69 ),
    inference(avatar_component_clause,[],[f566]) ).

fof(f12604,plain,
    ( ~ spl0_740
    | ~ spl0_737
    | spl0_739 ),
    inference(avatar_split_clause,[],[f12599,f12595,f12397,f12601]) ).

fof(f12601,plain,
    ( spl0_740
  <=> member(domain_of(intersection(composition_function,element_relation)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f12397,plain,
    ( spl0_737
  <=> ! [X0] : intersection(X0,composition_function) = intersection(composition_function,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f12595,plain,
    ( spl0_739
  <=> member(domain_of(intersection(element_relation,composition_function)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f12599,plain,
    ( ~ member(domain_of(intersection(composition_function,element_relation)),universal_class)
    | ~ spl0_737
    | spl0_739 ),
    inference(forward_demodulation,[],[f12596,f12398]) ).

fof(f12398,plain,
    ( ! [X0] : intersection(X0,composition_function) = intersection(composition_function,X0)
    | ~ spl0_737 ),
    inference(avatar_component_clause,[],[f12397]) ).

fof(f12596,plain,
    ( ~ member(domain_of(intersection(element_relation,composition_function)),universal_class)
    | spl0_739 ),
    inference(avatar_component_clause,[],[f12595]) ).

fof(f12598,plain,
    ( ~ spl0_738
    | spl0_739
    | ~ spl0_56
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12330,f1231,f478,f12595,f12591]) ).

fof(f12591,plain,
    ( spl0_738
  <=> member(cross_product(universal_class,universal_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f478,plain,
    ( spl0_56
  <=> ! [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_56])]) ).

fof(f12330,plain,
    ( member(domain_of(intersection(element_relation,composition_function)),universal_class)
    | ~ member(cross_product(universal_class,universal_class),universal_class)
    | ~ spl0_56
    | ~ spl0_148 ),
    inference(superposition,[],[f479,f1233]) ).

fof(f479,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f12399,plain,
    ( spl0_737
    | ~ spl0_51
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12331,f1231,f458,f12397]) ).

fof(f12331,plain,
    ( ! [X0] : intersection(X0,composition_function) = intersection(composition_function,X0)
    | ~ spl0_51
    | ~ spl0_148 ),
    inference(superposition,[],[f459,f1233]) ).

fof(f12391,plain,
    ( ~ spl0_736
    | ~ spl0_148
    | spl0_150 ),
    inference(avatar_split_clause,[],[f12323,f1240,f1231,f12388]) ).

fof(f12388,plain,
    ( spl0_736
  <=> composition_function = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f1240,plain,
    ( spl0_150
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f12323,plain,
    ( composition_function != application_function
    | ~ spl0_148
    | spl0_150 ),
    inference(superposition,[],[f1241,f1233]) ).

fof(f1241,plain,
    ( cross_product(universal_class,cross_product(universal_class,universal_class)) != application_function
    | spl0_150 ),
    inference(avatar_component_clause,[],[f1240]) ).

fof(f12386,plain,
    ( spl0_735
    | ~ spl0_26
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12321,f1231,f314,f12383]) ).

fof(f314,plain,
    ( spl0_26
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f12321,plain,
    ( subclass(application_function,composition_function)
    | ~ spl0_26
    | ~ spl0_148 ),
    inference(superposition,[],[f316,f1233]) ).

fof(f316,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f314]) ).

fof(f12319,plain,
    ( spl0_734
    | spl0_149
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1790,f1779,f1235,f12316]) ).

fof(f12316,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(f1235,plain,
    ( spl0_149
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1790,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_149
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1237]) ).

fof(f1237,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | spl0_149 ),
    inference(avatar_component_clause,[],[f1235]) ).

fof(f12314,plain,
    ( spl0_733
    | ~ spl0_140
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1789,f1779,f1110,f12312]) ).

fof(f12312,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(f1110,plain,
    ( spl0_140
  <=> ! [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_140])]) ).

fof(f1789,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_140
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1111]) ).

fof(f1111,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1110]) ).

fof(f11968,plain,
    ( spl0_732
    | ~ spl0_236
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f11930,f11927,f2317,f11966]) ).

fof(f11966,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(f11927,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(f11930,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_236
    | ~ spl0_723 ),
    inference(forward_demodulation,[],[f11928,f2319]) ).

fof(f11928,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,[],[f11927]) ).

fof(f11964,plain,
    ( spl0_731
    | ~ spl0_21
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11439,f11030,f293,f11962]) ).

fof(f11439,plain,
    ( ! [X0] :
        ( ~ subclass(y,complement(X0))
        | ~ member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_21
    | ~ spl0_685 ),
    inference(resolution,[],[f11031,f294]) ).

fof(f11960,plain,
    ( spl0_730
    | ~ spl0_236
    | ~ spl0_722 ),
    inference(avatar_split_clause,[],[f11925,f11922,f2317,f11958]) ).

fof(f11958,plain,
    ( spl0_730
  <=> ! [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_730])]) ).

fof(f11922,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(f11925,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_236
    | ~ spl0_722 ),
    inference(forward_demodulation,[],[f11923,f2319]) ).

fof(f11923,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,[],[f11922]) ).

fof(f11956,plain,
    ( spl0_729
    | ~ spl0_10
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1923,f1920,f246,f11954]) ).

fof(f11954,plain,
    ( spl0_729
  <=> ! [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_729])]) ).

fof(f1920,plain,
    ( spl0_208
  <=> ! [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_208])]) ).

fof(f1923,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_10
    | ~ spl0_208 ),
    inference(resolution,[],[f1921,f247]) ).

fof(f1921,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_208 ),
    inference(avatar_component_clause,[],[f1920]) ).

fof(f11952,plain,
    ( ~ spl0_728
    | ~ spl0_236
    | spl0_727 ),
    inference(avatar_split_clause,[],[f11947,f11943,f2317,f11949]) ).

fof(f11949,plain,
    ( spl0_728
  <=> subclass(composition_function,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f11943,plain,
    ( spl0_727
  <=> subclass(composition_function,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f11947,plain,
    ( ~ subclass(composition_function,singleton_relation)
    | ~ spl0_236
    | spl0_727 ),
    inference(forward_demodulation,[],[f11945,f2319]) ).

fof(f11945,plain,
    ( ~ subclass(composition_function,identity_relation)
    | spl0_727 ),
    inference(avatar_component_clause,[],[f11943]) ).

fof(f11946,plain,
    ( spl0_726
    | ~ spl0_727
    | ~ spl0_103
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1909,f1875,f763,f11943,f11940]) ).

fof(f11940,plain,
    ( spl0_726
  <=> ! [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_726])]) ).

fof(f1909,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_206 ),
    inference(resolution,[],[f1876,f764]) ).

fof(f11938,plain,
    ( spl0_725
    | ~ spl0_161
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1747,f1717,f1322,f11936]) ).

fof(f11936,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(f1322,plain,
    ( spl0_161
  <=> ! [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_161])]) ).

fof(f1747,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_161
    | ~ spl0_199 ),
    inference(superposition,[],[f1323,f1718]) ).

fof(f1323,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1322]) ).

fof(f11934,plain,
    ( spl0_724
    | ~ spl0_143
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1642,f1626,f1165,f11932]) ).

fof(f11932,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(f1642,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_143
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f1166]) ).

fof(f11929,plain,
    ( spl0_723
    | ~ spl0_145
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1639,f1626,f1173,f11927]) ).

fof(f1639,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_145
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f1174]) ).

fof(f11924,plain,
    ( spl0_722
    | ~ spl0_144
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1636,f1626,f1169,f11922]) ).

fof(f1636,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_144
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f1170]) ).

fof(f11884,plain,
    ( spl0_721
    | ~ spl0_40
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1795,f1779,f382,f11882]) ).

fof(f11882,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(f1795,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_40
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f383]) ).

fof(f11880,plain,
    ( spl0_720
    | ~ spl0_90
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1760,f1751,f688,f11878]) ).

fof(f11878,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(f1760,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_90
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f689]) ).

fof(f11876,plain,
    ( spl0_719
    | ~ spl0_95
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f887,f829,f724,f11874]) ).

fof(f11874,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(f724,plain,
    ( spl0_95
  <=> ! [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_95])]) ).

fof(f887,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_95
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f725]) ).

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

fof(f11785,plain,
    ( spl0_718
    | ~ spl0_51
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1845,f1815,f458,f11783]) ).

fof(f11783,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(f1845,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_51
    | ~ spl0_204 ),
    inference(superposition,[],[f1816,f459]) ).

fof(f11781,plain,
    ( spl0_717
    | ~ spl0_133
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1746,f1717,f1026,f11779]) ).

fof(f11779,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(f1026,plain,
    ( spl0_133
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1746,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_133
    | ~ spl0_199 ),
    inference(superposition,[],[f1027,f1718]) ).

fof(f1027,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1026]) ).

fof(f11777,plain,
    ( ~ spl0_716
    | ~ spl0_685
    | spl0_695 ),
    inference(avatar_split_clause,[],[f11702,f11592,f11030,f11774]) ).

fof(f11774,plain,
    ( spl0_716
  <=> subclass(y,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f11592,plain,
    ( spl0_695
  <=> member(second(not_subclass_element(cross_product(x,y),z)),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f11702,plain,
    ( ~ subclass(y,element_relation)
    | ~ spl0_685
    | spl0_695 ),
    inference(resolution,[],[f11593,f11031]) ).

fof(f11593,plain,
    ( ~ member(second(not_subclass_element(cross_product(x,y),z)),element_relation)
    | spl0_695 ),
    inference(avatar_component_clause,[],[f11592]) ).

fof(f11772,plain,
    ( spl0_715
    | ~ spl0_49
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1630,f1626,f450,f11770]) ).

fof(f11770,plain,
    ( spl0_715
  <=> ! [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_715])]) ).

fof(f1630,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_49
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f451]) ).

fof(f11743,plain,
    ( spl0_714
    | ~ spl0_51
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1811,f1800,f458,f11741]) ).

fof(f11741,plain,
    ( spl0_714
  <=> ! [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_714])]) ).

fof(f1811,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_51
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f459]) ).

fof(f11739,plain,
    ( spl0_713
    | ~ spl0_51
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1808,f1800,f458,f11737]) ).

fof(f11737,plain,
    ( spl0_713
  <=> ! [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_713])]) ).

fof(f1808,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_51
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f459]) ).

fof(f11735,plain,
    ( spl0_712
    | ~ spl0_90
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1730,f1717,f688,f11733]) ).

fof(f11733,plain,
    ( spl0_712
  <=> ! [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_712])]) ).

fof(f1730,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_90
    | ~ spl0_199 ),
    inference(superposition,[],[f689,f1718]) ).

fof(f11706,plain,
    ( spl0_711
    | ~ spl0_78
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1940,f1930,f619,f11704]) ).

fof(f11704,plain,
    ( spl0_711
  <=> ! [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_711])]) ).

fof(f1940,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_78
    | ~ spl0_209 ),
    inference(duplicate_literal_removal,[],[f1933]) ).

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(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_209 ),
    inference(resolution,[],[f1931,f620]) ).

fof(f11701,plain,
    ( spl0_710
    | ~ spl0_139
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1782,f1779,f1106,f11699]) ).

fof(f11699,plain,
    ( spl0_710
  <=> ! [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_710])]) ).

fof(f1106,plain,
    ( spl0_139
  <=> ! [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_139])]) ).

fof(f1782,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_139
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f1107]) ).

fof(f1107,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1106]) ).

fof(f11687,plain,
    ( spl0_709
    | ~ spl0_30
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1741,f1717,f333,f11685]) ).

fof(f11685,plain,
    ( spl0_709
  <=> ! [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_709])]) ).

fof(f1741,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_199 ),
    inference(superposition,[],[f334,f1718]) ).

fof(f11683,plain,
    ( ~ spl0_707
    | spl0_708
    | ~ spl0_166
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1574,f1562,f1375,f11681,f11677]) ).

fof(f11677,plain,
    ( spl0_707
  <=> 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_707])]) ).

fof(f11681,plain,
    ( spl0_708
  <=> ! [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_708])]) ).

fof(f1574,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_166
    | ~ spl0_186 ),
    inference(resolution,[],[f1563,f1376]) ).

fof(f11672,plain,
    ( spl0_706
    | ~ spl0_39
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1763,f1751,f378,f11670]) ).

fof(f11670,plain,
    ( spl0_706
  <=> ! [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_706])]) ).

fof(f1763,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_39
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f379]) ).

fof(f11666,plain,
    ( ~ spl0_705
    | ~ spl0_236
    | spl0_703 ),
    inference(avatar_split_clause,[],[f11661,f11653,f2317,f11663]) ).

fof(f11663,plain,
    ( spl0_705
  <=> 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_705])]) ).

fof(f11653,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(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_703])]) ).

fof(f11661,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_236
    | spl0_703 ),
    inference(forward_demodulation,[],[f11655,f2319]) ).

fof(f11655,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_703 ),
    inference(avatar_component_clause,[],[f11653]) ).

fof(f11660,plain,
    ( ~ spl0_703
    | ~ spl0_704
    | spl0_430
    | ~ spl0_126
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1657,f1645,f965,f5668,f11657,f11653]) ).

fof(f11657,plain,
    ( spl0_704
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f5668,plain,
    ( spl0_430
  <=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f1657,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_126
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f966]) ).

fof(f11649,plain,
    ( ~ spl0_702
    | ~ spl0_236
    | spl0_699 ),
    inference(avatar_split_clause,[],[f11639,f11630,f2317,f11646]) ).

fof(f11646,plain,
    ( spl0_702
  <=> 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_702])]) ).

fof(f11630,plain,
    ( spl0_699
  <=> 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_699])]) ).

fof(f11639,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_236
    | spl0_699 ),
    inference(forward_demodulation,[],[f11632,f2319]) ).

fof(f11632,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_699 ),
    inference(avatar_component_clause,[],[f11630]) ).

fof(f11644,plain,
    ( ~ spl0_701
    | ~ spl0_236
    | spl0_700 ),
    inference(avatar_split_clause,[],[f11638,f11634,f2317,f11641]) ).

fof(f11641,plain,
    ( spl0_701
  <=> member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f11634,plain,
    ( spl0_700
  <=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f11638,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class)
    | ~ spl0_236
    | spl0_700 ),
    inference(forward_demodulation,[],[f11636,f2319]) ).

fof(f11636,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | spl0_700 ),
    inference(avatar_component_clause,[],[f11634]) ).

fof(f11637,plain,
    ( ~ spl0_699
    | ~ spl0_700
    | spl0_426
    | ~ spl0_125
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1655,f1645,f961,f5646,f11634,f11630]) ).

fof(f5646,plain,
    ( spl0_426
  <=> null_class = complement(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f1655,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_125
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f962]) ).

fof(f11607,plain,
    ( spl0_698
    | ~ spl0_32
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1767,f1751,f341,f11605]) ).

fof(f11605,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)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f1767,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_32
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f342]) ).

fof(f11603,plain,
    ( spl0_697
    | ~ spl0_33
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1766,f1751,f345,f11601]) ).

fof(f11601,plain,
    ( spl0_697
  <=> ! [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_697])]) ).

fof(f1766,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_33
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f346]) ).

fof(f11599,plain,
    ( spl0_695
    | ~ spl0_696
    | ~ spl0_98
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11458,f11030,f737,f11596,f11592]) ).

fof(f11596,plain,
    ( spl0_696
  <=> subclass(y,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f11458,plain,
    ( ~ subclass(y,singleton_relation)
    | member(second(not_subclass_element(cross_product(x,y),z)),element_relation)
    | ~ spl0_98
    | ~ spl0_685 ),
    inference(resolution,[],[f11031,f738]) ).

fof(f11497,plain,
    ( spl0_694
    | ~ spl0_21
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1769,f1751,f293,f11495]) ).

fof(f11495,plain,
    ( spl0_694
  <=> ! [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_694])]) ).

fof(f1769,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_21
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f294]) ).

fof(f11493,plain,
    ( spl0_693
    | ~ spl0_49
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1742,f1717,f450,f11491]) ).

fof(f11491,plain,
    ( spl0_693
  <=> ! [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_693])]) ).

fof(f1742,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_49
    | ~ spl0_199 ),
    inference(superposition,[],[f451,f1718]) ).

fof(f11475,plain,
    ( spl0_692
    | ~ spl0_236
    | ~ spl0_690 ),
    inference(avatar_split_clause,[],[f11467,f11464,f2317,f11473]) ).

fof(f11473,plain,
    ( spl0_692
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f11464,plain,
    ( spl0_690
  <=> ! [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_690])]) ).

fof(f11467,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_236
    | ~ spl0_690 ),
    inference(forward_demodulation,[],[f11465,f2319]) ).

fof(f11465,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_690 ),
    inference(avatar_component_clause,[],[f11464]) ).

fof(f11471,plain,
    ( spl0_691
    | ~ spl0_98
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1777,f1751,f737,f11469]) ).

fof(f11469,plain,
    ( spl0_691
  <=> ! [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_691])]) ).

fof(f1777,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_98
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f738]) ).

fof(f11466,plain,
    ( spl0_690
    | ~ spl0_103
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1775,f1751,f763,f11464]) ).

fof(f1775,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_200 ),
    inference(resolution,[],[f1752,f764]) ).

fof(f11420,plain,
    ( spl0_689
    | ~ spl0_127
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1744,f1717,f969,f11418]) ).

fof(f11418,plain,
    ( spl0_689
  <=> ! [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_689])]) ).

fof(f969,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1744,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_127
    | ~ spl0_199 ),
    inference(superposition,[],[f970,f1718]) ).

fof(f970,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | null_class = X1
        | null_class = X0 )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f969]) ).

fof(f11044,plain,
    ( spl0_688
    | ~ spl0_39
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1715,f1711,f378,f11042]) ).

fof(f11042,plain,
    ( spl0_688
  <=> ! [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_688])]) ).

fof(f1715,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_39
    | ~ spl0_198 ),
    inference(resolution,[],[f1712,f379]) ).

fof(f11040,plain,
    ( spl0_687
    | ~ spl0_32
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1694,f1666,f341,f11038]) ).

fof(f11038,plain,
    ( spl0_687
  <=> ! [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_687])]) ).

fof(f1694,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_32
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f342]) ).

fof(f11036,plain,
    ( spl0_686
    | ~ spl0_33
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1693,f1666,f345,f11034]) ).

fof(f11034,plain,
    ( spl0_686
  <=> ! [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_686])]) ).

fof(f1693,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_33
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f346]) ).

fof(f11032,plain,
    ( spl0_685
    | ~ spl0_39
    | ~ spl0_672 ),
    inference(avatar_split_clause,[],[f10777,f10551,f378,f11030]) ).

fof(f10777,plain,
    ( ! [X0] :
        ( ~ subclass(y,X0)
        | member(second(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_39
    | ~ spl0_672 ),
    inference(resolution,[],[f10553,f379]) ).

fof(f11028,plain,
    ( spl0_684
    | ~ spl0_32
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1673,f1662,f341,f11026]) ).

fof(f11026,plain,
    ( spl0_684
  <=> ! [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_684])]) ).

fof(f1673,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_32
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f342]) ).

fof(f11024,plain,
    ( spl0_683
    | ~ spl0_33
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1672,f1662,f345,f11022]) ).

fof(f11022,plain,
    ( spl0_683
  <=> ! [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_683])]) ).

fof(f1672,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_33
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f346]) ).

fof(f11020,plain,
    ( spl0_682
    | ~ spl0_51
    | ~ spl0_72
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1414,f1371,f579,f458,f11018]) ).

fof(f11018,plain,
    ( spl0_682
  <=> ! [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_682])]) ).

fof(f1414,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_51
    | ~ spl0_72
    | ~ spl0_165 ),
    inference(forward_demodulation,[],[f1401,f459]) ).

fof(f1401,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_72
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f580]) ).

fof(f10794,plain,
    ( spl0_681
    | spl0_123
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1791,f1779,f952,f10791]) ).

fof(f952,plain,
    ( spl0_123
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1791,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_123
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f954]) ).

fof(f954,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | spl0_123 ),
    inference(avatar_component_clause,[],[f952]) ).

fof(f10789,plain,
    ( spl0_680
    | spl0_121
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1787,f1779,f943,f10786]) ).

fof(f943,plain,
    ( spl0_121
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f1787,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_121
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f945]) ).

fof(f945,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_121 ),
    inference(avatar_component_clause,[],[f943]) ).

fof(f10784,plain,
    ( spl0_679
    | spl0_119
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1784,f1779,f933,f10781]) ).

fof(f933,plain,
    ( spl0_119
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1784,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_119
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f935]) ).

fof(f935,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_119 ),
    inference(avatar_component_clause,[],[f933]) ).

fof(f10607,plain,
    ( spl0_678
    | ~ spl0_153
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1318,f1300,f1253,f10605]) ).

fof(f10605,plain,
    ( spl0_678
  <=> ! [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_678])]) ).

fof(f1318,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_153
    | ~ spl0_159 ),
    inference(resolution,[],[f1301,f1254]) ).

fof(f10603,plain,
    ( spl0_677
    | ~ spl0_97
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f848,f817,f733,f10601]) ).

fof(f848,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_97
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f734]) ).

fof(f10599,plain,
    ( spl0_676
    | ~ spl0_96
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f847,f817,f729,f10597]) ).

fof(f847,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_96
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f730]) ).

fof(f10566,plain,
    ( spl0_674
    | ~ spl0_675
    | ~ spl0_79
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1887,f1875,f630,f10563,f10560]) ).

fof(f10560,plain,
    ( spl0_674
  <=> ! [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_674])]) ).

fof(f10563,plain,
    ( spl0_675
  <=> subclass(composition_function,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1887,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_79
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f631]) ).

fof(f10558,plain,
    ( spl0_673
    | ~ spl0_79
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1759,f1751,f630,f10556]) ).

fof(f10556,plain,
    ( spl0_673
  <=> ! [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_673])]) ).

fof(f1759,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_79
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f631]) ).

fof(f10554,plain,
    ( spl0_1
    | spl0_672
    | ~ spl0_27
    | ~ spl0_655 ),
    inference(avatar_split_clause,[],[f10428,f10057,f321,f10551,f205]) ).

fof(f10057,plain,
    ( spl0_655
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f10428,plain,
    ( member(second(not_subclass_element(cross_product(x,y),z)),y)
    | subclass(cross_product(x,y),z)
    | ~ spl0_27
    | ~ spl0_655 ),
    inference(resolution,[],[f10058,f322]) ).

fof(f10058,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_655 ),
    inference(avatar_component_clause,[],[f10057]) ).

fof(f10549,plain,
    ( spl0_671
    | ~ spl0_143
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1516,f1462,f1165,f10547]) ).

fof(f10547,plain,
    ( spl0_671
  <=> ! [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_671])]) ).

fof(f1516,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_143
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f1166]) ).

fof(f10545,plain,
    ( spl0_670
    | ~ spl0_435
    | ~ spl0_144
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1510,f1462,f1169,f5696,f10543]) ).

fof(f10543,plain,
    ( spl0_670
  <=> ! [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_670])]) ).

fof(f5696,plain,
    ( spl0_435
  <=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1510,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_144
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f1170]) ).

fof(f10445,plain,
    ( spl0_669
    | ~ spl0_132
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1745,f1717,f1022,f10443]) ).

fof(f10443,plain,
    ( spl0_669
  <=> ! [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_669])]) ).

fof(f1022,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1745,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_132
    | ~ spl0_199 ),
    inference(superposition,[],[f1023,f1718]) ).

fof(f1023,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1022]) ).

fof(f10441,plain,
    ( spl0_668
    | ~ spl0_79
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1726,f1717,f630,f10439]) ).

fof(f10439,plain,
    ( spl0_668
  <=> ! [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_668])]) ).

fof(f1726,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_79
    | ~ spl0_199 ),
    inference(superposition,[],[f631,f1718]) ).

fof(f10437,plain,
    ( spl0_667
    | ~ spl0_21
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1696,f1666,f293,f10435]) ).

fof(f10435,plain,
    ( spl0_667
  <=> ! [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_667])]) ).

fof(f1696,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_21
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f294]) ).

fof(f10433,plain,
    ( spl0_666
    | ~ spl0_21
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1675,f1662,f293,f10431]) ).

