TSTP Solution File: SET473-6 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET473-6 : 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 : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:18:52 EDT 2024

% Result   : Unsatisfiable 54.43s 8.11s
% Output   : Refutation 54.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1430
% Syntax   : Number of formulae    : 4555 ( 137 unt;   0 def)
%            Number of atoms       : 17359 (2282 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives : 22524 (9720   ~;11479   |;   0   &)
%                                         (1325 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   28 (   4 avg)
%            Number of predicates  : 1337 (1335 usr;1326 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;  14 con; 0-3 aty)
%            Number of variables   : 6188 (6188   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f54540,plain,
    $false,
    inference(avatar_sat_refutation,[],[f211,f215,f220,f226,f231,f236,f240,f244,f249,f253,f257,f263,f267,f271,f275,f280,f285,f290,f294,f299,f308,f312,f316,f320,f324,f328,f332,f336,f340,f344,f350,f355,f363,f367,f371,f375,f379,f383,f387,f391,f395,f399,f403,f407,f426,f430,f434,f439,f444,f474,f478,f482,f486,f494,f498,f502,f506,f510,f514,f518,f553,f557,f561,f571,f575,f579,f585,f594,f598,f607,f611,f615,f619,f627,f631,f635,f645,f649,f663,f667,f676,f681,f685,f690,f695,f699,f703,f708,f712,f717,f721,f727,f743,f748,f757,f761,f765,f769,f775,f780,f787,f791,f812,f816,f828,f833,f837,f854,f858,f890,f895,f899,f914,f921,f927,f955,f968,f976,f989,f994,f999,f1003,f1007,f1011,f1035,f1039,f1045,f1061,f1068,f1080,f1084,f1091,f1141,f1145,f1183,f1197,f1201,f1231,f1240,f1249,f1258,f1262,f1266,f1289,f1293,f1297,f1302,f1306,f1339,f1349,f1353,f1357,f1361,f1365,f1418,f1422,f1426,f1435,f1493,f1499,f1506,f1513,f1522,f1531,f1535,f1539,f1568,f1577,f1587,f1591,f1595,f1599,f1608,f1620,f1627,f1640,f1644,f1648,f1652,f1740,f1744,f1748,f1752,f1756,f1761,f1800,f1807,f1811,f1818,f1843,f1858,f1862,f1868,f1881,f1885,f1891,f1920,f1941,f1945,f2001,f2040,f2092,f2106,f2110,f2120,f2124,f2177,f2188,f2201,f2205,f2222,f2226,f2233,f2237,f2246,f2250,f2266,f2272,f2277,f2286,f2309,f2315,f2319,f2325,f2335,f2336,f2424,f2428,f2448,f2452,f2457,f2485,f2493,f2510,f2524,f2529,f2534,f2539,f2548,f2554,f2558,f2564,f2708,f2745,f2749,f2757,f2766,f2808,f2813,f2820,f2824,f2828,f2832,f2836,f2840,f2849,f2945,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3017,f3021,f3025,f3144,f3199,f3203,f3207,f3211,f3220,f3225,f3229,f3233,f3237,f3424,f3428,f3432,f3436,f3440,f3441,f3487,f3492,f3567,f3576,f3581,f3590,f3594,f3598,f3602,f3606,f3610,f3619,f3630,f3636,f3697,f3701,f3709,f3807,f3812,f3816,f3820,f3824,f3828,f3980,f4023,f4029,f4034,f4039,f4044,f4090,f4094,f4098,f4102,f4106,f4188,f4192,f4234,f4238,f4242,f4285,f4289,f4293,f4297,f4305,f4360,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4468,f4481,f4499,f4790,f4957,f4968,f4972,f4991,f5000,f5007,f5013,f5017,f5021,f5025,f5029,f5033,f5229,f5233,f5264,f5271,f5275,f5279,f5304,f5308,f5312,f5341,f5346,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5521,f5525,f5529,f5533,f5537,f5560,f5601,f5646,f5650,f5654,f5658,f5665,f5673,f5681,f5690,f5694,f5698,f5754,f5758,f5762,f5766,f5770,f5779,f5817,f5845,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5887,f6105,f6109,f6113,f6117,f6283,f6290,f6294,f6298,f6302,f6390,f6414,f6478,f6482,f6486,f6490,f6498,f6535,f6568,f6572,f6576,f6580,f6584,f6816,f6820,f6863,f6867,f6871,f6875,f6879,f6973,f6984,f7028,f7074,f7089,f7108,f7112,f7116,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7257,f7261,f7265,f7269,f7273,f7277,f7281,f7285,f7550,f7557,f7561,f7569,f7583,f7605,f7611,f7615,f7619,f7623,f7627,f7795,f7915,f7919,f7923,f7927,f7931,f7935,f7939,f8086,f8090,f8094,f8098,f8102,f8306,f8314,f8326,f8330,f8334,f8343,f8352,f8386,f8390,f8394,f8398,f8424,f8479,f8483,f8487,f8491,f8495,f8499,f8503,f8588,f8592,f8596,f8733,f8862,f8866,f8870,f8905,f8991,f9047,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9083,f9414,f9419,f9424,f9476,f9480,f9487,f9495,f9591,f9631,f9635,f9639,f9643,f9647,f9651,f9655,f9659,f9663,f9667,f9671,f9675,f10517,f10521,f10525,f10531,f10599,f10715,f10719,f10848,f10852,f10865,f10894,f10925,f10930,f10939,f10945,f10949,f10953,f10961,f11090,f11094,f11104,f11108,f11152,f11156,f11160,f11218,f11232,f11236,f11244,f11252,f11377,f11507,f11516,f11523,f11540,f11545,f11550,f11554,f11558,f11656,f11661,f11752,f11829,f12139,f12593,f12621,f12625,f12629,f12633,f12637,f12641,f12649,f12672,f12911,f12915,f13048,f13053,f13057,f13061,f13065,f13069,f13073,f13143,f13178,f13199,f13277,f13281,f13285