fof(f10431,plain,
    ( spl0_666
  <=> ! [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_666])]) ).

fof(f1675,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_21
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f294]) ).

fof(f10422,plain,
    ( ~ spl0_664
    | ~ spl0_665
    | spl0_347
    | ~ spl0_112
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1651,f1645,f829,f3573,f10419,f10415]) ).

fof(f10415,plain,
    ( spl0_664
  <=> 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_664])]) ).

fof(f10419,plain,
    ( spl0_665
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f3573,plain,
    ( spl0_347
  <=> null_class = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f1651,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_112
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f830]) ).

fof(f10179,plain,
    ( spl0_663
    | ~ spl0_69
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2699,f2690,f566,f10177]) ).

fof(f2699,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | member(first(not_subclass_element(cross_product(x,y),z)),X0) )
    | ~ spl0_69
    | ~ spl0_278 ),
    inference(superposition,[],[f567,f2692]) ).

fof(f10087,plain,
    ( spl0_662
    | ~ spl0_177
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1738,f1717,f1483,f10085]) ).

fof(f10085,plain,
    ( spl0_662
  <=> ! [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_662])]) ).

fof(f1738,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_177
    | ~ spl0_199 ),
    inference(superposition,[],[f1484,f1718]) ).

fof(f10083,plain,
    ( spl0_661
    | ~ spl0_114
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1698,f1666,f894,f10081]) ).

fof(f10081,plain,
    ( spl0_661
  <=> ! [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_661])]) ).

fof(f894,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1698,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_114
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f895]) ).

fof(f895,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f894]) ).

fof(f10079,plain,
    ( spl0_660
    | ~ spl0_39
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1690,f1666,f378,f10077]) ).

fof(f10077,plain,
    ( spl0_660
  <=> ! [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_660])]) ).

fof(f1690,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_39
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f379]) ).

fof(f10075,plain,
    ( spl0_659
    | ~ spl0_114
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1677,f1662,f894,f10073]) ).

fof(f10073,plain,
    ( spl0_659
  <=> ! [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_659])]) ).

fof(f1677,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_114
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f895]) ).

fof(f10071,plain,
    ( spl0_658
    | ~ spl0_39
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1669,f1662,f378,f10069]) ).

fof(f10069,plain,
    ( spl0_658
  <=> ! [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_658])]) ).

fof(f1669,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_39
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f379]) ).

fof(f10067,plain,
    ( spl0_657
    | ~ spl0_124
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1658,f1645,f957,f10065]) ).

fof(f10065,plain,
    ( spl0_657
  <=> ! [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_657])]) ).

fof(f1658,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_124
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f958]) ).

fof(f10063,plain,
    ( spl0_656
    | ~ spl0_49
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1505,f1462,f450,f10061]) ).

fof(f10061,plain,
    ( spl0_656
  <=> ! [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_656])]) ).

fof(f1505,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_49
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f451]) ).

fof(f10059,plain,
    ( spl0_655
    | ~ spl0_68
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2698,f2690,f562,f10057]) ).

fof(f2698,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1))
        | member(second(not_subclass_element(cross_product(x,y),z)),X1) )
    | ~ spl0_68
    | ~ spl0_278 ),
    inference(superposition,[],[f563,f2692]) ).

fof(f10055,plain,
    ( spl0_654
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1498,f1458,f1165,f10053]) ).

fof(f10053,plain,
    ( spl0_654
  <=> ! [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_654])]) ).

fof(f1498,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_143
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f1166]) ).

fof(f10051,plain,
    ( ~ spl0_435
    | spl0_653
    | ~ spl0_144
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1492,f1458,f1169,f10049,f5696]) ).

fof(f10049,plain,
    ( spl0_653
  <=> ! [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_653])]) ).

fof(f1492,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_144
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f1170]) ).

fof(f10047,plain,
    ( spl0_652
    | ~ spl0_143
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1440,f1375,f1165,f10045]) ).

fof(f10045,plain,
    ( spl0_652
  <=> ! [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_652])]) ).

fof(f1440,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_143
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f1166]) ).

fof(f10042,plain,
    ( spl0_650
    | ~ spl0_651
    | ~ spl0_145
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1437,f1375,f1173,f10039,f10036]) ).

fof(f10036,plain,
    ( spl0_650
  <=> ! [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_650])]) ).

fof(f10039,plain,
    ( spl0_651
  <=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f1437,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_145
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f1174]) ).

fof(f10034,plain,
    ( ~ spl0_649
    | ~ spl0_236
    | spl0_648 ),
    inference(avatar_split_clause,[],[f10029,f10025,f2317,f10031]) ).

fof(f10031,plain,
    ( spl0_649
  <=> subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f10025,plain,
    ( spl0_648
  <=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f10029,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_236
    | spl0_648 ),
    inference(forward_demodulation,[],[f10027,f2319]) ).

fof(f10027,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
    | spl0_648 ),
    inference(avatar_component_clause,[],[f10025]) ).

fof(f10028,plain,
    ( spl0_647
    | ~ spl0_648
    | ~ spl0_144
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1434,f1375,f1169,f10025,f10022]) ).

fof(f10022,plain,
    ( spl0_647
  <=> ! [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_647])]) ).

fof(f1434,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_144
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f1170]) ).

fof(f10020,plain,
    ( spl0_646
    | ~ spl0_80
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1069,f1018,f634,f10018]) ).

fof(f10018,plain,
    ( spl0_646
  <=> ! [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_646])]) ).

fof(f1069,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_80
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f635]) ).

fof(f10014,plain,
    ( spl0_645
    | ~ spl0_88
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1729,f1717,f679,f10012]) ).

fof(f10012,plain,
    ( spl0_645
  <=> ! [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_645])]) ).

fof(f1729,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_88
    | ~ spl0_199 ),
    inference(superposition,[],[f680,f1718]) ).

fof(f9891,plain,
    ( spl0_644
    | ~ spl0_73
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1889,f1875,f590,f9889]) ).

fof(f9889,plain,
    ( spl0_644
  <=> ! [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_644])]) ).

fof(f1889,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_73
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f591]) ).

fof(f9887,plain,
    ( spl0_643
    | ~ spl0_29
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1740,f1717,f329,f9885]) ).

fof(f9885,plain,
    ( spl0_643
  <=> ! [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_643])]) ).

fof(f1740,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_199 ),
    inference(superposition,[],[f330,f1718]) ).

fof(f9883,plain,
    ( spl0_642
    | ~ spl0_49
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1487,f1458,f450,f9881]) ).

fof(f9881,plain,
    ( spl0_642
  <=> ! [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_642])]) ).

fof(f1487,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_49
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f451]) ).

fof(f9879,plain,
    ( spl0_641
    | ~ spl0_49
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1429,f1375,f450,f9877]) ).

fof(f9877,plain,
    ( spl0_641
  <=> ! [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_641])]) ).

fof(f1429,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_49
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f451]) ).

fof(f9875,plain,
    ( spl0_640
    | ~ spl0_50
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1397,f1371,f454,f9873]) ).

fof(f9873,plain,
    ( spl0_640
  <=> ! [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_640])]) ).

fof(f1397,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_50
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f455]) ).

fof(f9871,plain,
    ( spl0_639
    | ~ spl0_116
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1364,f1357,f921,f9869]) ).

fof(f9869,plain,
    ( spl0_639
  <=> ! [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_639])]) ).

fof(f921,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1364,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_116
    | ~ spl0_163 ),
    inference(resolution,[],[f1358,f922]) ).

fof(f922,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f921]) ).

fof(f9829,plain,
    ( spl0_638
    | ~ spl0_236
    | ~ spl0_632 ),
    inference(avatar_split_clause,[],[f9795,f9790,f2317,f9827]) ).

fof(f9827,plain,
    ( spl0_638
  <=> ! [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_638])]) ).

fof(f9790,plain,
    ( spl0_632
  <=> ! [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_632])]) ).

fof(f9795,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_236
    | ~ spl0_632 ),
    inference(forward_demodulation,[],[f9794,f2319]) ).

fof(f9794,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_236
    | ~ spl0_632 ),
    inference(forward_demodulation,[],[f9793,f2319]) ).

fof(f9793,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_236
    | ~ spl0_632 ),
    inference(forward_demodulation,[],[f9791,f2319]) ).

fof(f9791,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_632 ),
    inference(avatar_component_clause,[],[f9790]) ).

fof(f9816,plain,
    ( spl0_637
    | ~ spl0_236
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f9784,f9779,f2317,f9814]) ).

fof(f9814,plain,
    ( spl0_637
  <=> ! [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_637])]) ).

fof(f9779,plain,
    ( spl0_630
  <=> ! [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_630])]) ).

fof(f9784,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_236
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f9783,f2319]) ).

fof(f9783,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_236
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f9782,f2319]) ).

fof(f9782,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_236
    | ~ spl0_630 ),
    inference(forward_demodulation,[],[f9780,f2319]) ).

fof(f9780,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_630 ),
    inference(avatar_component_clause,[],[f9779]) ).

fof(f9812,plain,
    ( ~ spl0_635
    | spl0_636
    | ~ spl0_115
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f4390,f3977,f898,f9809,f9805]) ).

fof(f9805,plain,
    ( spl0_635
  <=> single_valued_class(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f9809,plain,
    ( spl0_636
  <=> function(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f3977,plain,
    ( spl0_383
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f4390,plain,
    ( function(null_class)
    | ~ single_valued_class(null_class)
    | ~ spl0_115
    | ~ spl0_383 ),
    inference(resolution,[],[f3978,f899]) ).

fof(f3978,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f3977]) ).

fof(f9803,plain,
    ( spl0_634
    | ~ spl0_68
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1883,f1875,f562,f9801]) ).

fof(f9801,plain,
    ( spl0_634
  <=> ! [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_634])]) ).

fof(f1883,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_68
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f563]) ).

fof(f9799,plain,
    ( spl0_633
    | ~ spl0_98
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1703,f1666,f737,f9797]) ).

fof(f9797,plain,
    ( spl0_633
  <=> ! [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_633])]) ).

fof(f1703,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_98
    | ~ spl0_197 ),
    inference(resolution,[],[f1667,f738]) ).

fof(f9792,plain,
    ( spl0_632
    | ~ spl0_103
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1701,f1666,f763,f9790]) ).

fof(f1701,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_197 ),
    inference(resolution,[],[f1667,f764]) ).

fof(f9788,plain,
    ( spl0_631
    | ~ spl0_98
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1682,f1662,f737,f9786]) ).

fof(f9786,plain,
    ( spl0_631
  <=> ! [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_631])]) ).

fof(f1682,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_98
    | ~ spl0_196 ),
    inference(resolution,[],[f1663,f738]) ).

fof(f9781,plain,
    ( spl0_630
    | ~ spl0_103
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1680,f1662,f763,f9779]) ).

fof(f1680,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_196 ),
    inference(resolution,[],[f1663,f764]) ).

fof(f9774,plain,
    ( spl0_628
    | ~ spl0_629
    | ~ spl0_113
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1365,f1357,f890,f9771,f9767]) ).

fof(f9771,plain,
    ( spl0_629
  <=> 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_629])]) ).

fof(f1365,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_113
    | ~ spl0_163 ),
    inference(resolution,[],[f1358,f891]) ).

fof(f9694,plain,
    ( spl0_626
    | spl0_627
    | ~ spl0_80
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f853,f817,f634,f9692,f9689]) ).

fof(f9689,plain,
    ( spl0_626
  <=> ! [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_626])]) ).

fof(f853,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_80
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f635]) ).

fof(f9631,plain,
    ( spl0_624
    | ~ spl0_625
    | ~ spl0_65
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1890,f1875,f545,f9628,f9625]) ).

fof(f9625,plain,
    ( spl0_624
  <=> ! [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_624])]) ).

fof(f9628,plain,
    ( spl0_625
  <=> subclass(composition_function,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f1890,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_65
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f546]) ).

fof(f9623,plain,
    ( spl0_623
    | ~ spl0_90
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1421,f1375,f688,f9621]) ).

fof(f9621,plain,
    ( spl0_623
  <=> ! [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_623])]) ).

fof(f1421,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,compose(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_90
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f689]) ).

fof(f9619,plain,
    ( spl0_622
    | ~ spl0_28
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1363,f1357,f325,f9617]) ).

fof(f9617,plain,
    ( spl0_622
  <=> ! [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_622])]) ).

fof(f1363,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_163 ),
    inference(resolution,[],[f1358,f326]) ).

fof(f9503,plain,
    ( spl0_621
    | ~ spl0_236
    | ~ spl0_616 ),
    inference(avatar_split_clause,[],[f9446,f9443,f2317,f9501]) ).

fof(f9501,plain,
    ( spl0_621
  <=> ! [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_621])]) ).

fof(f9443,plain,
    ( spl0_616
  <=> ! [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_616])]) ).

fof(f9446,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_236
    | ~ spl0_616 ),
    inference(forward_demodulation,[],[f9444,f2319]) ).

fof(f9444,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_616 ),
    inference(avatar_component_clause,[],[f9443]) ).

fof(f9470,plain,
    ( spl0_620
    | ~ spl0_236
    | ~ spl0_615 ),
    inference(avatar_split_clause,[],[f9441,f9436,f2317,f9468]) ).

fof(f9468,plain,
    ( spl0_620
  <=> ! [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_620])]) ).

fof(f9436,plain,
    ( spl0_615
  <=> ! [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_615])]) ).

fof(f9441,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_236
    | ~ spl0_615 ),
    inference(forward_demodulation,[],[f9440,f2319]) ).

fof(f9440,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_236
    | ~ spl0_615 ),
    inference(forward_demodulation,[],[f9439,f2319]) ).

fof(f9439,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_236
    | ~ spl0_615 ),
    inference(forward_demodulation,[],[f9437,f2319]) ).

fof(f9437,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_615 ),
    inference(avatar_component_clause,[],[f9436]) ).

fof(f9458,plain,
    ( spl0_618
    | ~ spl0_619
    | ~ spl0_62
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1885,f1875,f530,f9455,f9452]) ).

fof(f9452,plain,
    ( spl0_618
  <=> ! [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_618])]) ).

fof(f9455,plain,
    ( spl0_619
  <=> subclass(composition_function,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f1885,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_62
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f531]) ).

fof(f9450,plain,
    ( spl0_617
    | ~ spl0_39
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1629,f1626,f378,f9448]) ).

fof(f9448,plain,
    ( spl0_617
  <=> ! [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_617])]) ).

fof(f1629,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_39
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f379]) ).

fof(f9445,plain,
    ( spl0_616
    | ~ spl0_126
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1402,f1371,f965,f9443]) ).

fof(f1402,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_126
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f966]) ).

fof(f9438,plain,
    ( spl0_615
    | ~ spl0_125
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1400,f1371,f961,f9436]) ).

fof(f1400,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_125
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f962]) ).

fof(f9433,plain,
    ( spl0_614
    | ~ spl0_136
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1220,f1173,f1093,f9431]) ).

fof(f9431,plain,
    ( spl0_614
  <=> ! [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_614])]) ).

fof(f1220,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_136
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f1094]) ).

fof(f9428,plain,
    ( spl0_613
    | ~ spl0_135
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1213,f1173,f1089,f9426]) ).

fof(f9426,plain,
    ( spl0_613
  <=> ! [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_613])]) ).

fof(f1213,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_135
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f1090]) ).

fof(f9421,plain,
    ( spl0_612
    | ~ spl0_136
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1206,f1169,f1093,f9419]) ).

fof(f9419,plain,
    ( spl0_612
  <=> ! [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_612])]) ).

fof(f1206,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_136
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f1094]) ).

fof(f9417,plain,
    ( spl0_611
    | ~ spl0_235
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2949,f2317,f2311,f9414]) ).

fof(f2949,plain,
    ( member(regular(singleton_relation),subset_relation)
    | ~ spl0_235
    | ~ spl0_236 ),
    inference(superposition,[],[f2313,f2319]) ).

fof(f9409,plain,
    ( spl0_610
    | ~ spl0_135
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1199,f1169,f1089,f9407]) ).

fof(f9407,plain,
    ( spl0_610
  <=> ! [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_610])]) ).

fof(f1199,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_135
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f1090]) ).

fof(f9405,plain,
    ( spl0_609
    | ~ spl0_89
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f888,f829,f683,f9403]) ).

fof(f9403,plain,
    ( spl0_609
  <=> ! [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_609])]) ).

fof(f683,plain,
    ( spl0_89
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f888,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) )
    | ~ spl0_89
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f684]) ).

fof(f684,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f683]) ).

fof(f9301,plain,
    ( spl0_608
    | ~ spl0_87
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1728,f1717,f675,f9299]) ).

fof(f9299,plain,
    ( spl0_608
  <=> ! [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_608])]) ).

fof(f1728,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_87
    | ~ spl0_199 ),
    inference(superposition,[],[f676,f1718]) ).

fof(f9297,plain,
    ( spl0_607
    | ~ spl0_5
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2491,f2459,f225,f9294]) ).

fof(f9292,plain,
    ( spl0_606
    | ~ spl0_86
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1727,f1717,f670,f9290]) ).

fof(f9290,plain,
    ( spl0_606
  <=> ! [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_606])]) ).

fof(f1727,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_86
    | ~ spl0_199 ),
    inference(superposition,[],[f671,f1718]) ).

fof(f9288,plain,
    ( spl0_605
    | ~ spl0_32
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1633,f1626,f341,f9286]) ).

fof(f9286,plain,
    ( spl0_605
  <=> ! [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_605])]) ).

fof(f1633,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_32
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f342]) ).

fof(f9284,plain,
    ( spl0_604
    | ~ spl0_33
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1632,f1626,f345,f9282]) ).

fof(f9282,plain,
    ( spl0_604
  <=> ! [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_604])]) ).

fof(f1632,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_33
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f346]) ).

fof(f9280,plain,
    ( spl0_603
    | ~ spl0_131
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1580,f1562,f1018,f9278]) ).

fof(f9278,plain,
    ( spl0_603
  <=> ! [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_603])]) ).

fof(f1580,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_131
    | ~ spl0_186 ),
    inference(resolution,[],[f1563,f1019]) ).

fof(f9276,plain,
    ( spl0_602
    | ~ spl0_45
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1399,f1371,f430,f9274]) ).

fof(f9274,plain,
    ( spl0_602
  <=> ! [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_602])]) ).

fof(f1399,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_45
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f431]) ).

fof(f9272,plain,
    ( spl0_601
    | ~ spl0_80
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f985,f925,f634,f9270]) ).

fof(f9270,plain,
    ( spl0_601
  <=> ! [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_601])]) ).

fof(f985,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_80
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f635]) ).

fof(f9223,plain,
    ( ~ spl0_600
    | ~ spl0_236
    | spl0_599 ),
    inference(avatar_split_clause,[],[f9216,f9212,f2317,f9220]) ).

fof(f9220,plain,
    ( spl0_600
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f9212,plain,
    ( spl0_599
  <=> 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_599])]) ).

fof(f9216,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_236
    | spl0_599 ),
    inference(forward_demodulation,[],[f9213,f2319]) ).

fof(f9213,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_599 ),
    inference(avatar_component_clause,[],[f9212]) ).

fof(f9215,plain,
    ( ~ spl0_548
    | spl0_234
    | spl0_599
    | ~ spl0_44
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1709,f1666,f399,f9212,f2307,f8335]) ).

fof(f8335,plain,
    ( spl0_548
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f2307,plain,
    ( spl0_234
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f1709,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_44
    | ~ spl0_197 ),
    inference(superposition,[],[f1667,f401]) ).

fof(f9210,plain,
    ( spl0_598
    | ~ spl0_21
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1635,f1626,f293,f9208]) ).

fof(f9208,plain,
    ( spl0_598
  <=> ! [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_598])]) ).

fof(f1635,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_21
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f294]) ).

fof(f9205,plain,
    ( spl0_597
    | ~ spl0_130
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1219,f1173,f1014,f9203]) ).

fof(f9203,plain,
    ( spl0_597
  <=> ! [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_597])]) ).

fof(f1219,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_130
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f1015]) ).

fof(f9200,plain,
    ( spl0_596
    | ~ spl0_129
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1217,f1173,f1010,f9198]) ).

fof(f9198,plain,
    ( spl0_596
  <=> ! [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_596])]) ).

fof(f1217,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_129
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f1011]) ).

fof(f9193,plain,
    ( spl0_595
    | ~ spl0_130
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1205,f1169,f1014,f9191]) ).

fof(f9191,plain,
    ( spl0_595
  <=> ! [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_595])]) ).

fof(f1205,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_130
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f1015]) ).

fof(f9186,plain,
    ( spl0_594
    | ~ spl0_129
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1203,f1169,f1010,f9184]) ).

fof(f9184,plain,
    ( spl0_594
  <=> ! [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_594])]) ).

fof(f1203,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_129
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f1011]) ).

fof(f9182,plain,
    ( spl0_593
    | ~ spl0_51
    | ~ spl0_72
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f981,f921,f579,f458,f9180]) ).

fof(f9180,plain,
    ( spl0_593
  <=> ! [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_593])]) ).

fof(f981,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_51
    | ~ spl0_72
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f980,f459]) ).

fof(f980,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_72
    | ~ spl0_116 ),
    inference(resolution,[],[f922,f580]) ).

fof(f9159,plain,
    ( ~ spl0_591
    | spl0_592
    | ~ spl0_124
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3598,f3334,f957,f9157,f9153]) ).

fof(f9153,plain,
    ( spl0_591
  <=> member(not_subclass_element(cross_product(x,y),z),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f9157,plain,
    ( spl0_592
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(regular(X0)))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f3334,plain,
    ( spl0_334
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f3598,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(regular(X0)))
        | ~ member(not_subclass_element(cross_product(x,y),z),null_class)
        | null_class = X0 )
    | ~ spl0_124
    | ~ spl0_334 ),
    inference(resolution,[],[f3335,f958]) ).

fof(f3335,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f3334]) ).

fof(f9151,plain,
    ( spl0_590
    | ~ spl0_236
    | ~ spl0_587 ),
    inference(avatar_split_clause,[],[f9081,f9078,f2317,f9149]) ).

fof(f9149,plain,
    ( spl0_590
  <=> ! [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_590])]) ).

fof(f9078,plain,
    ( spl0_587
  <=> ! [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_587])]) ).

fof(f9081,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_236
    | ~ spl0_587 ),
    inference(forward_demodulation,[],[f9079,f2319]) ).

fof(f9079,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_587 ),
    inference(avatar_component_clause,[],[f9078]) ).

fof(f9089,plain,
    ( spl0_589
    | ~ spl0_73
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1761,f1751,f590,f9087]) ).

fof(f9087,plain,
    ( spl0_589
  <=> ! [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_589])]) ).

fof(f1761,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_73
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f591]) ).

fof(f9085,plain,
    ( spl0_588
    | ~ spl0_98
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1643,f1626,f737,f9083]) ).

fof(f9083,plain,
    ( spl0_588
  <=> ! [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_588])]) ).

fof(f1643,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_98
    | ~ spl0_194 ),
    inference(resolution,[],[f1627,f738]) ).

fof(f9080,plain,
    ( spl0_587
    | ~ spl0_103
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1641,f1626,f763,f9078]) ).

fof(f1641,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_194 ),
    inference(resolution,[],[f1627,f764]) ).

fof(f9076,plain,
    ( spl0_586
    | ~ spl0_117
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1577,f1562,f925,f9074]) ).

fof(f9074,plain,
    ( spl0_586
  <=> ! [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_586])]) ).

fof(f1577,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_117
    | ~ spl0_186 ),
    inference(resolution,[],[f1563,f926]) ).

fof(f9072,plain,
    ( spl0_585
    | ~ spl0_90
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f838,f817,f688,f9070]) ).

fof(f9070,plain,
    ( spl0_585
  <=> ! [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_585])]) ).

fof(f838,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_90
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f689]) ).

fof(f8941,plain,
    ( spl0_584
    | ~ spl0_78
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1725,f1717,f619,f8939]) ).

fof(f8939,plain,
    ( spl0_584
  <=> ! [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_584])]) ).

fof(f1725,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_78
    | ~ spl0_199 ),
    inference(superposition,[],[f620,f1718]) ).

fof(f8934,plain,
    ( ~ spl0_582
    | spl0_275
    | spl0_583
    | ~ spl0_77
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1707,f1666,f614,f8931,f2540,f8927]) ).

fof(f8927,plain,
    ( spl0_582
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f8931,plain,
    ( spl0_583
  <=> 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_583])]) ).

fof(f1707,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_77
    | ~ spl0_197 ),
    inference(superposition,[],[f1667,f616]) ).

fof(f8925,plain,
    ( spl0_581
    | ~ spl0_153
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1649,f1645,f1253,f8923]) ).

fof(f8923,plain,
    ( spl0_581
  <=> ! [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_581])]) ).

fof(f1649,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_153
    | ~ spl0_195 ),
    inference(resolution,[],[f1646,f1254]) ).

fof(f8921,plain,
    ( spl0_580
    | ~ spl0_39
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1588,f1584,f378,f8919]) ).

fof(f8919,plain,
    ( spl0_580
  <=> ! [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_580])]) ).

fof(f1588,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_39
    | ~ spl0_187 ),
    inference(resolution,[],[f1585,f379]) ).

fof(f8917,plain,
    ( spl0_1
    | spl0_579
    | ~ spl0_131
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3586,f3334,f1018,f8915,f205]) ).

fof(f3586,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(cross_product(x,y),X0)
        | subclass(cross_product(x,y),z) )
    | ~ spl0_131
    | ~ spl0_334 ),
    inference(resolution,[],[f3335,f1019]) ).

fof(f8913,plain,
    ( ~ spl0_577
    | spl0_578
    | ~ spl0_109
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1579,f1562,f817,f8911,f8907]) ).

fof(f8907,plain,
    ( spl0_577
  <=> 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_577])]) ).

fof(f8911,plain,
    ( spl0_578
  <=> ! [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_578])]) ).

fof(f1579,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_109
    | ~ spl0_186 ),
    inference(resolution,[],[f1563,f818]) ).

fof(f8905,plain,
    ( spl0_576
    | ~ spl0_77
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1407,f1371,f614,f8903]) ).

fof(f8903,plain,
    ( spl0_576
  <=> ! [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_576])]) ).

fof(f1407,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_77
    | ~ spl0_165 ),
    inference(superposition,[],[f1372,f616]) ).

fof(f8901,plain,
    ( spl0_575
    | ~ spl0_131
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1320,f1300,f1018,f8899]) ).

fof(f8899,plain,
    ( spl0_575
  <=> ! [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_575])]) ).

fof(f1320,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_131
    | ~ spl0_159 ),
    inference(resolution,[],[f1301,f1019]) ).

fof(f8812,plain,
    ( spl0_574
    | ~ spl0_65
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1762,f1751,f545,f8810]) ).

fof(f8810,plain,
    ( spl0_574
  <=> ! [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_574])]) ).

fof(f1762,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_65
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f546]) ).

fof(f8808,plain,
    ( spl0_573
    | ~ spl0_115
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1391,f1367,f898,f8806]) ).

fof(f8806,plain,
    ( spl0_573
  <=> ! [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_573])]) ).

fof(f1391,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_115
    | ~ spl0_164 ),
    inference(resolution,[],[f1368,f899]) ).

fof(f8803,plain,
    ( spl0_572
    | ~ spl0_143
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1276,f1253,f1165,f8801]) ).

fof(f8801,plain,
    ( spl0_572
  <=> ! [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_572])]) ).

fof(f1276,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_143
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f1166]) ).

fof(f8799,plain,
    ( spl0_571
    | ~ spl0_435
    | ~ spl0_144
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1271,f1253,f1169,f5696,f8797]) ).

fof(f8797,plain,
    ( spl0_571
  <=> ! [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_571])]) ).

fof(f1271,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_144
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f1170]) ).

fof(f8795,plain,
    ( spl0_570
    | ~ spl0_77
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1262,f1249,f614,f8793]) ).

fof(f8793,plain,
    ( spl0_570
  <=> ! [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_570])]) ).

fof(f1249,plain,
    ( spl0_152
  <=> ! [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_152])]) ).

fof(f1262,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_77
    | ~ spl0_152 ),
    inference(superposition,[],[f1250,f616]) ).

fof(f1250,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1249]) ).

fof(f8791,plain,
    ( spl0_569
    | ~ spl0_51
    | ~ spl0_72
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f905,f890,f579,f458,f8789]) ).

fof(f8789,plain,
    ( spl0_569
  <=> ! [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_569])]) ).

fof(f905,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_51
    | ~ spl0_72
    | ~ spl0_113 ),
    inference(forward_demodulation,[],[f904,f459]) ).

fof(f904,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_72
    | ~ spl0_113 ),
    inference(resolution,[],[f891,f580]) ).

fof(f8661,plain,
    ( spl0_568
    | spl0_1
    | ~ spl0_298
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3354,f3236,f2895,f205,f8659]) ).

fof(f8659,plain,
    ( spl0_568
  <=> ! [X0] :
        ( ~ subclass(cross_product(x,y),complement(X0))
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f2895,plain,
    ( spl0_298
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(x,y),z),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f3354,plain,
    ( ! [X0] :
        ( subclass(cross_product(x,y),z)
        | ~ subclass(cross_product(x,y),complement(X0))
        | ~ subclass(universal_class,X0) )
    | ~ spl0_298
    | ~ spl0_319 ),
    inference(resolution,[],[f3237,f2896]) ).

fof(f2896,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(x,y),z),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_298 ),
    inference(avatar_component_clause,[],[f2895]) ).

fof(f8441,plain,
    ( spl0_567
    | ~ spl0_62
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1757,f1751,f530,f8439]) ).

fof(f8439,plain,
    ( spl0_567
  <=> ! [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_567])]) ).

fof(f1757,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_62
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f531]) ).

fof(f8437,plain,
    ( spl0_566
    | ~ spl0_73
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1724,f1717,f590,f8435]) ).

fof(f8435,plain,
    ( spl0_566
  <=> ! [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_566])]) ).

fof(f1724,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_73
    | ~ spl0_199 ),
    inference(superposition,[],[f591,f1718]) ).

fof(f8433,plain,
    ( spl0_565
    | ~ spl0_135
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1617,f1590,f1089,f8431]) ).

fof(f8431,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(f1590,plain,
    ( spl0_188
  <=> ! [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_188])]) ).

fof(f1617,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_135
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1612]) ).

fof(f1612,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_135
    | ~ spl0_188 ),
    inference(resolution,[],[f1591,f1090]) ).

fof(f1591,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_188 ),
    inference(avatar_component_clause,[],[f1590]) ).

fof(f8429,plain,
    ( spl0_564
    | ~ spl0_136
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1616,f1590,f1093,f8427]) ).

fof(f8427,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(f1616,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_136
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1613]) ).

fof(f1613,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_136
    | ~ spl0_188 ),
    inference(resolution,[],[f1591,f1094]) ).

fof(f8420,plain,
    ( spl0_563
    | ~ spl0_64
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1443,f1379,f538,f8418]) ).

fof(f8418,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(f538,plain,
    ( spl0_64
  <=> ! [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_64])]) ).

fof(f1379,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

fof(f1443,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_64
    | ~ spl0_167 ),
    inference(resolution,[],[f1380,f539]) ).

fof(f539,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f538]) ).

fof(f1380,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_167 ),
    inference(avatar_component_clause,[],[f1379]) ).

fof(f8406,plain,
    ( spl0_562
    | ~ spl0_15
    | ~ spl0_86
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1417,f1375,f670,f268,f8404]) ).

fof(f8404,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(f1417,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | ~ member(X0,domain_of(X0)) )
    | ~ spl0_86
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f671]) ).

fof(f8402,plain,
    ( spl0_561
    | ~ spl0_124
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1403,f1371,f957,f8400]) ).

fof(f8400,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(f1403,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_124
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f958]) ).

fof(f8398,plain,
    ( spl0_560
    | ~ spl0_112
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1396,f1371,f829,f8396]) ).

fof(f8396,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(f1396,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_112
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f830]) ).

fof(f8393,plain,
    ( spl0_559
    | ~ spl0_27
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1212,f1173,f321,f8391]) ).

fof(f8391,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(f1212,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_145 ),
    inference(resolution,[],[f1174,f322]) ).

fof(f8386,plain,
    ( spl0_558
    | ~ spl0_27
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1198,f1169,f321,f8384]) ).

fof(f8384,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(f1198,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_144 ),
    inference(resolution,[],[f1170,f322]) ).

fof(f8382,plain,
    ( spl0_557
    | ~ spl0_136
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1192,f1165,f1093,f8380]) ).

fof(f8380,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(f1192,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_136
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f1094]) ).

fof(f8378,plain,
    ( spl0_556
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1185,f1165,f1089,f8376]) ).

fof(f8376,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(f1185,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_135
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f1090]) ).

fof(f8374,plain,
    ( spl0_555
    | ~ spl0_49
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1137,f1093,f450,f8372]) ).

fof(f8372,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(f1137,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_49
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f451]) ).

fof(f8368,plain,
    ( spl0_554
    | ~ spl0_49
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1119,f1089,f450,f8366]) ).

fof(f8366,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(f1119,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_49
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f451]) ).

fof(f8364,plain,
    ( spl0_553
    | ~ spl0_86
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f884,f829,f670,f8362]) ).

fof(f8362,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(f884,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_86
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f671]) ).

fof(f8360,plain,
    ( ~ spl0_3
    | ~ spl0_551
    | spl0_552
    | ~ spl0_64
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f878,f825,f538,f8357,f8353,f215]) ).

fof(f215,plain,
    ( spl0_3
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f8353,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(f8357,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(f878,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_64
    | ~ spl0_111 ),
    inference(resolution,[],[f826,f539]) ).

fof(f8349,plain,
    ( ~ spl0_550
    | ~ spl0_236
    | spl0_549 ),
    inference(avatar_split_clause,[],[f8343,f8339,f2317,f8346]) ).

fof(f8346,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(f8339,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(f8343,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_236
    | spl0_549 ),
    inference(forward_demodulation,[],[f8340,f2319]) ).

fof(f8340,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,[],[f8339]) ).

fof(f8342,plain,
    ( spl0_234
    | ~ spl0_548
    | spl0_549
    | ~ spl0_85
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f782,f763,f660,f8339,f8335,f2307]) ).

fof(f782,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ member(identity_relation,universal_class)
    | null_class = identity_relation
    | ~ spl0_85
    | ~ spl0_103 ),
    inference(resolution,[],[f764,f661]) ).

fof(f8331,plain,
    ( spl0_232
    | ~ spl0_546
    | spl0_547
    | ~ spl0_85
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f778,f737,f660,f8328,f8324,f2289]) ).

fof(f8324,plain,
    ( spl0_546
  <=> member(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f8328,plain,
    ( spl0_547
  <=> 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_547])]) ).

fof(f778,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
    | ~ member(singleton_relation,universal_class)
    | null_class = singleton_relation
    | ~ spl0_85
    | ~ spl0_98 ),
    inference(resolution,[],[f738,f661]) ).

fof(f8302,plain,
    ( spl0_545
    | ~ spl0_68
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1755,f1751,f562,f8300]) ).

fof(f8300,plain,
    ( spl0_545
  <=> ! [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_545])]) ).

fof(f1755,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_68
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f563]) ).

fof(f8298,plain,
    ( spl0_544
    | ~ spl0_69
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1754,f1751,f566,f8296]) ).

fof(f8296,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_homomorphism1(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f1754,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_69
    | ~ spl0_200 ),
    inference(resolution,[],[f1752,f567]) ).

fof(f8294,plain,
    ( spl0_543
    | ~ spl0_40
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1389,f1367,f382,f8292]) ).

fof(f8292,plain,
    ( spl0_543
  <=> ! [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_543])]) ).

fof(f1389,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_40
    | ~ spl0_164 ),
    inference(resolution,[],[f1368,f383]) ).

fof(f8290,plain,
    ( spl0_542
    | ~ spl0_109
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1319,f1300,f817,f8288]) ).

fof(f8288,plain,
    ( spl0_542
  <=> ! [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_542])]) ).

fof(f1319,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_109
    | ~ spl0_159 ),
    inference(resolution,[],[f1301,f818]) ).

fof(f8286,plain,
    ( ~ spl0_540
    | ~ spl0_541
    | ~ spl0_236
    | ~ spl0_274
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3165,f2895,f2536,f2317,f8283,f8279]) ).

fof(f8279,plain,
    ( spl0_540
  <=> member(not_subclass_element(cross_product(x,y),z),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f8283,plain,
    ( spl0_541
  <=> subclass(universal_class,compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f3165,plain,
    ( ~ subclass(universal_class,compose(element_relation,complement(singleton_relation)))
    | ~ member(not_subclass_element(cross_product(x,y),z),singleton_relation)
    | ~ spl0_236
    | ~ spl0_274
    | ~ spl0_298 ),
    inference(forward_demodulation,[],[f3159,f2319]) ).

fof(f3159,plain,
    ( ~ subclass(universal_class,compose(element_relation,complement(identity_relation)))
    | ~ member(not_subclass_element(cross_product(x,y),z),singleton_relation)
    | ~ spl0_274
    | ~ spl0_298 ),
    inference(resolution,[],[f2896,f2537]) ).

fof(f8277,plain,
    ( spl0_539
    | ~ spl0_49
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1266,f1253,f450,f8275]) ).

fof(f8275,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(f1266,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_49
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f451]) ).

fof(f7943,plain,
    ( spl0_538
    | ~ spl0_39
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3145,f2895,f378,f7941]) ).

fof(f3145,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(not_subclass_element(cross_product(x,y),z),X1) )
    | ~ spl0_39
    | ~ spl0_298 ),
    inference(resolution,[],[f2896,f379]) ).

fof(f7604,plain,
    ( spl0_537
    | ~ spl0_65
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1721,f1717,f545,f7602]) ).

fof(f7602,plain,
    ( spl0_537
  <=> ! [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_537])]) ).

fof(f1721,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_65
    | ~ spl0_199 ),
    inference(superposition,[],[f546,f1718]) ).

fof(f7600,plain,
    ( spl0_536
    | ~ spl0_23
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1560,f1555,f301,f7598]) ).

fof(f7598,plain,
    ( spl0_536
  <=> ! [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_536])]) ).

fof(f1560,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_23
    | ~ spl0_185 ),
    inference(resolution,[],[f1556,f302]) ).

fof(f7596,plain,
    ( spl0_535
    | ~ spl0_39
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1519,f1483,f378,f7594]) ).

fof(f7594,plain,
    ( spl0_535
  <=> ! [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_535])]) ).

fof(f1519,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_39
    | ~ spl0_177 ),
    inference(resolution,[],[f1484,f379]) ).

fof(f7592,plain,
    ( spl0_534
    | ~ spl0_39
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1504,f1462,f378,f7590]) ).

fof(f7590,plain,
    ( spl0_534
  <=> ! [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_534])]) ).

fof(f1504,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_39
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f379]) ).

fof(f7588,plain,
    ( spl0_533
    | ~ spl0_39
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1486,f1458,f378,f7586]) ).

fof(f7586,plain,
    ( spl0_533
  <=> ! [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_533])]) ).

fof(f1486,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_39
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f379]) ).

fof(f7584,plain,
    ( spl0_532
    | ~ spl0_58
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1442,f1379,f509,f7582]) ).

fof(f7582,plain,
    ( spl0_532
  <=> ! [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_532])]) ).

fof(f509,plain,
    ( spl0_58
  <=> ! [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_58])]) ).

fof(f1442,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_58
    | ~ spl0_167 ),
    inference(resolution,[],[f1380,f510]) ).

fof(f510,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f509]) ).

fof(f7580,plain,
    ( spl0_531
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1390,f1367,f825,f7578]) ).

fof(f7578,plain,
    ( spl0_531
  <=> ! [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_531])]) ).

fof(f1390,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_111
    | ~ spl0_164 ),
    inference(resolution,[],[f1368,f826]) ).

fof(f7576,plain,
    ( spl0_530
    | ~ spl0_117
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1317,f1300,f925,f7574]) ).

fof(f7574,plain,
    ( spl0_530
  <=> ! [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_530])]) ).

fof(f1317,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_117
    | ~ spl0_159 ),
    inference(resolution,[],[f1301,f926]) ).

fof(f7571,plain,
    ( ~ spl0_529
    | ~ spl0_236
    | spl0_527 ),
    inference(avatar_split_clause,[],[f7563,f7555,f2317,f7568]) ).

fof(f7568,plain,
    ( spl0_529
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f7555,plain,
    ( spl0_527
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f7563,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
    | ~ spl0_236
    | spl0_527 ),
    inference(forward_demodulation,[],[f7556,f2319]) ).

fof(f7556,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | spl0_527 ),
    inference(avatar_component_clause,[],[f7555]) ).

fof(f7562,plain,
    ( spl0_526
    | spl0_527
    | ~ spl0_528
    | ~ spl0_24
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1216,f1173,f305,f7559,f7555,f7551]) ).

fof(f7559,plain,
    ( spl0_528
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f1216,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_24
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f306]) ).

fof(f7546,plain,
    ( ~ spl0_525
    | ~ spl0_236
    | spl0_520 ),
    inference(avatar_split_clause,[],[f7525,f7516,f2317,f7543]) ).

fof(f7543,plain,
    ( spl0_525
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f7516,plain,
    ( spl0_520
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f7525,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
    | ~ spl0_236
    | spl0_520 ),
    inference(forward_demodulation,[],[f7517,f2319]) ).

fof(f7517,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | spl0_520 ),
    inference(avatar_component_clause,[],[f7516]) ).

fof(f7541,plain,
    ( ~ spl0_524
    | ~ spl0_236
    | spl0_521 ),
    inference(avatar_split_clause,[],[f7524,f7520,f2317,f7538]) ).

fof(f7538,plain,
    ( spl0_524
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f7520,plain,
    ( spl0_521
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f7524,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
    | ~ spl0_236
    | spl0_521 ),
    inference(forward_demodulation,[],[f7522,f2319]) ).

fof(f7522,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | spl0_521 ),
    inference(avatar_component_clause,[],[f7520]) ).

fof(f7536,plain,
    ( ~ spl0_523
    | ~ spl0_23
    | spl0_511 ),
    inference(avatar_split_clause,[],[f7450,f7206,f301,f7533]) ).

fof(f7533,plain,
    ( spl0_523
  <=> function(cross_product(x,y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f7206,plain,
    ( spl0_511
  <=> subclass(cross_product(x,y),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f7450,plain,
    ( ~ function(cross_product(x,y))
    | ~ spl0_23
    | spl0_511 ),
    inference(resolution,[],[f7208,f302]) ).

fof(f7208,plain,
    ( ~ subclass(cross_product(x,y),cross_product(universal_class,universal_class))
    | spl0_511 ),
    inference(avatar_component_clause,[],[f7206]) ).

fof(f7531,plain,
    ( ~ spl0_522
    | ~ spl0_236
    | spl0_519 ),
    inference(avatar_split_clause,[],[f7526,f7512,f2317,f7528]) ).

fof(f7528,plain,
    ( spl0_522
  <=> null_class = complement(compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f7526,plain,
    ( null_class != complement(compose(element_relation,complement(singleton_relation)))
    | ~ spl0_236
    | spl0_519 ),
    inference(forward_demodulation,[],[f7513,f2319]) ).

fof(f7513,plain,
    ( null_class != complement(compose(element_relation,complement(identity_relation)))
    | spl0_519 ),
    inference(avatar_component_clause,[],[f7512]) ).

fof(f7523,plain,
    ( spl0_519
    | spl0_520
    | ~ spl0_521
    | ~ spl0_24
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1202,f1169,f305,f7520,f7516,f7512]) ).

fof(f1202,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_24
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f306]) ).

fof(f7510,plain,
    ( spl0_518
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1191,f1165,f1014,f7508]) ).

fof(f7508,plain,
    ( spl0_518
  <=> ! [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_518])]) ).

fof(f1191,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_130
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f1015]) ).

fof(f7506,plain,
    ( spl0_517
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1189,f1165,f1010,f7504]) ).

fof(f7504,plain,
    ( spl0_517
  <=> ! [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_517])]) ).

fof(f1189,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_129
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f1011]) ).

fof(f7502,plain,
    ( spl0_516
    | ~ spl0_49
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1050,f1014,f450,f7500]) ).

fof(f7500,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f1050,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_49
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f451]) ).

fof(f7498,plain,
    ( spl0_515
    | ~ spl0_49
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1034,f1010,f450,f7496]) ).

fof(f7496,plain,
    ( spl0_515
  <=> ! [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_515])]) ).

fof(f1034,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_49
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f451]) ).

fof(f7221,plain,
    ( spl0_514
    | ~ spl0_62
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1720,f1717,f530,f7219]) ).

fof(f7219,plain,
    ( spl0_514
  <=> ! [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_514])]) ).

fof(f1720,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_62
    | ~ spl0_199 ),
    inference(superposition,[],[f531,f1718]) ).

fof(f7217,plain,
    ( spl0_513
    | ~ spl0_131
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1615,f1590,f1018,f7215]) ).

fof(f7215,plain,
    ( spl0_513
  <=> ! [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_513])]) ).

fof(f1615,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_131
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1614]) ).

fof(f1614,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_131
    | ~ spl0_188 ),
    inference(resolution,[],[f1591,f1019]) ).

fof(f7213,plain,
    ( spl0_512
    | ~ spl0_32
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1508,f1462,f341,f7211]) ).

fof(f7211,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))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f1508,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_32
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f342]) ).

fof(f7209,plain,
    ( spl0_1
    | ~ spl0_511
    | ~ spl0_131
    | spl0_440 ),
    inference(avatar_split_clause,[],[f6066,f5718,f1018,f7206,f205]) ).

fof(f5718,plain,
    ( spl0_440
  <=> member(not_subclass_element(cross_product(x,y),z),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f6066,plain,
    ( ~ subclass(cross_product(x,y),cross_product(universal_class,universal_class))
    | subclass(cross_product(x,y),z)
    | ~ spl0_131
    | spl0_440 ),
    inference(resolution,[],[f5719,f1019]) ).

fof(f5719,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(universal_class,universal_class))
    | spl0_440 ),
    inference(avatar_component_clause,[],[f5718]) ).

fof(f7204,plain,
    ( spl0_510
    | ~ spl0_33
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1507,f1462,f345,f7202]) ).

fof(f7202,plain,
    ( spl0_510
  <=> ! [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_510])]) ).

fof(f1507,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_33
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f346]) ).

fof(f7200,plain,
    ( spl0_509
    | ~ spl0_32
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1490,f1458,f341,f7198]) ).

fof(f7198,plain,
    ( spl0_509
  <=> ! [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_509])]) ).

fof(f1490,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_32
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f342]) ).

fof(f7196,plain,
    ( spl0_508
    | ~ spl0_33
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1489,f1458,f345,f7194]) ).

fof(f7194,plain,
    ( spl0_508
  <=> ! [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_508])]) ).

fof(f1489,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_33
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f346]) ).

fof(f7192,plain,
    ( spl0_507
    | ~ spl0_39
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1428,f1375,f378,f7190]) ).

fof(f7190,plain,
    ( spl0_507
  <=> ! [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_507])]) ).

fof(f1428,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_39
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f379]) ).

fof(f7188,plain,
    ( spl0_506
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1352,f1322,f1165,f7186]) ).

fof(f7186,plain,
    ( spl0_506
  <=> ! [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_506])]) ).

fof(f1352,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_143
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1331]) ).

fof(f1331,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_143
    | ~ spl0_161 ),
    inference(superposition,[],[f1166,f1323]) ).

fof(f7184,plain,
    ( spl0_505
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1347,f1322,f1165,f7182]) ).

fof(f7182,plain,
    ( spl0_505
  <=> ! [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_505])]) ).

fof(f1347,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_143
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1336]) ).

fof(f1336,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_143
    | ~ spl0_161 ),
    inference(superposition,[],[f1166,f1323]) ).

fof(f7180,plain,
    ( spl0_504
    | ~ spl0_50
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f978,f921,f454,f7178]) ).

fof(f7178,plain,
    ( spl0_504
  <=> ! [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_504])]) ).

fof(f978,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_50
    | ~ spl0_116 ),
    inference(resolution,[],[f922,f455]) ).

fof(f7030,plain,
    ( spl0_503
    | ~ spl0_236
    | ~ spl0_494 ),
    inference(avatar_split_clause,[],[f6993,f6990,f2317,f7028]) ).