,f13289,f13290,f13296,f13300,f13487,f13530,f13534,f13538,f13558,f13562,f13566,f13570,f13574,f13802,f13806,f13810,f13814,f13863,f13867,f13871,f13875,f13879,f13883,f13887,f13891,f13965,f14098,f14152,f14331,f14691,f14695,f14707,f14729,f14833,f14888,f14892,f14896,f14965,f14969,f15084,f15092,f15096,f15211,f15216,f15220,f15302,f15309,f15326,f15375,f15379,f15383,f15387,f15433,f15437,f15441,f15492,f15496,f15500,f15660,f15665,f15690,f15694,f15698,f15702,f15706,f15710,f15715,f15719,f15727,f15926,f15930,f15938,f16003,f16038,f16070,f16077,f16167,f16186,f16190,f16226,f16230,f16234,f16238,f16242,f16391,f16395,f16443,f16447,f16451,f16455,f16605,f16609,f16617,f16625,f16630,f16660,f16713,f16717,f16767,f16775,f16782,f16786,f17001,f17005,f17026,f17226,f17231,f17329,f17359,f17736,f17743,f18377,f18515,f18715,f18721,f18726,f18743,f18943,f18948,f18953,f19234,f19238,f19242,f19246,f19352,f19434,f19439,f19443,f19465,f19483,f19525,f19529,f19545,f19549,f19593,f19600,f19622,f19626,f19632,f19713,f19717,f19721,f19748,f19782,f19790,f19794,f19799,f19884,f19889,f19895,f19899,f19903,f19907,f20288,f20292,f20296,f20300,f20386,f20391,f20417,f20421,f20425,f20466,f20520,f20535,f20539,f20543,f20547,f20724,f20754,f20787,f20791,f20795,f20985,f20989,f20993,f20997,f21001,f21091,f21115,f21119,f21123,f21327,f21331,f21335,f21448,f21510,f21532,f21536,f21540,f21544,f21548,f21591,f21623,f21627,f21663,f21696,f21700,f21733,f21737,f21741,f21745,f21760,f21764,f21889,f21904,f21908,f21924,f21954,f21958,f22011,f22015,f22019,f22027,f22035,f22040,f22122,f22126,f22130,f22134,f22236,f22247,f22251,f22255,f22259,f22287,f22333,f22377,f22381,f22385,f22410,f22414,f22472,f22480,f22488,f22492,f22499,f22539,f22540,f22541,f24016,f24326,f25005,f25485,f25843,f26653,f27612,f27719,f27758,f27864,f27868,f27873,f27877,f27881,f27950,f27954,f28018,f28128,f28133,f28137,f28141,f28145,f28307,f28311,f28911,f29107,f29306,f29526,f29788,f29836,f29840,f29877,f29887,f29908,f29930,f29934,f29938,f29943,f29947,f30195,f30199,f30266,f30271,f30275,f30647,f30651,f30814,f30862,f30866,f30929,f30933,f30937,f30941,f30945,f30949,f31216,f31220,f31224,f31249,f31307,f31331,f31368,f31432,f31469,f31533,f31537,f31541,f31566,f31607,f31611,f31779,f31783,f31820,f31824,f31846,f31883,f31920,f31966,f31970,f32007,f32047,f32091,f32095,f32161,f32166,f32171,f32242,f32247,f32251,f32263,f32268,f32273,f32278,f32283,f32290,f32295,f32300,f32345,f32346,f32347,f32359,f32364,f32369,f32374,f32379,f32384,f32389,f32397,f32421,f32450,f32475,f32480,f32484,f32488,f32490,f32494,f32498,f33132,f33137,f33142,f33146,f33152,f33158,f33163,f33168,f33178,f33182,f33268,f33273,f33278,f33283,f33288,f33293,f33299,f33303,f33318,f33322,f33326,f33330,f33334,f33338,f33530,f33534,f33538,f33543,f33549,f33554,f33558,f33562,f33567,f33572,f33577,f33582,f33606,f33630,f33635,f33641,f33651,f33655,f33664,f33668,f33672,f33676,f33681,f33883,f33889,f33894,f33898,f33903,f33908,f33913,f33918,f33923,f33928,f33933,f33938,f33944,f33948,f33961,f33967,f33972,f33976,f33981,f33986,f33991,f33997,f34001,f34005,f34009,f34013,f34017,f34032,f34036,f34177,f34613,f34623,f34628,f34633,f34722,f34727,f34732,f34737,f34744,f34748,f34752,f34756,f34760,f34764,f35066,f35071,f35076,f35081,f35086,f35091,f35096,f35101,f35106,f35111,f35116,f35121,f35126,f35131,f35137,f35141,f35146,f35151,f35156,f35161,f35171,f35175,f35180,f35186,f35250,f35255,f35260,f35264,f35269,f35274,f35280,f35284,f35288,f35295,f35306,f35310,f35314,f35318,f35322,f35326,f35330,f35334,f35338,f35342,f35346,f35350,f35354,f35358,f35362,f35366,f35370,f36098,f36741,f36746,f36751,f37050,f37055,f37060,f37065,f37070,f37076,f37081,f37086,f37092,f37097,f37624,f37629,f37634,f37640,f37645,f37650,f37656,f37661,f37666,f37671,f37675,f37698,f37703,f37727,f37734,f37740,f37745,f37750,f37754,f37758,f37762,f37766,f37770,f37774,f37778,f37782,f37786,f37790,f37794,f37798,f37923,f37927,f37931,f37935,f37939,f37943,f38122,f41453,f41468,f41495,f41665,f41704,f41722,f41726,f41775,f41776,f41796,f41803,f41806,f42137,f42324,f42336,f42337,f42531,f42667,f44121,f44127,f44331,f44360,f44528,f44947,f44999,f45033,f45066,f45074,f45148,f45159,f45899,f46130,f46481,f46670,f46685,f46691,f46700,f46702,f47449,f49210,f49619,f49661,f49696,f49747,f49809,f51469,f52693,f52730,f52850,f52912,f52916,f52920,f52924,f52928,f52932,f52936,f52940,f52946,f52950,f52956,f52961,f52965,f52978,f52991,f52995,f53004,f53158,f53298,f53307,f53461,f53603,f53892,f54020,f54024,f54028,f54032,f54036,f54040,f54044,f54180,f54185,f54190,f54195,f54200,f54205,f54210,f54215,f54222,f54229,f54232,f54433,f54450,f54463,f54489,f54506,f54510,f54514,f54518,f54522,f54526,f54530,f54534,f54538,f54539]) ).