fof(f7028,plain,
    ( spl0_503
  <=> ! [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_503])]) ).

fof(f6990,plain,
    ( spl0_494
  <=> ! [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_494])]) ).

fof(f6993,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_236
    | ~ spl0_494 ),
    inference(forward_demodulation,[],[f6991,f2319]) ).

fof(f6991,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_494 ),
    inference(avatar_component_clause,[],[f6990]) ).

fof(f7026,plain,
    ( spl0_502
    | ~ spl0_69
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1882,f1875,f566,f7024]) ).

fof(f7024,plain,
    ( spl0_502
  <=> ! [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_502])]) ).

fof(f1882,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_69
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f567]) ).

fof(f7022,plain,
    ( spl0_501
    | ~ spl0_21
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1509,f1462,f293,f7020]) ).

fof(f7020,plain,
    ( spl0_501
  <=> ! [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_501])]) ).

fof(f1509,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_21
    | ~ spl0_172 ),
    inference(resolution,[],[f1463,f294]) ).

fof(f7018,plain,
    ( spl0_500
    | ~ spl0_21
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1491,f1458,f293,f7016]) ).

fof(f7016,plain,
    ( spl0_500
  <=> ! [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_500])]) ).

fof(f1491,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_21
    | ~ spl0_171 ),
    inference(resolution,[],[f1459,f294]) ).

fof(f7014,plain,
    ( spl0_499
    | ~ spl0_32
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1432,f1375,f341,f7012]) ).

fof(f7012,plain,
    ( spl0_499
  <=> ! [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_499])]) ).

fof(f1432,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_32
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f342]) ).

fof(f7010,plain,
    ( spl0_1
    | ~ spl0_498
    | ~ spl0_131
    | spl0_475 ),
    inference(avatar_split_clause,[],[f6588,f6413,f1018,f7007,f205]) ).

fof(f7007,plain,
    ( spl0_498
  <=> subclass(cross_product(x,y),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f6413,plain,
    ( spl0_475
  <=> member(not_subclass_element(cross_product(x,y),z),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f6588,plain,
    ( ~ subclass(cross_product(x,y),subset_relation)
    | subclass(cross_product(x,y),z)
    | ~ spl0_131
    | spl0_475 ),
    inference(resolution,[],[f6415,f1019]) ).

fof(f6415,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),subset_relation)
    | spl0_475 ),
    inference(avatar_component_clause,[],[f6413]) ).

fof(f7005,plain,
    ( spl0_497
    | ~ spl0_33
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1431,f1375,f345,f7003]) ).

fof(f7003,plain,
    ( spl0_497
  <=> ! [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_497])]) ).

fof(f1431,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_33
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f346]) ).

fof(f7001,plain,
    ( spl0_496
    | ~ spl0_110
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1388,f1367,f821,f6999]) ).

fof(f6999,plain,
    ( spl0_496
  <=> ! [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_496])]) ).

fof(f821,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1388,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_110
    | ~ spl0_164 ),
    inference(resolution,[],[f1368,f822]) ).

fof(f822,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f821]) ).

fof(f6997,plain,
    ( spl0_495
    | ~ spl0_39
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1362,f1357,f378,f6995]) ).

fof(f6995,plain,
    ( spl0_495
  <=> ! [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_495])]) ).

fof(f1362,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_39
    | ~ spl0_163 ),
    inference(resolution,[],[f1358,f379]) ).

fof(f6992,plain,
    ( spl0_494
    | ~ spl0_51
    | ~ spl0_72
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1223,f1173,f579,f458,f6990]) ).

fof(f1223,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_51
    | ~ spl0_72
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1210,f459]) ).

fof(f1210,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_72
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f580]) ).

fof(f6781,plain,
    ( spl0_493
    | ~ spl0_236
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f6602,f6599,f2317,f6779]) ).

fof(f6779,plain,
    ( spl0_493
  <=> ! [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_493])]) ).

fof(f6599,plain,
    ( spl0_481
  <=> ! [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_481])]) ).

fof(f6602,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_236
    | ~ spl0_481 ),
    inference(forward_demodulation,[],[f6600,f2319]) ).

fof(f6600,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_481 ),
    inference(avatar_component_clause,[],[f6599]) ).

fof(f6777,plain,
    ( spl0_492
    | ~ spl0_236
    | ~ spl0_480 ),
    inference(avatar_split_clause,[],[f6597,f6594,f2317,f6775]) ).

fof(f6775,plain,
    ( spl0_492
  <=> ! [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_492])]) ).

fof(f6594,plain,
    ( spl0_480
  <=> ! [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_480])]) ).

fof(f6597,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_236
    | ~ spl0_480 ),
    inference(forward_demodulation,[],[f6595,f2319]) ).

fof(f6595,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_480 ),
    inference(avatar_component_clause,[],[f6594]) ).

fof(f6643,plain,
    ( spl0_490
    | ~ spl0_491
    | ~ spl0_87
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1879,f1875,f675,f6640,f6637]) ).

fof(f6637,plain,
    ( spl0_490
  <=> ! [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_490])]) ).

fof(f6640,plain,
    ( spl0_491
  <=> subclass(composition_function,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f1879,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X1,domain_of(X0)) )
    | ~ spl0_87
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f676]) ).

fof(f6635,plain,
    ( ~ spl0_489
    | spl0_1
    | ~ spl0_313
    | spl0_475 ),
    inference(avatar_split_clause,[],[f6586,f6413,f3179,f205,f6632]) ).

fof(f6632,plain,
    ( spl0_489
  <=> subclass(cross_product(x,y),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f6586,plain,
    ( subclass(cross_product(x,y),z)
    | ~ subclass(cross_product(x,y),singleton_relation)
    | ~ spl0_313
    | spl0_475 ),
    inference(resolution,[],[f6415,f3180]) ).

fof(f6630,plain,
    ( spl0_488
    | ~ spl0_69
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1723,f1717,f566,f6628]) ).

fof(f6628,plain,
    ( spl0_488
  <=> ! [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_488])]) ).

fof(f1723,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_69
    | ~ spl0_199 ),
    inference(superposition,[],[f567,f1718]) ).

fof(f6626,plain,
    ( spl0_487
    | ~ spl0_68
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1722,f1717,f562,f6624]) ).

fof(f6624,plain,
    ( spl0_487
  <=> ! [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_487])]) ).

fof(f1722,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_68
    | ~ spl0_199 ),
    inference(superposition,[],[f563,f1718]) ).

fof(f6622,plain,
    ( spl0_486
    | ~ spl0_23
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1446,f1379,f301,f6620]) ).

fof(f6620,plain,
    ( spl0_486
  <=> ! [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_486])]) ).

fof(f1446,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_23
    | ~ spl0_167 ),
    inference(resolution,[],[f1380,f302]) ).

fof(f6618,plain,
    ( spl0_485
    | ~ spl0_21
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1433,f1375,f293,f6616]) ).

fof(f1433,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_21
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f294]) ).

fof(f6614,plain,
    ( spl0_484
    | ~ spl0_132
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1387,f1367,f1022,f6612]) ).

fof(f6612,plain,
    ( spl0_484
  <=> ! [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_484])]) ).

fof(f1387,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_132
    | ~ spl0_164 ),
    inference(resolution,[],[f1368,f1023]) ).

fof(f6610,plain,
    ( spl0_483
    | ~ spl0_133
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1386,f1367,f1026,f6608]) ).

fof(f6608,plain,
    ( spl0_483
  <=> ! [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_483])]) ).

fof(f1386,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_133
    | ~ spl0_164 ),
    inference(resolution,[],[f1368,f1027]) ).

fof(f6606,plain,
    ( spl0_482
    | ~ spl0_39
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1353,f1326,f378,f6604]) ).

fof(f6604,plain,
    ( spl0_482
  <=> ! [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_482])]) ).

fof(f1326,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

fof(f1353,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_39
    | ~ spl0_162 ),
    inference(resolution,[],[f1327,f379]) ).

fof(f1327,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_162 ),
    inference(avatar_component_clause,[],[f1326]) ).

fof(f6601,plain,
    ( spl0_481
    | ~ spl0_131
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1222,f1173,f1018,f6599]) ).

fof(f1222,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_131
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f1019]) ).

fof(f6596,plain,
    ( spl0_480
    | ~ spl0_131
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1208,f1169,f1018,f6594]) ).

fof(f1208,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_131
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f1019]) ).

fof(f6592,plain,
    ( spl0_479
    | ~ spl0_131
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1194,f1165,f1018,f6590]) ).

fof(f6590,plain,
    ( spl0_479
  <=> ! [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_479])]) ).

fof(f1194,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_131
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f1019]) ).

fof(f6585,plain,
    ( spl0_478
    | ~ spl0_77
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1149,f1093,f614,f6583]) ).

fof(f6583,plain,
    ( spl0_478
  <=> ! [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_478])]) ).

fof(f1149,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_77
    | ~ spl0_136 ),
    inference(superposition,[],[f1094,f616]) ).

fof(f6581,plain,
    ( spl0_477
    | ~ spl0_50
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f902,f890,f454,f6579]) ).

fof(f6579,plain,
    ( spl0_477
  <=> ! [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_477])]) ).

fof(f902,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_50
    | ~ spl0_113 ),
    inference(resolution,[],[f891,f455]) ).

fof(f6420,plain,
    ( spl0_476
    | ~ spl0_27
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1618,f1590,f321,f6418]) ).

fof(f6418,plain,
    ( spl0_476
  <=> ! [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_476])]) ).

fof(f1618,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_188 ),
    inference(duplicate_literal_removal,[],[f1611]) ).

fof(f1611,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_188 ),
    inference(resolution,[],[f1591,f322]) ).

fof(f6416,plain,
    ( ~ spl0_475
    | ~ spl0_112
    | spl0_440 ),
    inference(avatar_split_clause,[],[f6064,f5718,f829,f6413]) ).

fof(f6064,plain,
    ( ~ member(not_subclass_element(cross_product(x,y),z),subset_relation)
    | ~ spl0_112
    | spl0_440 ),
    inference(resolution,[],[f5719,f830]) ).

fof(f6411,plain,
    ( spl0_474
    | ~ spl0_50
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1582,f1562,f454,f6409]) ).

fof(f6409,plain,
    ( spl0_474
  <=> ! [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_474])]) ).

fof(f1582,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_50
    | ~ spl0_186 ),
    inference(duplicate_literal_removal,[],[f1566]) ).

fof(f1566,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_50
    | ~ spl0_186 ),
    inference(resolution,[],[f1563,f455]) ).

fof(f6407,plain,
    ( ~ spl0_473
    | ~ spl0_236
    | spl0_472 ),
    inference(avatar_split_clause,[],[f6402,f6398,f2317,f6404]) ).

fof(f6404,plain,
    ( spl0_473
  <=> subclass(domain_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f6398,plain,
    ( spl0_472
  <=> subclass(domain_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f6402,plain,
    ( ~ subclass(domain_relation,singleton_relation)
    | ~ spl0_236
    | spl0_472 ),
    inference(forward_demodulation,[],[f6400,f2319]) ).

fof(f6400,plain,
    ( ~ subclass(domain_relation,identity_relation)
    | spl0_472 ),
    inference(avatar_component_clause,[],[f6398]) ).

fof(f6401,plain,
    ( spl0_471
    | ~ spl0_472
    | ~ spl0_103
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1439,f1375,f763,f6398,f6395]) ).

fof(f6395,plain,
    ( spl0_471
  <=> ! [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_471])]) ).

fof(f1439,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_166 ),
    inference(resolution,[],[f1376,f764]) ).

fof(f6393,plain,
    ( spl0_470
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1350,f1322,f925,f6391]) ).

fof(f6391,plain,
    ( spl0_470
  <=> ! [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_470])]) ).

fof(f1350,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_117
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1333]) ).

fof(f1333,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_117
    | ~ spl0_161 ),
    inference(superposition,[],[f926,f1323]) ).

fof(f6389,plain,
    ( spl0_469
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1345,f1322,f925,f6387]) ).

fof(f6387,plain,
    ( spl0_469
  <=> ! [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_469])]) ).

fof(f1345,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_117
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1338]) ).

fof(f1338,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_117
    | ~ spl0_161 ),
    inference(superposition,[],[f926,f1323]) ).

fof(f6385,plain,
    ( spl0_468
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1184,f1165,f321,f6383]) ).

fof(f6383,plain,
    ( spl0_468
  <=> ! [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_468])]) ).

fof(f1184,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_143 ),
    inference(resolution,[],[f1166,f322]) ).

fof(f6373,plain,
    ( spl0_275
    | spl0_467
    | ~ spl0_77
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1062,f1014,f614,f6370,f2540]) ).

fof(f1062,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_77
    | ~ spl0_130 ),
    inference(superposition,[],[f1015,f616]) ).

fof(f6368,plain,
    ( spl0_466
    | ~ spl0_45
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f979,f921,f430,f6366]) ).

fof(f6366,plain,
    ( spl0_466
  <=> ! [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_466])]) ).

fof(f979,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_45
    | ~ spl0_116 ),
    inference(resolution,[],[f922,f431]) ).

fof(f6363,plain,
    ( spl0_465
    | ~ spl0_80
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f881,f829,f634,f6361]) ).

fof(f6361,plain,
    ( spl0_465
  <=> ! [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_465])]) ).

fof(f881,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_80
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f635]) ).

fof(f6203,plain,
    ( spl0_464
    | ~ spl0_236
    | ~ spl0_457 ),
    inference(avatar_split_clause,[],[f6089,f6086,f2317,f6201]) ).

fof(f6201,plain,
    ( spl0_464
  <=> ! [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_464])]) ).

fof(f6086,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(f6089,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_236
    | ~ spl0_457 ),
    inference(forward_demodulation,[],[f6087,f2319]) ).

fof(f6087,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,[],[f6086]) ).

fof(f6199,plain,
    ( spl0_463
    | ~ spl0_236
    | ~ spl0_456 ),
    inference(avatar_split_clause,[],[f6084,f6081,f2317,f6197]) ).

fof(f6197,plain,
    ( spl0_463
  <=> ! [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_463])]) ).

fof(f6081,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(f6084,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_236
    | ~ spl0_456 ),
    inference(forward_demodulation,[],[f6082,f2319]) ).

fof(f6082,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,[],[f6081]) ).

fof(f6120,plain,
    ( ~ spl0_462
    | ~ spl0_298
    | spl0_440 ),
    inference(avatar_split_clause,[],[f6065,f5718,f2895,f6117]) ).

fof(f6117,plain,
    ( spl0_462
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f6065,plain,
    ( ~ subclass(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_298
    | spl0_440 ),
    inference(resolution,[],[f5719,f2896]) ).

fof(f6105,plain,
    ( spl0_461
    | ~ spl0_236
    | ~ spl0_453 ),
    inference(avatar_split_clause,[],[f6071,f6068,f2317,f6103]) ).

fof(f6103,plain,
    ( spl0_461
  <=> ! [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_461])]) ).

fof(f6068,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(f6071,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_236
    | ~ spl0_453 ),
    inference(forward_demodulation,[],[f6069,f2319]) ).

fof(f6069,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,[],[f6068]) ).

fof(f6101,plain,
    ( spl0_460
    | ~ spl0_236
    | ~ spl0_452 ),
    inference(avatar_split_clause,[],[f6063,f6059,f2317,f6099]) ).

fof(f6099,plain,
    ( spl0_460
  <=> ! [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_460])]) ).

fof(f6059,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(f6063,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_236
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f6062,f2319]) ).

fof(f6062,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_236
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f6060,f2319]) ).

fof(f6060,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,[],[f6059]) ).

fof(f6097,plain,
    ( spl0_459
    | ~ spl0_42
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1349,f1322,f390,f6095]) ).

fof(f6095,plain,
    ( spl0_459
  <=> ! [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_459])]) ).

fof(f1349,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_42
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1334]) ).

fof(f1334,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_42
    | ~ spl0_161 ),
    inference(superposition,[],[f391,f1323]) ).

fof(f6093,plain,
    ( spl0_458
    | ~ spl0_42
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1344,f1322,f390,f6091]) ).

fof(f6091,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(f1344,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_42
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1339]) ).

fof(f1339,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_42
    | ~ spl0_161 ),
    inference(superposition,[],[f391,f1323]) ).

fof(f6088,plain,
    ( spl0_457
    | ~ spl0_117
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1218,f1173,f925,f6086]) ).

fof(f1218,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_117
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f926]) ).

fof(f6083,plain,
    ( spl0_456
    | ~ spl0_117
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1204,f1169,f925,f6081]) ).

fof(f1204,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_117
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f926]) ).

fof(f6079,plain,
    ( spl0_455
    | ~ spl0_117
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1190,f1165,f925,f6077]) ).

fof(f6077,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(f1190,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f926]) ).

fof(f6075,plain,
    ( spl0_454
    | ~ spl0_49
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1068,f1018,f450,f6073]) ).

fof(f6073,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(f1068,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_49
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f451]) ).

fof(f6070,plain,
    ( spl0_453
    | ~ spl0_116
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1005,f965,f921,f6068]) ).

fof(f1005,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_116
    | ~ spl0_126 ),
    inference(resolution,[],[f966,f922]) ).

fof(f6061,plain,
    ( spl0_452
    | ~ spl0_116
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1001,f961,f921,f6059]) ).

fof(f1001,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_116
    | ~ spl0_125 ),
    inference(resolution,[],[f962,f922]) ).

fof(f6000,plain,
    ( spl0_451
    | ~ spl0_236
    | ~ spl0_447 ),
    inference(avatar_split_clause,[],[f5753,f5748,f2317,f5998]) ).

fof(f5998,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(f5748,plain,
    ( spl0_447
  <=> ! [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_447])]) ).

fof(f5753,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_236
    | ~ spl0_447 ),
    inference(forward_demodulation,[],[f5752,f2319]) ).

fof(f5752,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_236
    | ~ spl0_447 ),
    inference(forward_demodulation,[],[f5751,f2319]) ).

fof(f5751,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_236
    | ~ spl0_447 ),
    inference(forward_demodulation,[],[f5749,f2319]) ).

fof(f5749,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_447 ),
    inference(avatar_component_clause,[],[f5748]) ).

fof(f5996,plain,
    ( spl0_450
    | ~ spl0_236
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f5746,f5743,f2317,f5994]) ).

fof(f5994,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(f5743,plain,
    ( spl0_446
  <=> ! [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_446])]) ).

fof(f5746,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_236
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5744,f2319]) ).

fof(f5744,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_446 ),
    inference(avatar_component_clause,[],[f5743]) ).

fof(f5761,plain,
    ( spl0_448
    | ~ spl0_449
    | ~ spl0_79
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1420,f1375,f630,f5758,f5755]) ).

fof(f5755,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(f5758,plain,
    ( spl0_449
  <=> subclass(domain_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1420,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,successor_relation)
        | ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
    | ~ spl0_79
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f631]) ).

fof(f5750,plain,
    ( spl0_447
    | ~ spl0_44
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1409,f1371,f399,f5748]) ).

fof(f1409,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_44
    | ~ spl0_165 ),
    inference(superposition,[],[f1372,f401]) ).

fof(f5745,plain,
    ( spl0_446
    | ~ spl0_43
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1408,f1371,f394,f5743]) ).

fof(f1408,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_43
    | ~ spl0_165 ),
    inference(superposition,[],[f1372,f396]) ).

fof(f5741,plain,
    ( spl0_445
    | ~ spl0_42
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1404,f1371,f390,f5739]) ).

fof(f5739,plain,
    ( spl0_445
  <=> ! [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_445])]) ).

fof(f1404,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_42
    | ~ spl0_165 ),
    inference(superposition,[],[f1372,f391]) ).

fof(f5737,plain,
    ( spl0_444
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1351,f1322,f957,f5735]) ).

fof(f5735,plain,
    ( spl0_444
  <=> ! [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_444])]) ).

fof(f1351,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1332]) ).

fof(f1332,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_124
    | ~ spl0_161 ),
    inference(superposition,[],[f958,f1323]) ).

fof(f5733,plain,
    ( spl0_443
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1346,f1322,f957,f5731]) ).

fof(f5731,plain,
    ( spl0_443
  <=> ! [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_443])]) ).

fof(f1346,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1337]) ).

fof(f1337,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_124
    | ~ spl0_161 ),
    inference(superposition,[],[f958,f1323]) ).

fof(f5729,plain,
    ( spl0_442
    | ~ spl0_39
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1265,f1253,f378,f5727]) ).

fof(f5727,plain,
    ( spl0_442
  <=> ! [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_442])]) ).

fof(f1265,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_39
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f379]) ).

fof(f5725,plain,
    ( spl0_440
    | ~ spl0_441
    | ~ spl0_77
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f5263,f4945,f614,f5722,f5718]) ).

fof(f5722,plain,
    ( spl0_441
  <=> subclass(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f4945,plain,
    ( spl0_406
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(not_subclass_element(cross_product(x,y),z),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f5263,plain,
    ( ~ subclass(universal_class,subset_relation)
    | member(not_subclass_element(cross_product(x,y),z),cross_product(universal_class,universal_class))
    | ~ spl0_77
    | ~ spl0_406 ),
    inference(superposition,[],[f4946,f616]) ).

fof(f4946,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(not_subclass_element(cross_product(x,y),z),X0) )
    | ~ spl0_406 ),
    inference(avatar_component_clause,[],[f4945]) ).

fof(f5716,plain,
    ( ~ spl0_438
    | spl0_439
    | ~ spl0_109
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1221,f1173,f817,f5714,f5710]) ).

fof(f5710,plain,
    ( spl0_438
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f5714,plain,
    ( spl0_439
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f1221,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_109
    | ~ spl0_145 ),
    inference(resolution,[],[f1174,f818]) ).

fof(f5708,plain,
    ( ~ spl0_437
    | ~ spl0_236
    | spl0_435 ),
    inference(avatar_split_clause,[],[f5703,f5696,f2317,f5705]) ).

fof(f5705,plain,
    ( spl0_437
  <=> subclass(universal_class,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f5703,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_236
    | spl0_435 ),
    inference(forward_demodulation,[],[f5698,f2319]) ).

fof(f5698,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
    | spl0_435 ),
    inference(avatar_component_clause,[],[f5696]) ).

fof(f5702,plain,
    ( ~ spl0_435
    | spl0_436
    | ~ spl0_109
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1207,f1169,f817,f5700,f5696]) ).

fof(f5700,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(f1207,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_109
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f818]) ).

fof(f5694,plain,
    ( spl0_434
    | ~ spl0_109
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1193,f1165,f817,f5692]) ).

fof(f5692,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(f1193,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_109
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f818]) ).

fof(f5690,plain,
    ( spl0_433
    | ~ spl0_24
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1188,f1165,f305,f5688]) ).

fof(f5688,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(f1188,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) )
    | ~ spl0_24
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f306]) ).

fof(f5685,plain,
    ( ~ spl0_432
    | ~ spl0_236
    | spl0_431 ),
    inference(avatar_split_clause,[],[f5676,f5672,f2317,f5682]) ).

fof(f5682,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(f5672,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(f5676,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
    | ~ spl0_236
    | spl0_431 ),
    inference(forward_demodulation,[],[f5674,f2319]) ).

fof(f5674,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | spl0_431 ),
    inference(avatar_component_clause,[],[f5672]) ).

fof(f5675,plain,
    ( spl0_430
    | ~ spl0_431
    | ~ spl0_113
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1007,f965,f890,f5672,f5668]) ).

fof(f1007,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_113
    | ~ spl0_126 ),
    inference(resolution,[],[f966,f891]) ).

fof(f5665,plain,
    ( ~ spl0_429
    | ~ spl0_236
    | spl0_427 ),
    inference(avatar_split_clause,[],[f5654,f5650,f2317,f5662]) ).

fof(f5662,plain,
    ( spl0_429
  <=> member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f5650,plain,
    ( spl0_427
  <=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f5654,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
    | ~ spl0_236
    | spl0_427 ),
    inference(forward_demodulation,[],[f5652,f2319]) ).

fof(f5652,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | spl0_427 ),
    inference(avatar_component_clause,[],[f5650]) ).

fof(f5660,plain,
    ( ~ spl0_428
    | ~ spl0_236
    | spl0_426 ),
    inference(avatar_split_clause,[],[f5655,f5646,f2317,f5657]) ).

fof(f5657,plain,
    ( spl0_428
  <=> null_class = complement(complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f5655,plain,
    ( null_class != complement(complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_236
    | spl0_426 ),
    inference(forward_demodulation,[],[f5647,f2319]) ).

fof(f5647,plain,
    ( null_class != complement(complement(compose(element_relation,complement(identity_relation))))
    | spl0_426 ),
    inference(avatar_component_clause,[],[f5646]) ).

fof(f5653,plain,
    ( spl0_426
    | ~ spl0_427
    | ~ spl0_113
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1002,f961,f890,f5650,f5646]) ).

fof(f1002,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_113
    | ~ spl0_125 ),
    inference(resolution,[],[f962,f891]) ).

fof(f5644,plain,
    ( spl0_425
    | ~ spl0_45
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f903,f890,f430,f5642]) ).

fof(f5642,plain,
    ( spl0_425
  <=> ! [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_425])]) ).

fof(f903,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_45
    | ~ spl0_113 ),
    inference(resolution,[],[f891,f431]) ).

fof(f5522,plain,
    ( spl0_424
    | ~ spl0_236
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f3887,f2467,f2317,f5519]) ).

fof(f5519,plain,
    ( spl0_424
  <=> subclass(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f2467,plain,
    ( spl0_265
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f3887,plain,
    ( subclass(singleton_relation,subset_relation)
    | ~ spl0_236
    | ~ spl0_265 ),
    inference(superposition,[],[f2469,f2319]) ).

fof(f2469,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f2467]) ).

fof(f5321,plain,
    ( spl0_423
    | ~ spl0_236
    | ~ spl0_413 ),
    inference(avatar_split_clause,[],[f4977,f4974,f2317,f5319]) ).

fof(f5319,plain,
    ( spl0_423
  <=> ! [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_423])]) ).

fof(f4974,plain,
    ( spl0_413
  <=> ! [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_413])]) ).

fof(f4977,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_236
    | ~ spl0_413 ),
    inference(forward_demodulation,[],[f4975,f2319]) ).

fof(f4975,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_413 ),
    inference(avatar_component_clause,[],[f4974]) ).

fof(f5317,plain,
    ( spl0_422
    | ~ spl0_236
    | ~ spl0_412 ),
    inference(avatar_split_clause,[],[f4972,f4969,f2317,f5315]) ).

fof(f5315,plain,
    ( spl0_422
  <=> ! [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_422])]) ).

fof(f4969,plain,
    ( spl0_412
  <=> ! [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_412])]) ).

fof(f4972,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_236
    | ~ spl0_412 ),
    inference(forward_demodulation,[],[f4970,f2319]) ).

fof(f4970,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_412 ),
    inference(avatar_component_clause,[],[f4969]) ).

fof(f5025,plain,
    ( spl0_421
    | ~ spl0_236
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4943,f4940,f2317,f5023]) ).

fof(f4940,plain,
    ( spl0_405
  <=> ! [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_405])]) ).

fof(f4943,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_236
    | ~ spl0_405 ),
    inference(forward_demodulation,[],[f4941,f2319]) ).

fof(f4941,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_405 ),
    inference(avatar_component_clause,[],[f4940]) ).

fof(f5021,plain,
    ( spl0_420
    | ~ spl0_236
    | ~ spl0_404 ),
    inference(avatar_split_clause,[],[f4938,f4934,f2317,f5019]) ).

fof(f4934,plain,
    ( spl0_404
  <=> ! [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_404])]) ).

fof(f4938,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_236
    | ~ spl0_404 ),
    inference(forward_demodulation,[],[f4937,f2319]) ).

fof(f4937,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_236
    | ~ spl0_404 ),
    inference(forward_demodulation,[],[f4935,f2319]) ).

fof(f4935,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_404 ),
    inference(avatar_component_clause,[],[f4934]) ).

fof(f5007,plain,
    ( spl0_419
    | ~ spl0_135
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1412,f1371,f1089,f5005]) ).

fof(f1412,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_135
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1393]) ).

fof(f1393,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_135
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f1090]) ).

fof(f5003,plain,
    ( spl0_418
    | ~ spl0_136
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1411,f1371,f1093,f5001]) ).

fof(f1411,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_136
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1394]) ).

fof(f1394,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_136
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f1094]) ).

fof(f4999,plain,
    ( spl0_417
    | ~ spl0_24
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1348,f1322,f305,f4997]) ).

fof(f4997,plain,
    ( spl0_417
  <=> ! [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_417])]) ).

fof(f1348,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_24
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1335]) ).

fof(f1335,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_24
    | ~ spl0_161 ),
    inference(superposition,[],[f306,f1323]) ).

fof(f4989,plain,
    ( spl0_416
    | ~ spl0_24
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1343,f1322,f305,f4987]) ).

fof(f4987,plain,
    ( spl0_416
  <=> ! [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_416])]) ).

fof(f1343,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_24
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1340]) ).

fof(f1340,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_24
    | ~ spl0_161 ),
    inference(superposition,[],[f306,f1323]) ).

fof(f4985,plain,
    ( spl0_415
    | ~ spl0_32
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1269,f1253,f341,f4983]) ).

fof(f4983,plain,
    ( spl0_415
  <=> ! [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_415])]) ).

fof(f1269,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_32
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f342]) ).

fof(f4981,plain,
    ( spl0_414
    | ~ spl0_33
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1268,f1253,f345,f4979]) ).

fof(f4979,plain,
    ( spl0_414
  <=> ! [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_414])]) ).

fof(f1268,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_33
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f346]) ).

fof(f4976,plain,
    ( spl0_413
    | ~ spl0_44
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1264,f1249,f399,f4974]) ).

fof(f1264,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_44
    | ~ spl0_152 ),
    inference(superposition,[],[f1250,f401]) ).

fof(f4971,plain,
    ( spl0_412
    | ~ spl0_43
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1263,f1249,f394,f4969]) ).

fof(f1263,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_43
    | ~ spl0_152 ),
    inference(superposition,[],[f1250,f396]) ).

fof(f4967,plain,
    ( spl0_411
    | ~ spl0_42
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1259,f1249,f390,f4965]) ).

fof(f4965,plain,
    ( spl0_411
  <=> ! [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_411])]) ).

fof(f1259,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 )
    | ~ spl0_42
    | ~ spl0_152 ),
    inference(superposition,[],[f1250,f391]) ).

fof(f4963,plain,
    ( spl0_410
    | ~ spl0_32
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1140,f1093,f341,f4961]) ).

fof(f1140,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_32
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f342]) ).

fof(f4959,plain,
    ( spl0_409
    | ~ spl0_33
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1139,f1093,f345,f4957]) ).

fof(f1139,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_33
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f346]) ).

fof(f4955,plain,
    ( spl0_408
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1122,f1089,f341,f4953]) ).

fof(f1122,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f342]) ).

fof(f4951,plain,
    ( spl0_407
    | ~ spl0_33
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1121,f1089,f345,f4949]) ).

fof(f1121,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_33
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f346]) ).

fof(f4947,plain,
    ( spl0_406
    | ~ spl0_32
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3149,f2895,f341,f4945]) ).

fof(f3149,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(not_subclass_element(cross_product(x,y),z),X0) )
    | ~ spl0_32
    | ~ spl0_298 ),
    inference(resolution,[],[f2896,f342]) ).

fof(f4942,plain,
    ( spl0_405
    | ~ spl0_28
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1004,f965,f325,f4940]) ).

fof(f1004,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_126 ),
    inference(resolution,[],[f966,f326]) ).

fof(f4936,plain,
    ( spl0_404
    | ~ spl0_28
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1000,f961,f325,f4934]) ).

fof(f1000,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_125 ),
    inference(resolution,[],[f962,f326]) ).

fof(f4932,plain,
    ( spl0_403
    | ~ spl0_49
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f984,f925,f450,f4930]) ).

fof(f4930,plain,
    ( spl0_403
  <=> ! [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_403])]) ).

fof(f984,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_49
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f451]) ).

fof(f4813,plain,
    ( spl0_402
    | ~ spl0_236
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f4421,f4418,f2317,f4811]) ).

fof(f4811,plain,
    ( spl0_402
  <=> ! [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_402])]) ).

fof(f4418,plain,
    ( spl0_395
  <=> ! [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_395])]) ).

fof(f4421,plain,
    ( ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_236
    | ~ spl0_395 ),
    inference(forward_demodulation,[],[f4419,f2319]) ).

fof(f4419,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_395 ),
    inference(avatar_component_clause,[],[f4418]) ).

fof(f4716,plain,
    ( spl0_401
    | ~ spl0_33
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3148,f2895,f345,f4714]) ).

fof(f4714,plain,
    ( spl0_401
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(not_subclass_element(cross_product(x,y),z),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f3148,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(not_subclass_element(cross_product(x,y),z),X1) )
    | ~ spl0_33
    | ~ spl0_298 ),
    inference(resolution,[],[f2896,f346]) ).

fof(f4442,plain,
    ( spl0_400
    | ~ spl0_131
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1410,f1371,f1018,f4440]) ).

fof(f1410,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_131
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1395]) ).

fof(f1395,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_131
    | ~ spl0_165 ),
    inference(resolution,[],[f1372,f1019]) ).

fof(f4438,plain,
    ( ~ spl0_398
    | spl0_399
    | ~ spl0_13
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1316,f1300,f260,f4435,f4431]) ).

fof(f4431,plain,
    ( spl0_398
  <=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f4435,plain,
    ( spl0_399
  <=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f1316,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_13
    | ~ spl0_159 ),
    inference(resolution,[],[f1301,f261]) ).

fof(f4429,plain,
    ( spl0_397
    | ~ spl0_21
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1270,f1253,f293,f4427]) ).

fof(f4427,plain,
    ( spl0_397
  <=> ! [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_397])]) ).

fof(f1270,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_21
    | ~ spl0_153 ),
    inference(resolution,[],[f1254,f294]) ).

fof(f4425,plain,
    ( spl0_396
    | ~ spl0_23
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1258,f1249,f301,f4423]) ).

fof(f4423,plain,
    ( spl0_396
  <=> ! [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_396])]) ).

fof(f1258,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) )
    | ~ spl0_23
    | ~ spl0_152 ),
    inference(resolution,[],[f1250,f302]) ).

fof(f4420,plain,
    ( spl0_395
    | ~ spl0_45
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1197,f1169,f430,f4418]) ).

fof(f1197,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_45
    | ~ spl0_144 ),
    inference(resolution,[],[f1170,f431]) ).

fof(f4416,plain,
    ( spl0_394
    | ~ spl0_114
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1142,f1093,f894,f4414]) ).

fof(f4414,plain,
    ( spl0_394
  <=> ! [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_394])]) ).

fof(f1142,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f895]) ).

fof(f4412,plain,
    ( spl0_393
    | ~ spl0_39
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1136,f1093,f378,f4410]) ).

fof(f1136,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_39
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f379]) ).

fof(f4408,plain,
    ( spl0_392
    | ~ spl0_114
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1124,f1089,f894,f4406]) ).

fof(f4406,plain,
    ( spl0_392
  <=> ! [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_392])]) ).

fof(f1124,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f895]) ).

fof(f4404,plain,
    ( spl0_391
    | ~ spl0_39
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1118,f1089,f378,f4402]) ).

fof(f1118,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_39
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f379]) ).

fof(f4400,plain,
    ( spl0_390
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1053,f1014,f341,f4398]) ).

fof(f1053,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f342]) ).

fof(f4385,plain,
    ( spl0_389
    | ~ spl0_33
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1052,f1014,f345,f4383]) ).

fof(f1052,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_33
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f346]) ).

fof(f4381,plain,
    ( spl0_388
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1037,f1010,f341,f4379]) ).

fof(f1037,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f342]) ).

fof(f4377,plain,
    ( spl0_387
    | ~ spl0_33
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1036,f1010,f345,f4375]) ).

fof(f1036,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_33
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f346]) ).

fof(f4373,plain,
    ( spl0_386
    | ~ spl0_116
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f996,f957,f921,f4371]) ).

fof(f4371,plain,
    ( spl0_386
  <=> ! [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_386])]) ).

fof(f996,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) )
    | ~ spl0_116
    | ~ spl0_124 ),
    inference(resolution,[],[f958,f922]) ).

fof(f4369,plain,
    ( spl0_385
    | ~ spl0_49
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f852,f817,f450,f4367]) ).

fof(f4367,plain,
    ( spl0_385
  <=> ! [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_385])]) ).

fof(f852,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_49
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f451]) ).

fof(f4286,plain,
    ( ~ spl0_384
    | ~ spl0_5
    | ~ spl0_10
    | ~ spl0_263
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2591,f2506,f2459,f246,f225,f4283]) ).

fof(f4283,plain,
    ( spl0_384
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f2591,plain,
    ( ~ subclass(universal_class,null_class)
    | ~ spl0_5
    | ~ spl0_10
    | ~ spl0_263
    | ~ spl0_269 ),
    inference(forward_demodulation,[],[f2570,f2491]) ).

fof(f2570,plain,
    ( ~ subclass(universal_class,complement(universal_class))
    | ~ spl0_10
    | ~ spl0_269 ),
    inference(resolution,[],[f2507,f247]) ).

fof(f3979,plain,
    ( spl0_383
    | ~ spl0_5
    | ~ spl0_263
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2500,f2463,f2459,f225,f3977]) ).

fof(f2463,plain,
    ( spl0_264
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2500,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_5
    | ~ spl0_263
    | ~ spl0_264 ),
    inference(forward_demodulation,[],[f2498,f2491]) ).

fof(f2498,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_5
    | ~ spl0_264 ),
    inference(resolution,[],[f2464,f226]) ).

fof(f2464,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f2463]) ).

fof(f3949,plain,
    ( spl0_382
    | ~ spl0_109
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1743,f1717,f817,f3947]) ).

fof(f3947,plain,
    ( spl0_382
  <=> ! [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_382])]) ).

fof(f1743,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_109
    | ~ spl0_199 ),
    inference(superposition,[],[f818,f1718]) ).

fof(f3945,plain,
    ( spl0_381
    | ~ spl0_33
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1360,f1357,f345,f3943]) ).

fof(f3943,plain,
    ( spl0_381
  <=> ! [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_381])]) ).

fof(f1360,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_33
    | ~ spl0_163 ),
    inference(resolution,[],[f1358,f346]) ).

fof(f3941,plain,
    ( spl0_380
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1342,f1322,f3939]) ).

fof(f3939,plain,
    ( spl0_380
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f1342,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_161 ),
    inference(equality_factoring,[],[f1323]) ).

fof(f3937,plain,
    ( spl0_379
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1341,f1322,f3935]) ).

fof(f3935,plain,
    ( spl0_379
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f1341,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_161 ),
    inference(equality_factoring,[],[f1323]) ).

fof(f3933,plain,
    ( spl0_378
    | ~ spl0_135
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1313,f1296,f1089,f3931]) ).

fof(f3931,plain,
    ( spl0_378
  <=> ! [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_378])]) ).

fof(f1296,plain,
    ( spl0_158
  <=> ! [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_158])]) ).

fof(f1313,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1308]) ).

fof(f1308,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_135
    | ~ spl0_158 ),
    inference(resolution,[],[f1297,f1090]) ).

fof(f1297,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_158 ),
    inference(avatar_component_clause,[],[f1296]) ).

fof(f3929,plain,
    ( spl0_377
    | ~ spl0_136
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1312,f1296,f1093,f3927]) ).

fof(f3927,plain,
    ( spl0_377
  <=> ! [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_377])]) ).

fof(f1312,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_136
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1309]) ).

fof(f1309,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_136
    | ~ spl0_158 ),
    inference(resolution,[],[f1297,f1094]) ).

fof(f3925,plain,
    ( spl0_376
    | ~ spl0_23
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1182,f1161,f301,f3923]) ).

fof(f3923,plain,
    ( spl0_376
  <=> ! [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_376])]) ).

fof(f1161,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1182,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_23
    | ~ spl0_142 ),
    inference(resolution,[],[f1162,f302]) ).

fof(f1162,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1161]) ).

fof(f3921,plain,
    ( spl0_375
    | ~ spl0_21
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1141,f1093,f293,f3919]) ).

fof(f1141,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_21
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f294]) ).

fof(f3917,plain,
    ( spl0_374
    | ~ spl0_21
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1123,f1089,f293,f3915]) ).

fof(f1123,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_21
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f294]) ).

fof(f3913,plain,
    ( spl0_373
    | ~ spl0_114
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1073,f1018,f894,f3911]) ).

fof(f1073,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f895]) ).

fof(f3909,plain,
    ( spl0_372
    | ~ spl0_39
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1067,f1018,f378,f3907]) ).

fof(f3907,plain,
    ( spl0_372
  <=> ! [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_372])]) ).

fof(f1067,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_39
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f379]) ).

fof(f3905,plain,
    ( spl0_371
    | ~ spl0_114
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1055,f1014,f894,f3903]) ).

fof(f3903,plain,
    ( spl0_371
  <=> ! [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_371])]) ).

fof(f1055,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f895]) ).

fof(f3901,plain,
    ( spl0_370
    | ~ spl0_39
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1049,f1014,f378,f3899]) ).

fof(f1049,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_39
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f379]) ).

fof(f3897,plain,
    ( spl0_369
    | ~ spl0_114
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1039,f1010,f894,f3895]) ).

fof(f3895,plain,
    ( spl0_369
  <=> ! [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_369])]) ).

fof(f1039,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f895]) ).

fof(f3893,plain,
    ( spl0_368
    | ~ spl0_39
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1033,f1010,f378,f3891]) ).

fof(f1033,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_39
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f379]) ).

fof(f3883,plain,
    ( spl0_367
    | ~ spl0_113
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f997,f957,f890,f3881]) ).

fof(f3881,plain,
    ( spl0_367
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f997,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) )
    | ~ spl0_113
    | ~ spl0_124 ),
    inference(resolution,[],[f958,f891]) ).

fof(f3879,plain,
    ( spl0_366
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f977,f921,f829,f3877]) ).

fof(f3877,plain,
    ( spl0_366
  <=> ! [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_366])]) ).

fof(f977,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_112
    | ~ spl0_116 ),
    inference(resolution,[],[f922,f830]) ).

fof(f3875,plain,
    ( spl0_365
    | ~ spl0_68
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f886,f829,f562,f3873]) ).

fof(f886,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_68
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f563]) ).

fof(f3871,plain,
    ( spl0_364
    | ~ spl0_69
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f885,f829,f566,f3869]) ).

fof(f3869,plain,
    ( spl0_364
  <=> ! [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_364])]) ).

fof(f885,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_69
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f567]) ).

fof(f3867,plain,
    ( spl0_363
    | ~ spl0_58
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f864,f821,f509,f3865]) ).

fof(f3865,plain,
    ( spl0_363
  <=> ! [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_363])]) ).

fof(f864,plain,
    ( ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_58
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f510]) ).

fof(f3737,plain,
    ( spl0_362
    | ~ spl0_236
    | ~ spl0_353 ),
    inference(avatar_split_clause,[],[f3624,f3621,f2317,f3735]) ).

fof(f3621,plain,
    ( spl0_353
  <=> ! [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_353])]) ).

fof(f3624,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_236
    | ~ spl0_353 ),
    inference(forward_demodulation,[],[f3622,f2319]) ).

fof(f3622,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f3621]) ).

fof(f3733,plain,
    ( spl0_361
    | ~ spl0_236
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3619,f3616,f2317,f3731]) ).

fof(f3616,plain,
    ( spl0_352
  <=> ! [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_352])]) ).

fof(f3619,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_236
    | ~ spl0_352 ),
    inference(forward_demodulation,[],[f3617,f2319]) ).

fof(f3617,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_352 ),
    inference(avatar_component_clause,[],[f3616]) ).

fof(f3653,plain,
    ( spl0_360
    | ~ spl0_73
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1422,f1375,f590,f3651]) ).

fof(f3651,plain,
    ( spl0_360
  <=> ! [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_360])]) ).

fof(f1422,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) )
    | ~ spl0_73
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f591]) ).

fof(f3649,plain,
    ( spl0_1
    | ~ spl0_359
    | ~ spl0_27
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3585,f3334,f321,f3646,f205]) ).

fof(f3646,plain,
    ( spl0_359
  <=> subclass(universal_class,complement(cross_product(x,y))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f3585,plain,
    ( ~ subclass(universal_class,complement(cross_product(x,y)))
    | subclass(cross_product(x,y),z)
    | ~ spl0_27
    | ~ spl0_334 ),
    inference(resolution,[],[f3335,f322]) ).

fof(f3644,plain,
    ( spl0_358
    | ~ spl0_131
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1311,f1296,f1018,f3642]) ).

fof(f3642,plain,
    ( spl0_358
  <=> ! [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_358])]) ).

fof(f1311,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_131
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1310]) ).

fof(f1310,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_131
    | ~ spl0_158 ),
    inference(resolution,[],[f1297,f1019]) ).

fof(f3640,plain,
    ( spl0_357
    | ~ spl0_32
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1071,f1018,f341,f3638]) ).

fof(f3638,plain,
    ( spl0_357
  <=> ! [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_357])]) ).

fof(f1071,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_32
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f342]) ).

fof(f3636,plain,
    ( spl0_356
    | ~ spl0_33
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1070,f1018,f345,f3634]) ).

fof(f3634,plain,
    ( spl0_356
  <=> ! [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_356])]) ).

fof(f1070,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_33
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f346]) ).

fof(f3632,plain,
    ( spl0_355
    | ~ spl0_21
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1054,f1014,f293,f3630]) ).

fof(f1054,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_21
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f294]) ).

fof(f3628,plain,
    ( spl0_354
    | ~ spl0_21
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1038,f1010,f293,f3626]) ).

fof(f1038,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_21
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f294]) ).

fof(f3623,plain,
    ( spl0_353
    | ~ spl0_39
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1003,f965,f378,f3621]) ).

fof(f1003,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_39
    | ~ spl0_126 ),
    inference(resolution,[],[f966,f379]) ).

fof(f3618,plain,
    ( spl0_352
    | ~ spl0_39
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f999,f961,f378,f3616]) ).

fof(f999,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_39
    | ~ spl0_125 ),
    inference(resolution,[],[f962,f379]) ).

fof(f3614,plain,
    ( spl0_351
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f995,f957,f325,f3612]) ).

fof(f995,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(resolution,[],[f958,f326]) ).

fof(f3610,plain,
    ( spl0_350
    | ~ spl0_39
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f994,f957,f378,f3608]) ).

fof(f3608,plain,
    ( spl0_350
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f994,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_39
    | ~ spl0_124 ),
    inference(resolution,[],[f958,f379]) ).

fof(f3606,plain,
    ( spl0_349
    | ~ spl0_114
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f989,f925,f894,f3604]) ).

fof(f3604,plain,
    ( spl0_349
  <=> ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f989,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f895]) ).

fof(f3583,plain,
    ( spl0_348
    | ~ spl0_39
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f983,f925,f378,f3581]) ).

fof(f983,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_39
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f379]) ).

fof(f3576,plain,
    ( ~ spl0_346
    | spl0_347
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f901,f890,f829,f3573,f3569]) ).

fof(f3569,plain,
    ( spl0_346
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f901,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(resolution,[],[f891,f830]) ).

fof(f3567,plain,
    ( spl0_345
    | spl0_343
    | ~ spl0_52
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f872,f821,f462,f3553,f3565]) ).

fof(f3565,plain,
    ( spl0_345
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f3553,plain,
    ( spl0_343
  <=> member(null_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f462,plain,
    ( spl0_52
  <=> ! [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_52])]) ).

fof(f872,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) )
    | ~ spl0_52
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f463]) ).

fof(f463,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f462]) ).

fof(f3562,plain,
    ( ~ spl0_344
    | ~ spl0_236
    | spl0_343 ),
    inference(avatar_split_clause,[],[f3557,f3553,f2317,f3559]) ).

fof(f3559,plain,
    ( spl0_344
  <=> member(null_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f3557,plain,
    ( ~ member(null_class,singleton_relation)
    | ~ spl0_236
    | spl0_343 ),
    inference(forward_demodulation,[],[f3554,f2319]) ).

fof(f3554,plain,
    ( ~ member(null_class,identity_relation)
    | spl0_343 ),
    inference(avatar_component_clause,[],[f3553]) ).

fof(f3556,plain,
    ( spl0_342
    | spl0_343
    | ~ spl0_53
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f871,f821,f466,f3553,f3550]) ).

fof(f3550,plain,
    ( spl0_342
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f466,plain,
    ( spl0_53
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f871,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_53
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f467]) ).

fof(f467,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f466]) ).

fof(f3547,plain,
    ( spl0_340
    | ~ spl0_341
    | ~ spl0_79
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f837,f817,f630,f3544,f3541]) ).

fof(f3541,plain,
    ( spl0_340
  <=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f3544,plain,
    ( spl0_341
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f837,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_79
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f631]) ).

fof(f3433,plain,
    ( spl0_1
    | ~ spl0_339
    | ~ spl0_5
    | ~ spl0_263
    | ~ spl0_285
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f3384,f3236,f2771,f2459,f225,f3430,f205]) ).

fof(f3430,plain,
    ( spl0_339
  <=> subclass(cross_product(x,y),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f2771,plain,
    ( spl0_285
  <=> member(not_subclass_element(cross_product(x,y),z),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f3384,plain,
    ( ~ subclass(cross_product(x,y),null_class)
    | subclass(cross_product(x,y),z)
    | ~ spl0_5
    | ~ spl0_263
    | ~ spl0_285
    | ~ spl0_319 ),
    inference(forward_demodulation,[],[f3358,f2491]) ).

fof(f3358,plain,
    ( subclass(cross_product(x,y),z)
    | ~ subclass(cross_product(x,y),complement(universal_class))
    | ~ spl0_285
    | ~ spl0_319 ),
    inference(resolution,[],[f3237,f2773]) ).

fof(f2773,plain,
    ( member(not_subclass_element(cross_product(x,y),z),universal_class)
    | ~ spl0_285 ),
    inference(avatar_component_clause,[],[f2771]) ).

fof(f3418,plain,
    ( spl0_338
    | ~ spl0_236
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f3273,f3269,f2317,f3416]) ).

fof(f3269,plain,
    ( spl0_326
  <=> ! [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_326])]) ).

fof(f3273,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_236
    | ~ spl0_326 ),
    inference(forward_demodulation,[],[f3272,f2319]) ).

fof(f3272,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_236
    | ~ spl0_326 ),
    inference(forward_demodulation,[],[f3270,f2319]) ).

fof(f3270,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_326 ),
    inference(avatar_component_clause,[],[f3269]) ).

fof(f3414,plain,
    ( spl0_337
    | ~ spl0_236
    | ~ spl0_325 ),
    inference(avatar_split_clause,[],[f3267,f3263,f2317,f3412]) ).

fof(f3263,plain,
    ( spl0_325
  <=> ! [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_325])]) ).

fof(f3267,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_236
    | ~ spl0_325 ),
    inference(forward_demodulation,[],[f3266,f2319]) ).

fof(f3266,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_236
    | ~ spl0_325 ),
    inference(forward_demodulation,[],[f3264,f2319]) ).

fof(f3264,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_325 ),
    inference(avatar_component_clause,[],[f3263]) ).

fof(f3410,plain,
    ( spl0_336
    | ~ spl0_236
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f3261,f3258,f2317,f3408]) ).

fof(f3258,plain,
    ( spl0_324
  <=> ! [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_324])]) ).

fof(f3261,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_236
    | ~ spl0_324 ),
    inference(forward_demodulation,[],[f3259,f2319]) ).

fof(f3259,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f3258]) ).

fof(f3396,plain,
    ( spl0_335
    | ~ spl0_236
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3252,f3248,f2317,f3394]) ).

fof(f3248,plain,
    ( spl0_322
  <=> ! [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_322])]) ).

fof(f3252,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_236
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f3251,f2319]) ).

fof(f3251,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_236
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f3249,f2319]) ).

fof(f3249,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f3248]) ).

fof(f3336,plain,
    ( spl0_334
    | ~ spl0_269
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2732,f2690,f2506,f3334]) ).

fof(f2732,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(x,y),z),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_269
    | ~ spl0_278 ),
    inference(superposition,[],[f2507,f2692]) ).

fof(f3306,plain,
    ( spl0_333
    | ~ spl0_7
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1448,f1383,f234,f3304]) ).

fof(f3304,plain,
    ( spl0_333
  <=> ! [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_333])]) ).

fof(f1383,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

fof(f1448,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_7
    | ~ spl0_168 ),
    inference(resolution,[],[f1384,f235]) ).

fof(f1384,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_168 ),
    inference(avatar_component_clause,[],[f1383]) ).

fof(f3302,plain,
    ( spl0_332
    | ~ spl0_58
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1447,f1383,f509,f3300]) ).

fof(f3300,plain,
    ( spl0_332
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1447,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_58
    | ~ spl0_168 ),
    inference(resolution,[],[f1384,f510]) ).

fof(f3298,plain,
    ( spl0_331
    | ~ spl0_68
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1416,f1375,f562,f3296]) ).

fof(f1416,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_68
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f563]) ).

fof(f3294,plain,
    ( spl0_330
    | ~ spl0_27
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1413,f1371,f321,f3292]) ).

fof(f1413,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1392]) ).

fof(f1392,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_165 ),
    inference(resolution,[],[f1372,f322]) ).

fof(f3285,plain,
    ( spl0_328
    | spl0_329
    | ~ spl0_13
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1186,f1165,f260,f3282,f3279]) ).

fof(f3279,plain,
    ( spl0_328
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f3282,plain,
    ( spl0_329
  <=> member(null_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f1186,plain,
    ( ! [X0] :
        ( member(null_class,null_class)
        | ~ member(null_class,X0)
        | null_class = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_13
    | ~ spl0_143 ),
    inference(resolution,[],[f1166,f261]) ).

fof(f3277,plain,
    ( spl0_327
    | ~ spl0_98
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1145,f1093,f737,f3275]) ).

fof(f1145,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
    | ~ spl0_98
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f738]) ).

fof(f3271,plain,
    ( spl0_326
    | ~ spl0_103
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1144,f1093,f763,f3269]) ).

fof(f1144,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f764]) ).

fof(f3265,plain,
    ( spl0_325
    | ~ spl0_44
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1133,f1089,f399,f3263]) ).

fof(f1133,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_44
    | ~ spl0_135 ),
    inference(superposition,[],[f1090,f401]) ).

fof(f3260,plain,
    ( spl0_324
    | ~ spl0_43
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1132,f1089,f394,f3258]) ).

fof(f1132,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_43
    | ~ spl0_135 ),
    inference(superposition,[],[f1090,f396]) ).

fof(f3256,plain,
    ( spl0_323
    | ~ spl0_98
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1127,f1089,f737,f3254]) ).

fof(f1127,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
    | ~ spl0_98
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f738]) ).

fof(f3250,plain,
    ( spl0_322
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1126,f1089,f763,f3248]) ).

fof(f1126,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f764]) ).

fof(f3246,plain,
    ( spl0_321
    | ~ spl0_23
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1084,f1026,f301,f3244]) ).

fof(f3244,plain,
    ( spl0_321
  <=> ! [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_321])]) ).

fof(f1084,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_23
    | ~ spl0_133 ),
    inference(resolution,[],[f1027,f302]) ).

fof(f3242,plain,
    ( spl0_320
    | ~ spl0_23
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1081,f1022,f301,f3240]) ).

fof(f1081,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_23
    | ~ spl0_132 ),
    inference(resolution,[],[f1023,f302]) ).

fof(f3238,plain,
    ( spl0_319
    | ~ spl0_21
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1072,f1018,f293,f3236]) ).

fof(f1072,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_21
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f294]) ).

fof(f3234,plain,
    ( spl0_318
    | ~ spl0_32
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f987,f925,f341,f3232]) ).

fof(f3232,plain,
    ( spl0_318
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f987,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_32
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f342]) ).

fof(f3230,plain,
    ( spl0_317
    | ~ spl0_33
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f986,f925,f345,f3228]) ).

fof(f3228,plain,
    ( spl0_317
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f986,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_33
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f346]) ).

fof(f3226,plain,
    ( spl0_1
    | ~ spl0_316
    | ~ spl0_28
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3142,f2895,f325,f3223,f205]) ).

fof(f3223,plain,
    ( spl0_316
  <=> subclass(universal_class,z) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f3142,plain,
    ( ~ subclass(universal_class,z)
    | subclass(cross_product(x,y),z)
    | ~ spl0_28
    | ~ spl0_298 ),
    inference(resolution,[],[f2896,f326]) ).

fof(f3221,plain,
    ( spl0_315
    | ~ spl0_28
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f883,f829,f325,f3219]) ).

fof(f883,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_112 ),
    inference(resolution,[],[f830,f326]) ).

fof(f3202,plain,
    ( spl0_314
    | ~ spl0_236
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f3114,f2991,f2317,f3200]) ).

fof(f2991,plain,
    ( spl0_303
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f3114,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_236
    | ~ spl0_303 ),
    inference(forward_demodulation,[],[f2994,f2319]) ).

fof(f2994,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_236
    | ~ spl0_303 ),
    inference(forward_demodulation,[],[f2992,f2319]) ).

fof(f2992,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_303 ),
    inference(avatar_component_clause,[],[f2991]) ).

fof(f3181,plain,
    ( spl0_313
    | ~ spl0_236
    | ~ spl0_305 ),
    inference(avatar_split_clause,[],[f3006,f3003,f2317,f3179]) ).

fof(f3003,plain,
    ( spl0_305
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f3006,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_236
    | ~ spl0_305 ),
    inference(forward_demodulation,[],[f3004,f2319]) ).

fof(f3004,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_305 ),
    inference(avatar_component_clause,[],[f3003]) ).

fof(f3136,plain,
    ( spl0_312
    | ~ spl0_236
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f3120,f2915,f2317,f3133]) ).

fof(f2915,plain,
    ( spl0_299
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f3120,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_236
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2917,f2319]) ).

fof(f2917,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f2915]) ).

fof(f3131,plain,
    ( spl0_311
    | ~ spl0_236
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f3115,f2890,f2317,f3128]) ).

fof(f2890,plain,
    ( spl0_297
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f3115,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_236
    | ~ spl0_297 ),
    inference(forward_demodulation,[],[f2892,f2319]) ).

fof(f2892,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f2890]) ).

fof(f3126,plain,
    ( ~ spl0_310
    | ~ spl0_112
    | spl0_301 ),
    inference(avatar_split_clause,[],[f2982,f2978,f829,f3123]) ).

fof(f3123,plain,
    ( spl0_310
  <=> member(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f2978,plain,
    ( spl0_301
  <=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f2982,plain,
    ( ~ member(singleton_relation,subset_relation)
    | ~ spl0_112
    | spl0_301 ),
    inference(resolution,[],[f2980,f830]) ).

fof(f2980,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | spl0_301 ),
    inference(avatar_component_clause,[],[f2978]) ).

fof(f3118,plain,
    ( spl0_232
    | ~ spl0_234
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2928,f2317,f2307,f2289]) ).

fof(f2928,plain,
    ( null_class = singleton_relation
    | ~ spl0_234
    | ~ spl0_236 ),
    inference(forward_demodulation,[],[f2309,f2319]) ).

fof(f2309,plain,
    ( null_class = identity_relation
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2307]) ).

fof(f3107,plain,
    ( spl0_309
    | ~ spl0_232
    | ~ spl0_236
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f2996,f2991,f2317,f2289,f3105]) ).

fof(f3105,plain,
    ( spl0_309
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f2996,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) )
    | ~ spl0_232
    | ~ spl0_236
    | ~ spl0_303 ),
    inference(forward_demodulation,[],[f2995,f2319]) ).

fof(f2995,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_232
    | ~ spl0_236
    | ~ spl0_303 ),
    inference(forward_demodulation,[],[f2994,f2291]) ).

fof(f2291,plain,
    ( null_class = singleton_relation
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2289]) ).

fof(f3018,plain,
    ( spl0_308
    | ~ spl0_10
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1739,f1717,f246,f3016]) ).

fof(f1739,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_10
    | ~ spl0_199 ),
    inference(superposition,[],[f247,f1718]) ).

fof(f3014,plain,
    ( spl0_307
    | ~ spl0_69
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1415,f1375,f566,f3012]) ).

fof(f3012,plain,
    ( spl0_307
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f1415,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) )
    | ~ spl0_69
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f567]) ).

fof(f3010,plain,
    ( spl0_306
    | ~ spl0_98
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1076,f1018,f737,f3008]) ).

fof(f1076,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_98
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f738]) ).

fof(f3005,plain,
    ( spl0_305
    | ~ spl0_103
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1075,f1018,f763,f3003]) ).

fof(f1075,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f764]) ).

fof(f3000,plain,
    ( spl0_304
    | ~ spl0_98
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1058,f1014,f737,f2998]) ).

fof(f1058,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) )
    | ~ spl0_98
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f738]) ).

fof(f2993,plain,
    ( spl0_303
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1057,f1014,f763,f2991]) ).

fof(f1057,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(resolution,[],[f1015,f764]) ).

fof(f2989,plain,
    ( ~ spl0_302
    | ~ spl0_4
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2983,f2510,f220,f2986]) ).

fof(f2986,plain,
    ( spl0_302
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f220,plain,
    ( spl0_4
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f2983,plain,
    ( ~ inductive(choice)
    | ~ spl0_4
    | ~ spl0_270 ),
    inference(resolution,[],[f2511,f222]) ).

fof(f222,plain,
    ( function(choice)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f220]) ).

fof(f2981,plain,
    ( ~ spl0_301
    | ~ spl0_236
    | spl0_258 ),
    inference(avatar_split_clause,[],[f2974,f2430,f2317,f2978]) ).

fof(f2430,plain,
    ( spl0_258
  <=> member(identity_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f2974,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_236
    | spl0_258 ),
    inference(forward_demodulation,[],[f2431,f2319]) ).

fof(f2431,plain,
    ( ~ member(identity_relation,cross_product(universal_class,universal_class))
    | spl0_258 ),
    inference(avatar_component_clause,[],[f2430]) ).

fof(f2970,plain,
    ( spl0_300
    | ~ spl0_39
    | ~ spl0_236
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f2937,f2430,f2317,f378,f2968]) ).

fof(f2968,plain,
    ( spl0_300
  <=> ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f2937,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) )
    | ~ spl0_39
    | ~ spl0_236
    | ~ spl0_258 ),
    inference(forward_demodulation,[],[f2932,f2319]) ).

fof(f2932,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(identity_relation,X0) )
    | ~ spl0_39
    | ~ spl0_258 ),
    inference(resolution,[],[f2432,f379]) ).

fof(f2432,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_258 ),
    inference(avatar_component_clause,[],[f2430]) ).

fof(f2918,plain,
    ( spl0_234
    | spl0_299
    | ~ spl0_44
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1048,f1010,f399,f2915,f2307]) ).

fof(f1048,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ spl0_44
    | ~ spl0_129 ),
    inference(superposition,[],[f1011,f401]) ).

fof(f2897,plain,
    ( spl0_298
    | ~ spl0_109
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2725,f2690,f817,f2895]) ).

fof(f2725,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(x,y),z),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_278 ),
    inference(superposition,[],[f818,f2692]) ).

fof(f2893,plain,
    ( spl0_232
    | spl0_297
    | ~ spl0_43
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1047,f1010,f394,f2890,f2289]) ).

fof(f1047,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | null_class = singleton_relation
    | ~ spl0_43
    | ~ spl0_129 ),
    inference(superposition,[],[f1011,f396]) ).

fof(f2888,plain,
    ( spl0_296
    | ~ spl0_98
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1042,f1010,f737,f2886]) ).

fof(f1042,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) )
    | ~ spl0_98
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f738]) ).

fof(f2884,plain,
    ( spl0_295
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1041,f1010,f763,f2882]) ).

fof(f1041,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) )
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(resolution,[],[f1011,f764]) ).

fof(f2880,plain,
    ( spl0_294
    | ~ spl0_21
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f988,f925,f293,f2878]) ).

fof(f988,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_21
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f294]) ).

fof(f2876,plain,
    ( spl0_293
    | ~ spl0_39
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f882,f829,f378,f2874]) ).

fof(f882,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_39
    | ~ spl0_112 ),
    inference(resolution,[],[f830,f379]) ).

fof(f2872,plain,
    ( spl0_292
    | ~ spl0_39
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f851,f817,f378,f2870]) ).

fof(f2870,plain,
    ( spl0_292
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f851,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_39
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f379]) ).

fof(f2806,plain,
    ( spl0_290
    | ~ spl0_291
    | ~ spl0_62
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1418,f1375,f530,f2803,f2800]) ).

fof(f2800,plain,
    ( spl0_290
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f2803,plain,
    ( spl0_291
  <=> subclass(domain_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f1418,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,element_relation)
        | ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) )
    | ~ spl0_62
    | ~ spl0_166 ),
    inference(resolution,[],[f1376,f531]) ).

fof(f2798,plain,
    ( spl0_289
    | ~ spl0_27
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1314,f1296,f321,f2796]) ).

fof(f1314,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1307]) ).

fof(f1307,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_158 ),
    inference(resolution,[],[f1297,f322]) ).

fof(f2794,plain,
    ( spl0_288
    | ~ spl0_77
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1131,f1089,f614,f2792]) ).

fof(f1131,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_77
    | ~ spl0_135 ),
    inference(superposition,[],[f1090,f616]) ).

fof(f2790,plain,
    ( spl0_287
    | ~ spl0_98
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f992,f925,f737,f2788]) ).

fof(f992,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) )
    | ~ spl0_98
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f738]) ).

fof(f2786,plain,
    ( spl0_286
    | ~ spl0_103
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f991,f925,f763,f2784]) ).

fof(f991,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) )
    | ~ spl0_103
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f764]) ).

fof(f2774,plain,
    ( spl0_285
    | ~ spl0_10
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2721,f2690,f246,f2771]) ).

fof(f2721,plain,
    ( member(not_subclass_element(cross_product(x,y),z),universal_class)
    | ~ spl0_10
    | ~ spl0_278 ),
    inference(superposition,[],[f247,f2692]) ).

fof(f2769,plain,
    ( spl0_283
    | ~ spl0_275
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f2768,f2754,f2540,f2760]) ).

fof(f2760,plain,
    ( spl0_283
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f2768,plain,
    ( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_275
    | ~ spl0_282 ),
    inference(forward_demodulation,[],[f2756,f2542]) ).

fof(f2542,plain,
    ( null_class = subset_relation
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2540]) ).

fof(f2767,plain,
    ( spl0_284
    | spl0_282
    | ~ spl0_35
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f867,f821,f353,f2754,f2765]) ).

fof(f2765,plain,
    ( spl0_284
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f353,plain,
    ( spl0_35
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f867,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_35
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f354]) ).

fof(f354,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f353]) ).

fof(f2763,plain,
    ( ~ spl0_283
    | ~ spl0_275
    | spl0_282 ),
    inference(avatar_split_clause,[],[f2758,f2754,f2540,f2760]) ).

fof(f2758,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_275
    | spl0_282 ),
    inference(forward_demodulation,[],[f2755,f2542]) ).

fof(f2755,plain,
    ( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_282 ),
    inference(avatar_component_clause,[],[f2754]) ).

fof(f2757,plain,
    ( spl0_281
    | spl0_282
    | ~ spl0_34
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f866,f821,f349,f2754,f2751]) ).

fof(f2751,plain,
    ( spl0_281
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f349,plain,
    ( spl0_34
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f866,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_34
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f350]) ).

fof(f350,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f349]) ).

fof(f2749,plain,
    ( spl0_280
    | ~ spl0_32
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f855,f817,f341,f2747]) ).

fof(f2747,plain,
    ( spl0_280
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f855,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_32
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f342]) ).

fof(f2745,plain,
    ( spl0_279
    | ~ spl0_33
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f854,f817,f345,f2743]) ).

fof(f2743,plain,
    ( spl0_279
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f854,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_33
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f346]) ).

fof(f2693,plain,
    ( spl0_278
    | spl0_1
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1793,f1779,f205,f2690]) ).

fof(f1793,plain,
    ( not_subclass_element(cross_product(x,y),z) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,y),z)),first(not_subclass_element(cross_product(x,y),z))),unordered_pair(first(not_subclass_element(cross_product(x,y),z)),unordered_pair(second(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z)))))
    | spl0_1
    | ~ spl0_201 ),
    inference(resolution,[],[f1780,f207]) ).

fof(f207,plain,
    ( ~ subclass(cross_product(x,y),z)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f205]) ).

fof(f2565,plain,
    ( spl0_277
    | ~ spl0_5
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1256,f1249,f225,f2563]) ).

fof(f1256,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_5
    | ~ spl0_152 ),
    inference(resolution,[],[f1250,f226]) ).

fof(f2547,plain,
    ( spl0_275
    | spl0_276
    | ~ spl0_77
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1046,f1010,f614,f2544,f2540]) ).

fof(f1046,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_77
    | ~ spl0_129 ),
    inference(superposition,[],[f1011,f616]) ).

fof(f2538,plain,
    ( spl0_274
    | ~ spl0_21
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f998,f961,f293,f2536]) ).

fof(f998,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_21
    | ~ spl0_125 ),
    inference(resolution,[],[f962,f294]) ).

fof(f2534,plain,
    ( ~ spl0_273
    | spl0_272
    | ~ spl0_26
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f876,f821,f314,f2525,f2531]) ).

fof(f2531,plain,
    ( spl0_273
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f876,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_26
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f316]) ).

fof(f2528,plain,
    ( ~ spl0_271
    | spl0_272
    | ~ spl0_25
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f874,f821,f309,f2525,f2521]) ).

fof(f2521,plain,
    ( spl0_271
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f874,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_25
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f311]) ).

fof(f311,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f309]) ).

fof(f2512,plain,
    ( spl0_270
    | spl0_183
    | ~ spl0_23
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f862,f821,f301,f1544,f2510]) ).

fof(f862,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_23
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f302]) ).

fof(f2508,plain,
    ( spl0_269
    | ~ spl0_21
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f856,f817,f293,f2506]) ).

fof(f856,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_21
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f294]) ).

fof(f2504,plain,
    ( spl0_268
    | ~ spl0_73
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f839,f817,f590,f2502]) ).

fof(f2502,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f839,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_73
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f591]) ).

fof(f2497,plain,
    ( ~ spl0_267
    | ~ spl0_112
    | spl0_231 ),
    inference(avatar_split_clause,[],[f2287,f2283,f829,f2494]) ).

fof(f2494,plain,
    ( spl0_267
  <=> member(omega,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2283,plain,
    ( spl0_231
  <=> member(omega,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2287,plain,
    ( ~ member(omega,subset_relation)
    | ~ spl0_112
    | spl0_231 ),
    inference(resolution,[],[f2284,f830]) ).

fof(f2284,plain,
    ( ~ member(omega,cross_product(universal_class,universal_class))
    | spl0_231 ),
    inference(avatar_component_clause,[],[f2283]) ).

fof(f2488,plain,
    ( spl0_266
    | ~ spl0_39
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2436,f1544,f378,f2486]) ).

fof(f2436,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_39
    | ~ spl0_183 ),
    inference(resolution,[],[f1545,f379]) ).

fof(f1545,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1544]) ).

fof(f2470,plain,
    ( spl0_265
    | ~ spl0_44
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2258,f2234,f399,f2467]) ).

fof(f2258,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_44
    | ~ spl0_225 ),
    inference(superposition,[],[f2235,f401]) ).

fof(f2465,plain,
    ( spl0_264
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1077,f1018,f921,f2463]) ).

fof(f1077,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(duplicate_literal_removal,[],[f1066]) ).

fof(f1066,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(resolution,[],[f1019,f922]) ).

fof(f2461,plain,
    ( spl0_263
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f993,f925,f890,f2459]) ).

fof(f993,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(duplicate_literal_removal,[],[f982]) ).

fof(f982,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(resolution,[],[f926,f891]) ).

fof(f2457,plain,
    ( spl0_262
    | ~ spl0_22
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f917,f898,f297,f2455]) ).

fof(f2455,plain,
    ( spl0_262
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f297,plain,
    ( spl0_22
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f917,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_115 ),
    inference(resolution,[],[f899,f298]) ).

fof(f298,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f297]) ).

fof(f2453,plain,
    ( ~ spl0_260
    | spl0_261
    | ~ spl0_7
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f912,f898,f234,f2450,f2446]) ).

fof(f2446,plain,
    ( spl0_260
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f2450,plain,
    ( spl0_261
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f912,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_7
    | ~ spl0_115 ),
    inference(resolution,[],[f899,f235]) ).

fof(f2442,plain,
    ( ~ spl0_259
    | ~ spl0_112
    | spl0_258 ),
    inference(avatar_split_clause,[],[f2437,f2430,f829,f2439]) ).

fof(f2439,plain,
    ( spl0_259
  <=> member(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f2437,plain,
    ( ~ member(identity_relation,subset_relation)
    | ~ spl0_112
    | spl0_258 ),
    inference(resolution,[],[f2431,f830]) ).

fof(f2433,plain,
    ( spl0_258
    | ~ spl0_183
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2428,f2307,f1544,f2430]) ).

fof(f2428,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_183
    | ~ spl0_234 ),
    inference(forward_demodulation,[],[f1545,f2309]) ).

fof(f2423,plain,
    ( spl0_257
    | spl0_183
    | ~ spl0_19
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f873,f821,f285,f1544,f2421]) ).

fof(f2421,plain,
    ( spl0_257
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f285,plain,
    ( spl0_19
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f873,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_19
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f286]) ).

fof(f286,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f285]) ).

fof(f2419,plain,
    ( spl0_255
    | ~ spl0_256
    | ~ spl0_98
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f859,f817,f737,f2416,f2413]) ).

fof(f2413,plain,
    ( spl0_255
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f2416,plain,
    ( spl0_256
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f859,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_98
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f738]) ).

fof(f2411,plain,
    ( spl0_253
    | ~ spl0_254
    | ~ spl0_103
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f858,f817,f763,f2408,f2405]) ).

fof(f2405,plain,
    ( spl0_253
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f2408,plain,
    ( spl0_254
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f858,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_103
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f764]) ).

fof(f2403,plain,
    ( spl0_251
    | ~ spl0_252
    | ~ spl0_88
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f843,f817,f679,f2400,f2397]) ).

fof(f2397,plain,
    ( spl0_251
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f2400,plain,
    ( spl0_252
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f843,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_88
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f680]) ).

fof(f2395,plain,
    ( spl0_250
    | ~ spl0_43
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2257,f2234,f394,f2392]) ).

fof(f2392,plain,
    ( spl0_250
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f2257,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_43
    | ~ spl0_225 ),
    inference(superposition,[],[f2235,f396]) ).

fof(f2390,plain,
    ( spl0_249
    | ~ spl0_68
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f833,f817,f562,f2388]) ).

fof(f2388,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f833,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_68
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f563]) ).

fof(f2386,plain,
    ( spl0_248
    | ~ spl0_69
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f832,f817,f566,f2384]) ).

fof(f2384,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f832,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_69
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f567]) ).

fof(f2381,plain,
    ( spl0_246
    | ~ spl0_247
    | ~ spl0_41
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f788,f390,f386,f2378,f2375]) ).

fof(f2375,plain,
    ( spl0_246
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2378,plain,
    ( spl0_247
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f386,plain,
    ( spl0_41
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f788,plain,
    ( ! [X0] :
        ( ~ inductive(null_class)
        | member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_41
    | ~ spl0_42 ),
    inference(superposition,[],[f387,f391]) ).

fof(f387,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(null_class,X0) )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f386]) ).

fof(f2373,plain,
    ( spl0_245
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f780,f763,f321,f2371]) ).

fof(f780,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(resolution,[],[f764,f322]) ).

fof(f2369,plain,
    ( spl0_244
    | ~ spl0_27
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f776,f737,f321,f2367]) ).

fof(f776,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_27
    | ~ spl0_98 ),
    inference(resolution,[],[f738,f322]) ).

fof(f2365,plain,
    ( spl0_243
    | ~ spl0_38
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f542,f513,f365,f2363]) ).

fof(f2363,plain,
    ( spl0_243
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f513,plain,
    ( spl0_59
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f542,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_38
    | ~ spl0_59 ),
    inference(resolution,[],[f514,f366]) ).

fof(f514,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f513]) ).

fof(f2361,plain,
    ( ~ spl0_242
    | spl0_183
    | ~ spl0_15
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f875,f821,f268,f1544,f2358]) ).

fof(f2358,plain,
    ( spl0_242
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f875,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_15
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f270]) ).

fof(f2356,plain,
    ( ~ spl0_241
    | spl0_183
    | ~ spl0_12
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f868,f821,f255,f1544,f2353]) ).

fof(f2353,plain,
    ( spl0_241
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f255,plain,
    ( spl0_12
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f868,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_12
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f257]) ).

fof(f257,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f2351,plain,
    ( spl0_239
    | ~ spl0_240
    | ~ spl0_87
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f842,f817,f675,f2348,f2345]) ).

fof(f2345,plain,
    ( spl0_239
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f2348,plain,
    ( spl0_240
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f842,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_87
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f676]) ).

fof(f2343,plain,
    ( spl0_237
    | ~ spl0_238
    | ~ spl0_65
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f840,f817,f545,f2340,f2337]) ).

fof(f2337,plain,
    ( spl0_237
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f2340,plain,
    ( spl0_238
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f840,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_65
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f546]) ).

fof(f2320,plain,
    ( spl0_236
    | ~ spl0_232
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2315,f2307,f2289,f2317]) ).

fof(f2315,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_232
    | ~ spl0_234 ),
    inference(forward_demodulation,[],[f2309,f2291]) ).

fof(f2314,plain,
    ( spl0_234
    | spl0_235
    | ~ spl0_24
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f783,f763,f305,f2311,f2307]) ).

fof(f783,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_24
    | ~ spl0_103 ),
    inference(resolution,[],[f764,f306]) ).

fof(f2296,plain,
    ( spl0_232
    | spl0_233
    | ~ spl0_24
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f779,f737,f305,f2293,f2289]) ).

fof(f779,plain,
    ( member(regular(singleton_relation),element_relation)
    | null_class = singleton_relation
    | ~ spl0_24
    | ~ spl0_98 ),
    inference(resolution,[],[f738,f306]) ).

fof(f2286,plain,
    ( ~ spl0_230
    | spl0_231
    | ~ spl0_23
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f772,f438,f301,f2283,f2279]) ).

fof(f2279,plain,
    ( spl0_230
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f438,plain,
    ( spl0_47
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f772,plain,
    ( member(omega,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_23
    | ~ spl0_47 ),
    inference(resolution,[],[f439,f302]) ).

fof(f439,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f438]) ).

fof(f2274,plain,
    ( spl0_229
    | ~ spl0_39
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f2178,f638,f378,f2272]) ).

fof(f2272,plain,
    ( spl0_229
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f2178,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_39
    | ~ spl0_81 ),
    inference(resolution,[],[f639,f379]) ).

fof(f639,plain,
    ( member(null_class,universal_class)
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f638]) ).

fof(f2270,plain,
    ( spl0_228
    | ~ spl0_19
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f918,f898,f285,f2268]) ).

fof(f2268,plain,
    ( spl0_228
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f918,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_19
    | ~ spl0_115 ),
    inference(resolution,[],[f899,f286]) ).

fof(f2266,plain,
    ( spl0_226
    | ~ spl0_227
    | ~ spl0_62
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f835,f817,f530,f2263,f2260]) ).

fof(f2260,plain,
    ( spl0_226
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f2263,plain,
    ( spl0_227
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f835,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_62
    | ~ spl0_109 ),
    inference(resolution,[],[f818,f531]) ).

fof(f2236,plain,
    ( spl0_225
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1152,f1093,f325,f2234]) ).

fof(f1152,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1135]) ).

fof(f1135,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(resolution,[],[f1094,f326]) ).

fof(f2232,plain,
    ( spl0_224
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1134,f1089,f325,f2230]) ).

fof(f1134,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(duplicate_literal_removal,[],[f1117]) ).

fof(f1117,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(resolution,[],[f1090,f326]) ).

fof(f2148,plain,
    ( ~ spl0_3
    | ~ spl0_223 ),
    inference(avatar_contradiction_clause,[],[f2147]) ).

fof(f2147,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_223 ),
    inference(resolution,[],[f2145,f217]) ).

fof(f217,plain,
    ( inductive(omega)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f2145,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2144]) ).

fof(f2144,plain,
    ( spl0_223
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f2146,plain,
    ( spl0_223
    | spl0_81
    | ~ spl0_5
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f860,f821,f225,f638,f2144]) ).

fof(f860,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_5
    | ~ spl0_110 ),
    inference(resolution,[],[f822,f226]) ).

fof(f2133,plain,
    ( spl0_222
    | ~ spl0_91
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f712,f708,f692,f2131]) ).

fof(f712,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_91
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f693]) ).

fof(f2129,plain,
    ( spl0_221
    | ~ spl0_51
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f761,f756,f692,f458,f2127]) ).

fof(f2127,plain,
    ( spl0_221
  <=> ! [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_221])]) ).

fof(f761,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_51
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(forward_demodulation,[],[f759,f459]) ).

fof(f759,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_91
    | ~ spl0_102 ),
    inference(resolution,[],[f757,f693]) ).

fof(f2119,plain,
    ( spl0_220
    | ~ spl0_72
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f760,f756,f579,f2117]) ).

fof(f760,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_72
    | ~ spl0_102 ),
    inference(resolution,[],[f757,f580]) ).

fof(f2106,plain,
    ( spl0_219
    | ~ spl0_85
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f715,f708,f660,f2104]) ).

fof(f715,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_85
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f661]) ).

fof(f2102,plain,
    ( spl0_218
    | ~ spl0_80
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f665,f660,f634,f2100]) ).

fof(f665,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_80
    | ~ spl0_85 ),
    inference(resolution,[],[f661,f635]) ).

fof(f2089,plain,
    ( spl0_217
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f713,f708,f321,f2087]) ).

fof(f713,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_94 ),
    inference(resolution,[],[f709,f322]) ).

fof(f2076,plain,
    ( spl0_216
    | ~ spl0_24
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f716,f708,f305,f2074]) ).

fof(f716,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_24
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f306]) ).

fof(f2065,plain,
    ( spl0_215
    | ~ spl0_78
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f754,f751,f619,f2063]) ).

fof(f754,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_78
    | ~ spl0_101 ),
    inference(resolution,[],[f752,f620]) ).

fof(f2035,plain,
    ( ~ spl0_214
    | spl0_192
    | ~ spl0_13
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f781,f763,f260,f1607,f2032]) ).

fof(f2032,plain,
    ( spl0_214
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f781,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_13
    | ~ spl0_103 ),
    inference(resolution,[],[f764,f261]) ).

fof(f2007,plain,
    ( spl0_213
    | ~ spl0_78
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f749,f745,f619,f2005]) ).

fof(f749,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_78
    | ~ spl0_100 ),
    inference(resolution,[],[f746,f620]) ).

fof(f2003,plain,
    ( spl0_212
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f748,f741,f619,f2001]) ).

fof(f748,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_78
    | ~ spl0_99 ),
    inference(resolution,[],[f742,f620]) ).

fof(f1954,plain,
    ( spl0_211
    | ~ spl0_78
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f646,f634,f619,f1952]) ).

fof(f1952,plain,
    ( spl0_211
  <=> ! [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_211])]) ).

fof(f646,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_78
    | ~ spl0_80 ),
    inference(resolution,[],[f635,f620]) ).

fof(f1944,plain,
    ( spl0_210
    | ~ spl0_42
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f721,f708,f390,f1942]) ).

fof(f721,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_42
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f391]) ).

fof(f1932,plain,
    ( spl0_209
    | ~ spl0_72
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f711,f708,f579,f1930]) ).

fof(f711,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_72
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f580]) ).

fof(f1922,plain,
    ( spl0_208
    | ~ spl0_49
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f664,f660,f450,f1920]) ).

fof(f664,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_49
    | ~ spl0_85 ),
    inference(resolution,[],[f661,f451]) ).

fof(f1915,plain,
    ( spl0_207
    | ~ spl0_42
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f718,f708,f390,f1913]) ).

fof(f718,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_42
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f391]) ).

fof(f1877,plain,
    ( spl0_206
    | ~ spl0_39
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f706,f702,f378,f1875]) ).

fof(f706,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_39
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f379]) ).

fof(f1821,plain,
    ( spl0_205
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f720,f708,f458,f1819]) ).

fof(f720,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_51
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f459]) ).

fof(f1817,plain,
    ( spl0_204
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f717,f708,f458,f1815]) ).

fof(f717,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_51
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f459]) ).

fof(f1807,plain,
    ( ~ spl0_203
    | ~ spl0_13
    | spl0_192 ),
    inference(avatar_split_clause,[],[f1689,f1607,f260,f1804]) ).

fof(f1804,plain,
    ( spl0_203
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1689,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_13
    | spl0_192 ),
    inference(resolution,[],[f1609,f261]) ).

fof(f1609,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_192 ),
    inference(avatar_component_clause,[],[f1607]) ).

fof(f1802,plain,
    ( spl0_202
    | ~ spl0_13
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f714,f708,f260,f1800]) ).

fof(f714,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_13
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f261]) ).

fof(f1781,plain,
    ( spl0_201
    | ~ spl0_27
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f649,f634,f321,f1779]) ).

fof(f649,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_80 ),
    inference(resolution,[],[f635,f322]) ).

fof(f1753,plain,
    ( spl0_200
    | ~ spl0_39
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f695,f692,f378,f1751]) ).

fof(f695,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_39
    | ~ spl0_91 ),
    inference(resolution,[],[f693,f379]) ).

fof(f1719,plain,
    ( spl0_199
    | ~ spl0_24
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f648,f634,f305,f1717]) ).

fof(f648,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_24
    | ~ spl0_80 ),
    inference(resolution,[],[f635,f306]) ).

fof(f1713,plain,
    ( spl0_198
    | ~ spl0_78
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f727,f724,f619,f1711]) ).

fof(f727,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_78
    | ~ spl0_95 ),
    inference(resolution,[],[f725,f620]) ).

fof(f1668,plain,
    ( spl0_197
    | ~ spl0_32
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f667,f660,f341,f1666]) ).

fof(f667,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_32
    | ~ spl0_85 ),
    inference(resolution,[],[f661,f342]) ).

fof(f1664,plain,
    ( spl0_196
    | ~ spl0_33
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f666,f660,f345,f1662]) ).

fof(f666,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_33
    | ~ spl0_85 ),
    inference(resolution,[],[f661,f346]) ).

fof(f1647,plain,
    ( spl0_195
    | ~ spl0_21
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f668,f660,f293,f1645]) ).

fof(f668,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_21
    | ~ spl0_85 ),
    inference(resolution,[],[f661,f294]) ).

fof(f1628,plain,
    ( spl0_194
    | ~ spl0_39
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f663,f660,f378,f1626]) ).

fof(f663,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_39
    | ~ spl0_85 ),
    inference(resolution,[],[f661,f379]) ).

fof(f1622,plain,
    ( spl0_193
    | ~ spl0_40
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f543,f538,f382,f1620]) ).

fof(f543,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_40
    | ~ spl0_64 ),
    inference(resolution,[],[f539,f383]) ).

fof(f1610,plain,
    ( ~ spl0_192
    | ~ spl0_112
    | spl0_183 ),
    inference(avatar_split_clause,[],[f1552,f1544,f829,f1607]) ).

fof(f1552,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_112
    | spl0_183 ),
    inference(resolution,[],[f1546,f830]) ).

fof(f1546,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_183 ),
    inference(avatar_component_clause,[],[f1544]) ).

fof(f1605,plain,
    ( ~ spl0_189
    | ~ spl0_190
    | spl0_191
    | ~ spl0_74
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f622,f614,f594,f1602,f1598,f1594]) ).

fof(f1594,plain,
    ( spl0_189
  <=> 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_189])]) ).

fof(f1598,plain,
    ( spl0_190
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1602,plain,
    ( spl0_191
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f594,plain,
    ( spl0_74
  <=> ! [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_74])]) ).

fof(f622,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_74
    | ~ spl0_77 ),
    inference(superposition,[],[f595,f616]) ).

fof(f595,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_74 ),
    inference(avatar_component_clause,[],[f594]) ).

fof(f1592,plain,
    ( spl0_188
    | ~ spl0_28
    | ~ spl0_51
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f588,f579,f458,f325,f1590]) ).

fof(f588,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_51
    | ~ spl0_72 ),
    inference(forward_demodulation,[],[f587,f459]) ).

fof(f587,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_72 ),
    inference(resolution,[],[f580,f326]) ).

fof(f1586,plain,
    ( spl0_187
    | ~ spl0_78
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f686,f683,f619,f1584]) ).

fof(f686,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_78
    | ~ spl0_89 ),
    inference(resolution,[],[f684,f620]) ).

fof(f1564,plain,
    ( spl0_186
    | ~ spl0_50
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f623,f614,f454,f1562]) ).

fof(f623,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_50
    | ~ spl0_77 ),
    inference(superposition,[],[f455,f616]) ).

fof(f1557,plain,
    ( spl0_185
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f628,f619,f378,f1555]) ).

fof(f628,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_39
    | ~ spl0_78 ),
    inference(resolution,[],[f620,f379]) ).

fof(f1551,plain,
    ( ~ spl0_182
    | ~ spl0_183
    | spl0_184
    | ~ spl0_23
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f612,f602,f301,f1548,f1544,f1540]) ).

fof(f1540,plain,
    ( spl0_182
  <=> 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_182])]) ).

fof(f1548,plain,
    ( spl0_184
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f602,plain,
    ( spl0_76
  <=> ! [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_76])]) ).

fof(f612,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_23
    | ~ spl0_76 ),
    inference(resolution,[],[f603,f302]) ).

fof(f603,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_76 ),
    inference(avatar_component_clause,[],[f602]) ).

fof(f1538,plain,
    ( spl0_181
    | ~ spl0_40
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f520,f509,f382,f1536]) ).

fof(f1536,plain,
    ( spl0_181
  <=> ! [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_181])]) ).

fof(f520,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_40
    | ~ spl0_58 ),
    inference(resolution,[],[f510,f383]) ).

fof(f1531,plain,
    ( spl0_179
    | spl0_180
    | ~ spl0_42
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f607,f594,f390,f1528,f1525]) ).

fof(f1525,plain,
    ( spl0_179
  <=> ! [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_179])]) ).

fof(f607,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_42
    | ~ spl0_74 ),
    inference(superposition,[],[f595,f391]) ).

fof(f1523,plain,
    ( spl0_178
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f553,f549,f538,f1521]) ).

fof(f1521,plain,
    ( spl0_178
  <=> ! [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_178])]) ).

fof(f549,plain,
    ( spl0_66
  <=> ! [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_66])]) ).

fof(f553,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_64
    | ~ spl0_66 ),
    inference(resolution,[],[f550,f539]) ).

fof(f550,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f549]) ).

fof(f1485,plain,
    ( spl0_177
    | ~ spl0_78
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f673,f670,f619,f1483]) ).

fof(f673,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_78
    | ~ spl0_86 ),
    inference(resolution,[],[f671,f620]) ).

fof(f1481,plain,
    ( spl0_175
    | spl0_176
    | ~ spl0_13
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f647,f634,f260,f1478,f1475]) ).

fof(f1475,plain,
    ( spl0_175
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

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

fof(f647,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_13
    | ~ spl0_80 ),
    inference(resolution,[],[f635,f261]) ).

fof(f1473,plain,
    ( ~ spl0_173
    | spl0_174
    | ~ spl0_15
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f919,f898,f268,f1470,f1466]) ).

fof(f1466,plain,
    ( spl0_173
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1470,plain,
    ( spl0_174
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f919,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_15
    | ~ spl0_115 ),
    inference(resolution,[],[f899,f270]) ).

fof(f1464,plain,
    ( spl0_172
    | ~ spl0_39
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f609,f598,f378,f1462]) ).

fof(f598,plain,
    ( spl0_75
  <=> ! [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_75])]) ).

fof(f609,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_39
    | ~ spl0_75 ),
    inference(resolution,[],[f599,f379]) ).

fof(f599,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_75 ),
    inference(avatar_component_clause,[],[f598]) ).

fof(f1460,plain,
    ( spl0_171
    | ~ spl0_39
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f605,f594,f378,f1458]) ).

fof(f605,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_39
    | ~ spl0_74 ),
    inference(resolution,[],[f595,f379]) ).

fof(f1456,plain,
    ( spl0_170
    | ~ spl0_40
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f500,f466,f382,f1454]) ).

fof(f1454,plain,
    ( spl0_170
  <=> ! [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_170])]) ).

fof(f500,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_40
    | ~ spl0_53 ),
    inference(resolution,[],[f467,f383]) ).

fof(f1452,plain,
    ( spl0_169
    | ~ spl0_40
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f499,f462,f382,f1450]) ).

fof(f1450,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

fof(f499,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_40
    | ~ spl0_52 ),
    inference(resolution,[],[f463,f383]) ).

fof(f1385,plain,
    ( spl0_168
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f654,f651,f1383]) ).

fof(f651,plain,
    ( spl0_83
  <=> ! [X9,X11,X10] :
        ( ~ function(X9)
        | compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) != domain_of(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f654,plain,
    ( ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
    | ~ spl0_83 ),
    inference(equality_resolution,[],[f652]) ).

fof(f652,plain,
    ( ! [X10,X11,X9] :
        ( domain_of(domain_of(X10)) != domain_of(X9)
        | compatible(X9,X10,X11)
        | ~ function(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f651]) ).

fof(f1381,plain,
    ( spl0_167
    | ~ spl0_39
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f586,f579,f378,f1379]) ).

fof(f586,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_39
    | ~ spl0_72 ),
    inference(resolution,[],[f580,f379]) ).

fof(f1377,plain,
    ( spl0_166
    | ~ spl0_39
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f583,f558,f378,f1375]) ).

fof(f583,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_39
    | ~ spl0_67 ),
    inference(resolution,[],[f559,f379]) ).

fof(f1373,plain,
    ( spl0_165
    | ~ spl0_28
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f489,f454,f325,f1371]) ).

fof(f489,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_50 ),
    inference(resolution,[],[f455,f326]) ).

fof(f1369,plain,
    ( spl0_164
    | ~ spl0_27
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f485,f450,f321,f1367]) ).

fof(f485,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_49 ),
    inference(resolution,[],[f451,f322]) ).

fof(f1359,plain,
    ( spl0_163
    | ~ spl0_33
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f624,f614,f345,f1357]) ).

fof(f624,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_33
    | ~ spl0_77 ),
    inference(superposition,[],[f346,f616]) ).

fof(f1328,plain,
    ( spl0_162
    | ~ spl0_51
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f606,f594,f458,f1326]) ).

fof(f606,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_51
    | ~ spl0_74 ),
    inference(superposition,[],[f595,f459]) ).

fof(f1324,plain,
    ( spl0_161
    | ~ spl0_24
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f484,f450,f305,f1322]) ).

fof(f484,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_49 ),
    inference(resolution,[],[f451,f306]) ).

fof(f1306,plain,
    ( spl0_160
    | ~ spl0_23
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f556,f549,f301,f1304]) ).

fof(f1304,plain,
    ( spl0_160
  <=> ! [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_160])]) ).

fof(f556,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_23
    | ~ spl0_66 ),
    inference(resolution,[],[f550,f302]) ).

fof(f1302,plain,
    ( spl0_159
    | ~ spl0_42
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f528,f522,f390,f1300]) ).

fof(f522,plain,
    ( spl0_61
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f528,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_42
    | ~ spl0_61 ),
    inference(trivial_inequality_removal,[],[f526]) ).

fof(f526,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_42
    | ~ spl0_61 ),
    inference(superposition,[],[f523,f391]) ).

fof(f523,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f522]) ).

fof(f1298,plain,
    ( spl0_158
    | ~ spl0_28
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f447,f430,f325,f1296]) ).

fof(f447,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_45 ),
    inference(resolution,[],[f431,f326]) ).

fof(f1294,plain,
    ( spl0_157
    | ~ spl0_35
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f415,f382,f353,f1292]) ).

fof(f415,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_35
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f354]) ).

fof(f1290,plain,
    ( spl0_156
    | ~ spl0_34
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f414,f382,f349,f1288]) ).

fof(f414,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_34
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f350]) ).

fof(f1286,plain,
    ( ~ spl0_154
    | spl0_155
    | ~ spl0_12
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f915,f898,f255,f1283,f1279]) ).

fof(f1279,plain,
    ( spl0_154
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1283,plain,
    ( spl0_155
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f915,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_12
    | ~ spl0_115 ),
    inference(resolution,[],[f899,f257]) ).

fof(f1255,plain,
    ( spl0_153
    | ~ spl0_39
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f503,f478,f378,f1253]) ).

fof(f503,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_39
    | ~ spl0_56 ),
    inference(resolution,[],[f479,f379]) ).

fof(f1251,plain,
    ( spl0_152
    | ~ spl0_39
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f488,f454,f378,f1249]) ).

fof(f488,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_39
    | ~ spl0_50 ),
    inference(resolution,[],[f455,f379]) ).

fof(f1247,plain,
    ( spl0_150
    | ~ spl0_151
    | ~ spl0_26
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f422,f382,f314,f1244,f1240]) ).

fof(f422,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_26
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f316]) ).

fof(f1238,plain,
    ( spl0_148
    | ~ spl0_149
    | ~ spl0_25
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f420,f382,f309,f1235,f1231]) ).

fof(f420,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_25
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f311]) ).

fof(f1229,plain,
    ( spl0_147
    | ~ spl0_22
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f418,f382,f297,f1227]) ).

fof(f418,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_22
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f298]) ).

fof(f1179,plain,
    ( spl0_146
    | ~ spl0_51
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f525,f522,f458,f1177]) ).

fof(f1177,plain,
    ( spl0_146
  <=> ! [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_146])]) ).

fof(f525,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_51
    | ~ spl0_61 ),
    inference(superposition,[],[f523,f459]) ).

fof(f1175,plain,
    ( spl0_145
    | ~ spl0_44
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f492,f454,f399,f1173]) ).

fof(f492,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_44
    | ~ spl0_50 ),
    inference(superposition,[],[f455,f401]) ).

fof(f1171,plain,
    ( spl0_144
    | ~ spl0_43
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f491,f454,f394,f1169]) ).

fof(f491,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_43
    | ~ spl0_50 ),
    inference(superposition,[],[f455,f396]) ).

fof(f1167,plain,
    ( spl0_143
    | ~ spl0_42
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f490,f454,f390,f1165]) ).

fof(f490,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_42
    | ~ spl0_50 ),
    inference(superposition,[],[f455,f391]) ).

fof(f1163,plain,
    ( spl0_142
    | ~ spl0_39
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f446,f430,f378,f1161]) ).

fof(f446,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_39
    | ~ spl0_45 ),
    inference(resolution,[],[f431,f379]) ).

fof(f1116,plain,
    ( spl0_141
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f555,f549,f234,f1114]) ).

fof(f1114,plain,
    ( spl0_141
  <=> ! [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_141])]) ).

fof(f555,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(resolution,[],[f550,f235]) ).

fof(f1112,plain,
    ( spl0_140
    | ~ spl0_19
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f419,f382,f285,f1110]) ).

fof(f419,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_19
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f286]) ).

fof(f1108,plain,
    ( spl0_139
    | ~ spl0_23
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f412,f382,f301,f1106]) ).

fof(f412,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_23
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f302]) ).

fof(f1104,plain,
    ( ~ spl0_137
    | spl0_138
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f913,f898,f250,f1101,f1097]) ).

fof(f1097,plain,
    ( spl0_137
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1101,plain,
    ( spl0_138
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f250,plain,
    ( spl0_11
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f913,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(resolution,[],[f899,f252]) ).

fof(f252,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f1095,plain,
    ( spl0_136
    | ~ spl0_27
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f376,f345,f321,f1093]) ).

fof(f376,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_33 ),
    inference(resolution,[],[f346,f322]) ).

fof(f1091,plain,
    ( spl0_135
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f373,f341,f321,f1089]) ).

fof(f373,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(resolution,[],[f342,f322]) ).

fof(f1032,plain,
    ( spl0_134
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f552,f549,f509,f1030]) ).

fof(f1030,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f552,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(resolution,[],[f550,f510]) ).

fof(f1028,plain,
    ( spl0_133
    | ~ spl0_30
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f409,f378,f333,f1026]) ).

fof(f409,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_30
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f334]) ).

fof(f1024,plain,
    ( spl0_132
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f408,f378,f329,f1022]) ).

fof(f408,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f330]) ).

fof(f1020,plain,
    ( spl0_131
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f407,f378,f321,f1018]) ).

fof(f407,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f322]) ).

fof(f1016,plain,
    ( spl0_130
    | ~ spl0_24
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f375,f345,f305,f1014]) ).

fof(f375,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_33 ),
    inference(resolution,[],[f346,f306]) ).

fof(f1012,plain,
    ( spl0_129
    | ~ spl0_24
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f372,f341,f305,f1010]) ).

fof(f372,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_32 ),
    inference(resolution,[],[f342,f306]) ).

fof(f976,plain,
    ( ~ spl0_128
    | ~ spl0_13
    | spl0_108 ),
    inference(avatar_split_clause,[],[f937,f809,f260,f973]) ).

fof(f973,plain,
    ( spl0_128
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f809,plain,
    ( spl0_108
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f937,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_13
    | spl0_108 ),
    inference(resolution,[],[f810,f261]) ).

fof(f810,plain,
    ( ~ member(null_class,element_relation)
    | spl0_108 ),
    inference(avatar_component_clause,[],[f809]) ).

fof(f971,plain,
    ( spl0_127
    | ~ spl0_13
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f483,f450,f260,f969]) ).

fof(f483,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_49 ),
    inference(resolution,[],[f451,f261]) ).

fof(f967,plain,
    ( spl0_126
    | ~ spl0_32
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f428,f399,f341,f965]) ).

fof(f428,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_32
    | ~ spl0_44 ),
    inference(superposition,[],[f342,f401]) ).

fof(f963,plain,
    ( spl0_125
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f426,f394,f341,f961]) ).

fof(f426,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f342,f396]) ).

fof(f959,plain,
    ( spl0_124
    | ~ spl0_33
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f423,f390,f345,f957]) ).

fof(f423,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_33
    | ~ spl0_42 ),
    inference(superposition,[],[f346,f391]) ).

fof(f955,plain,
    ( spl0_122
    | ~ spl0_123
    | ~ spl0_15
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f421,f382,f268,f952,f948]) ).

fof(f948,plain,
    ( spl0_122
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f421,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_15
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f270]) ).

fof(f946,plain,
    ( spl0_120
    | ~ spl0_121
    | ~ spl0_12
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f416,f382,f255,f943,f939]) ).

fof(f939,plain,
    ( spl0_120
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f416,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_12
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f257]) ).

fof(f936,plain,
    ( spl0_118
    | ~ spl0_119
    | ~ spl0_11
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f413,f382,f250,f933,f929]) ).

fof(f929,plain,
    ( spl0_118
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f413,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_11
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f252]) ).

fof(f927,plain,
    ( spl0_117
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f406,f378,f305,f925]) ).

fof(f406,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f306]) ).

fof(f923,plain,
    ( spl0_116
    | ~ spl0_21
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f368,f321,f293,f921]) ).

fof(f368,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_21
    | ~ spl0_27 ),
    inference(resolution,[],[f322,f294]) ).

fof(f900,plain,
    ( spl0_115
    | ~ spl0_52
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f585,f570,f462,f898]) ).

fof(f570,plain,
    ( spl0_70
  <=> ! [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_70])]) ).

fof(f585,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_52
    | ~ spl0_70 ),
    inference(resolution,[],[f571,f463]) ).

fof(f571,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_70 ),
    inference(avatar_component_clause,[],[f570]) ).

fof(f896,plain,
    ( spl0_114
    | ~ spl0_32
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f424,f390,f341,f894]) ).

fof(f424,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_32
    | ~ spl0_42 ),
    inference(superposition,[],[f342,f391]) ).

fof(f892,plain,
    ( spl0_113
    | ~ spl0_21
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f319,f305,f293,f890]) ).

fof(f319,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_21
    | ~ spl0_24 ),
    inference(resolution,[],[f306,f294]) ).

fof(f831,plain,
    ( spl0_112
    | ~ spl0_32
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f625,f614,f341,f829]) ).

fof(f625,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_32
    | ~ spl0_77 ),
    inference(superposition,[],[f342,f616]) ).

fof(f827,plain,
    ( spl0_111
    | ~ spl0_14
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f417,f382,f264,f825]) ).

fof(f264,plain,
    ( spl0_14
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f417,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_14
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f265]) ).

fof(f265,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f823,plain,
    ( spl0_110
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f405,f378,f260,f821]) ).

fof(f405,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f261]) ).

fof(f819,plain,
    ( spl0_109
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f404,f378,f246,f817]) ).

fof(f404,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f247]) ).

fof(f812,plain,
    ( ~ spl0_107
    | spl0_108
    | ~ spl0_13
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f777,f737,f260,f809,f805]) ).

fof(f805,plain,
    ( spl0_107
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f777,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_13
    | ~ spl0_98 ),
    inference(resolution,[],[f738,f261]) ).

fof(f797,plain,
    ( spl0_106
    | ~ spl0_5
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f554,f549,f225,f795]) ).

fof(f795,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f554,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_5
    | ~ spl0_66 ),
    inference(resolution,[],[f550,f226]) ).

fof(f787,plain,
    ( spl0_105
    | ~ spl0_13
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f374,f345,f260,f785]) ).

fof(f785,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f374,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_13
    | ~ spl0_33 ),
    inference(resolution,[],[f346,f261]) ).

fof(f769,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f203,f767]) ).

fof(f767,plain,
    ( spl0_104
  <=> ! [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_104])]) ).

fof(f203,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f202,f129]) ).

fof(f129,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).

fof(f202,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f201,f129]) ).

fof(f201,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f200,f129]) ).

fof(f200,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f199,f129]) ).

fof(f199,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f198,f129]) ).

fof(f198,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f197,f129]) ).

fof(f197,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f196,f129]) ).

fof(f196,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f195,f129]) ).

fof(f195,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f194,f129]) ).

fof(f194,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f176,f129]) ).

fof(f176,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f91,f118,f119,f118,f118,f118,f118,f119]) ).

fof(f119,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

fof(f118,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,f115,f117,f12]) ).

fof(f117,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,f116,f29]) ).

fof(f116,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).

fof(f42,axiom,
    ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).

fof(f115,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f68,axiom,
    ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).

fof(f91,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).

fof(f765,plain,
    ( spl0_103
    | ~ spl0_33
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f427,f399,f345,f763]) ).

fof(f427,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_33
    | ~ spl0_44 ),
    inference(superposition,[],[f346,f401]) ).

fof(f758,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f193,f756]) ).

fof(f193,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f192,f129]) ).

fof(f192,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f191,f129]) ).

fof(f191,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f190,f129]) ).

fof(f190,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f189,f129]) ).

fof(f189,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f168,f129]) ).

fof(f168,plain,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f89,f119,f118,f119,f118,f118,f118,f118,f119]) ).

fof(f89,axiom,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(ordered_pair(X0,X1),domain_of(X10))
      | apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).

fof(f753,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f188,f751]) ).

fof(f188,plain,
    ! [X0,X1,X4] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
      | ~ member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(forward_demodulation,[],[f167,f129]) ).

fof(f167,plain,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(definition_unfolding,[],[f108,f119,f119,f118,f119,f119]) ).

fof(f108,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).

fof(f747,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f172,f745]) ).

fof(f172,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(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,f119,f119,f119,f119,f119,f119]) ).

fof(f37,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).

fof(f743,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f171,f741]) ).

fof(f171,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f34,f119,f119,f119,f119,f119,f119]) ).

fof(f34,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).

fof(f739,plain,
    ( spl0_98
    | ~ spl0_33
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f425,f394,f345,f737]) ).

fof(f425,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_33
    | ~ spl0_43 ),
    inference(superposition,[],[f346,f396]) ).

fof(f735,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f156,f733]) ).

fof(f156,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
    inference(definition_unfolding,[],[f36,f119,f119,f119,f119]) ).

fof(f36,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).

fof(f731,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f155,f729]) ).

fof(f155,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
    inference(definition_unfolding,[],[f33,f119,f119,f119,f119]) ).

fof(f33,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).

fof(f726,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f179,f724]) ).

fof(f179,plain,
    ! [X0] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f166]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f46,f125,f119,f119]) ).

fof(f125,plain,
    ! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
    inference(definition_unfolding,[],[f43,f26,f12]) ).

fof(f26,axiom,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).

fof(f43,axiom,
    ! [X0] : union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).

fof(f46,axiom,
    ! [X0,X1] :
      ( successor(X0) != X1
      | member(ordered_pair(X0,X1),successor_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).

fof(f710,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f170,f708]) ).

fof(f170,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f59,f119,f119,f117,f117,f12]) ).

fof(f59,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X1,X4),compose(X7,X5))
      | ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).

fof(f704,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f153,f702]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
    inference(definition_unfolding,[],[f97,f119,f119,f119]) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).

fof(f700,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f184,f698]) ).

fof(f184,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(forward_demodulation,[],[f150,f129]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f107,f118,f119,f119]) ).

fof(f107,axiom,
    ! [X0,X1,X4] :
      ( apply(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).

fof(f694,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f175,f692]) ).

fof(f175,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
    inference(definition_unfolding,[],[f90,f119]) ).

fof(f90,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).

fof(f690,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f154,f688]) ).

fof(f154,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f58,f119,f117,f117,f12]) ).

fof(f58,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),compose(X7,X5))
      | member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).

fof(f685,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f180,f683]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f169]) ).

fof(f169,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f94,f119,f119]) ).

fof(f94,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(ordered_pair(X1,X4),compose_class(X0))
      | ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).

fof(f681,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f152,f679]) ).

fof(f152,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
    inference(definition_unfolding,[],[f96,f119,f119]) ).

fof(f96,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).

fof(f677,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f148,f675]) ).

fof(f148,plain,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f106,f119,f119]) ).

fof(f106,axiom,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).

fof(f672,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f163,f670]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f20,f119,f119]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(ordered_pair(X0,X1),element_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).

fof(f662,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f187,f660]) ).

fof(f187,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f186,f129]) ).

fof(f186,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f164,f129]) ).

fof(f164,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
    inference(definition_unfolding,[],[f70,f118]) ).

fof(f70,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(apply(choice,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).

fof(f658,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f173,f656]) ).

fof(f656,plain,
    ( spl0_84
  <=> ! [X8] :
        ( ~ function(X8)
        | operation(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f173,plain,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f81,f116]) ).

fof(f81,axiom,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(range_of(X8),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).

fof(f653,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f174,f651]) ).

fof(f174,plain,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f85,f116]) ).

fof(f85,axiom,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).

fof(f645,plain,
    ( ~ spl0_81
    | spl0_82
    | ~ spl0_5
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f611,f602,f225,f642,f638]) ).

fof(f642,plain,
    ( spl0_82
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f611,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_5
    | ~ spl0_76 ),
    inference(resolution,[],[f603,f226]) ).

fof(f636,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f149,f634]) ).

fof(f149,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
    inference(definition_unfolding,[],[f17,f119]) ).

fof(f17,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).

fof(f632,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f146,f630]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
    inference(definition_unfolding,[],[f45,f125,f119]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( successor(X0) = X1
      | ~ member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).

fof(f621,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f162,f619]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f16,f119]) ).

fof(f16,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f617,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f130,f614]) ).

fof(f130,plain,
    subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
    inference(definition_unfolding,[],[f74,f38]) ).

fof(f74,axiom,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).

fof(f604,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f185,f602]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | inductive(X0)
      | ~ member(null_class,X0) ),
    inference(forward_demodulation,[],[f160,f129]) ).

fof(f160,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f117]) ).

fof(f49,axiom,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).

fof(f600,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f182,f598]) ).

fof(f182,plain,
    ! [X2] :
      ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
      | ~ member(X2,universal_class) ),
    inference(forward_demodulation,[],[f137,f129]) ).

fof(f137,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
    inference(definition_unfolding,[],[f56,f126]) ).

fof(f126,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,f117]) ).

fof(f55,axiom,
    ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).

fof(f56,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).

fof(f596,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f158,f594]) ).

fof(f158,plain,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
    inference(definition_unfolding,[],[f65,f117]) ).

fof(f65,axiom,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(image(X8,X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).

fof(f592,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f151,f590]) ).

fof(f151,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
    inference(definition_unfolding,[],[f93,f119]) ).

fof(f93,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).

fof(f581,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f165,f579]) ).

fof(f165,plain,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12]) ).

fof(f31,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

fof(f577,plain,
    ( spl0_71
    | ~ spl0_4
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f541,f513,f220,f574]) ).

fof(f574,plain,
    ( spl0_71
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f541,plain,
    ( single_valued_class(choice)
    | ~ spl0_4
    | ~ spl0_59 ),
    inference(resolution,[],[f514,f222]) ).

fof(f572,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f161,f570]) ).

fof(f161,plain,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f64,f38]) ).

fof(f64,axiom,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).

fof(f568,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f142,f566]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f14,f119]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f564,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f141,f562]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f15,f119]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f560,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f139,f558]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
    inference(definition_unfolding,[],[f100,f119]) ).

fof(f100,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).

fof(f551,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f159,f549]) ).

fof(f159,plain,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
      | maps(X8,domain_of(X8),X1) ),
    inference(definition_unfolding,[],[f112,f116]) ).

fof(f112,axiom,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(range_of(X8),X1)
      | maps(X8,domain_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).

fof(f547,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f147,f545]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
    inference(definition_unfolding,[],[f99,f119]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(ordered_pair(X0,X1),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).

fof(f540,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f181,f538]) ).

fof(f181,plain,
    ! [X0] :
      ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | ~ inductive(X0) ),
    inference(forward_demodulation,[],[f133,f129]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f48,f117]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).

fof(f536,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f145,f534]) ).

fof(f534,plain,
    ( spl0_63
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f145,plain,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f84,f116]) ).

fof(f84,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).

fof(f532,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f140,f530]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
    inference(definition_unfolding,[],[f19,f119]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).

fof(f524,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f143,f522]) ).

fof(f143,plain,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f30,f29,f12]) ).

fof(f30,axiom,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) != null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f519,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f144,f517]) ).

fof(f517,plain,
    ( spl0_60
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f144,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f116]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).

fof(f515,plain,
    ( spl0_59
    | ~ spl0_53
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f501,f470,f466,f513]) ).

fof(f470,plain,
    ( spl0_54
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f501,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_53
    | ~ spl0_54 ),
    inference(resolution,[],[f471,f467]) ).

fof(f471,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f470]) ).

fof(f511,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f134,f509]) ).

fof(f134,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f116]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).

fof(f507,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f79,f505]) ).

fof(f505,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).

fof(f480,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f183,f478]) ).

fof(f183,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f138,f129]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f115]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).

fof(f476,plain,
    ( spl0_55
    | ~ spl0_5
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f410,f382,f225,f474]) ).

fof(f474,plain,
    ( spl0_55
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f410,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_5
    | ~ spl0_40 ),
    inference(resolution,[],[f383,f226]) ).

fof(f472,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f136,f470]) ).

fof(f136,plain,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f61,f38]) ).

fof(f61,axiom,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f468,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f135,f466]) ).

fof(f135,plain,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f63,f38]) ).

fof(f63,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).

fof(f464,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f131,f462]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f460,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f129,f458]) ).

fof(f456,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f23,f454]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).

fof(f452,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f8,f450]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f444,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f157,f442]) ).

fof(f442,plain,
    ( spl0_48
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f157,plain,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f73,f38]) ).

fof(f73,axiom,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).

fof(f440,plain,
    ( spl0_47
    | ~ spl0_6
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f403,f378,f229,f438]) ).

fof(f229,plain,
    ( spl0_6
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f403,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_6
    | ~ spl0_39 ),
    inference(resolution,[],[f379,f231]) ).

fof(f231,plain,
    ( member(omega,universal_class)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f436,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f83,f434]) ).

fof(f434,plain,
    ( spl0_46
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).

fof(f432,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f25,f430]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).

fof(f402,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f128,f399]) ).

fof(f128,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).

fof(f397,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f104,f394]) ).

fof(f104,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).

fof(f392,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f67,f390]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f388,plain,
    ( spl0_41
    | ~ spl0_13
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f371,f341,f260,f386]) ).

fof(f371,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_32 ),
    inference(resolution,[],[f342,f261]) ).

fof(f384,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f7,f382]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f380,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f1,f378]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).

fof(f367,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f132,f365]) ).

fof(f132,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).

fof(f363,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f110,f361]) ).

fof(f361,plain,
    ( spl0_37
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).

fof(f359,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f88,f357]) ).

fof(f357,plain,
    ( spl0_36
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f355,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f35,f353]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).

fof(f351,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f32,f349]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).

fof(f347,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f22,f345]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f343,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f21,f341]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f339,plain,
    ( spl0_31
    | ~ spl0_13
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f318,f293,f260,f337]) ).

fof(f337,plain,
    ( spl0_31
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f318,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_13
    | ~ spl0_21 ),
    inference(resolution,[],[f294,f261]) ).

fof(f335,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f10,f333]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f331,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f9,f329]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f327,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f3,f325]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f323,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f2,f321]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f317,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f105,f314]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f312,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f95,f309]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f307,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f66,f305]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f303,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f62,f301]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f299,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f57,f297]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f295,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f24,f293]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f291,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f109,f289]) ).

fof(f289,plain,
    ( spl0_20
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).

fof(f287,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f92,f285]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f283,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f87,f281]) ).

fof(f281,plain,
    ( spl0_18
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f279,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f86,f277]) ).

fof(f277,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f275,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f82,f273]) ).

fof(f273,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f271,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f98,f268]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f266,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f51,f264]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f262,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f47,f260]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

fof(f258,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f44,f255]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f253,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f18,f250]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f248,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f11,f246]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f244,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f78,f242]) ).

fof(f242,plain,
    ( spl0_9
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f240,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f71,f238]) ).

fof(f238,plain,
    ( spl0_8
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f236,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f177,f234]) ).

fof(f177,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).

fof(f232,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f52,f229]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f227,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f4,f225]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f223,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f69,f220]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f218,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f50,f215]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f213,plain,
    ~ spl0_2,
    inference(avatar_split_clause,[],[f114,f210]) ).

fof(f114,axiom,
    ~ member(first(not_subclass_element(cross_product(x,y),z)),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property7_2) ).

fof(f208,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f113,f205]) ).

fof(f113,axiom,
    ~ subclass(cross_product(x,y),z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property7_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET232-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n010.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 12:00:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (9208)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (9211)WARNING: value z3 for option sas not known
% 0.14/0.37  % (9210)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  % (9209)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (9211)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  % (9214)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  % (9213)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)
% 0.14/0.37  % (9212)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (9215)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)
% 0.20/0.41  TRYING [1]
% 0.20/0.41  TRYING [2]
% 0.20/0.47  TRYING [3]
% 1.30/0.53  TRYING [1]
% 1.30/0.54  TRYING [2]
% 1.45/0.57  TRYING [4]
% 2.01/0.63  TRYING [3]
% 3.56/0.87  TRYING [5]
% 6.20/1.25  TRYING [4]
% 7.82/1.47  TRYING [1]
% 7.82/1.48  TRYING [2]
% 7.82/1.48  TRYING [3]
% 8.28/1.53  TRYING [4]
% 9.10/1.65  TRYING [5]
% 12.03/2.08  TRYING [6]
% 14.38/2.41  % (9213)First to succeed.
% 14.76/2.48  % (9213)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9208"
% 14.76/2.49  % (9213)Refutation found. Thanks to Tanya!
% 14.76/2.49  % SZS status Unsatisfiable for theBenchmark
% 14.76/2.49  % SZS output start Proof for theBenchmark
% See solution above
% 14.76/2.51  % (9213)------------------------------
% 14.76/2.51  % (9213)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 14.76/2.51  % (9213)Termination reason: Refutation
% 14.76/2.51  
% 14.76/2.51  % (9213)Memory used [KB]: 25768
% 14.76/2.51  % (9213)Time elapsed: 2.114 s
% 14.76/2.51  % (9213)Instructions burned: 6628 (million)
% 14.76/2.51  % (9208)Success in time 2.15 s
%------------------------------------------------------------------------------