fof(f54539,plain,
    ( ~ spl0_567
    | spl0_4
    | ~ spl0_539
    | ~ spl0_1291 ),
    inference(avatar_split_clause,[],[f54175,f53890,f8422,f223,f9421]) ).

fof(f9421,plain,
    ( spl0_567
  <=> y = domain_of(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f223,plain,
    ( spl0_4
  <=> y = domain_of(intersection(x,cross_product(y,y))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f8422,plain,
    ( spl0_539
  <=> ! [X0] : y = intersection(X0,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f53890,plain,
    ( spl0_1291
  <=> ! [X0] : y = cross_product(X0,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).

fof(f54175,plain,
    ( y != domain_of(y)
    | spl0_4
    | ~ spl0_539
    | ~ spl0_1291 ),
    inference(forward_demodulation,[],[f54129,f8423]) ).

fof(f8423,plain,
    ( ! [X0] : y = intersection(X0,y)
    | ~ spl0_539 ),
    inference(avatar_component_clause,[],[f8422]) ).

fof(f54129,plain,
    ( y != domain_of(intersection(x,y))
    | spl0_4
    | ~ spl0_1291 ),
    inference(superposition,[],[f225,f53891]) ).

fof(f53891,plain,
    ( ! [X0] : y = cross_product(X0,y)
    | ~ spl0_1291 ),
    inference(avatar_component_clause,[],[f53890]) ).

fof(f225,plain,
    ( y != domain_of(intersection(x,cross_product(y,y)))
    | spl0_4 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f54538,plain,
    ( spl0_1325
    | ~ spl0_280
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f6181,f6111,f2980,f54536]) ).

fof(f54536,plain,
    ( spl0_1325
  <=> ! [X0,X1] :
        ( ~ member(regular(intersection(X0,X1)),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | intersection(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).

fof(f2980,plain,
    ( spl0_280
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f6111,plain,
    ( spl0_445
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f6181,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,X1)),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | intersection(X0,X1) = y )
    | ~ spl0_280
    | ~ spl0_445 ),
    inference(resolution,[],[f6112,f2981]) ).

fof(f2981,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X0,X2)
        | intersection(X0,X1) = y )
    | ~ spl0_280 ),
    inference(avatar_component_clause,[],[f2980]) ).

fof(f6112,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_445 ),
    inference(avatar_component_clause,[],[f6111]) ).

fof(f54534,plain,
    ( spl0_1324
    | ~ spl0_282
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f6180,f6111,f2988,f54532]) ).

fof(f54532,plain,
    ( spl0_1324
  <=> ! [X0,X1] :
        ( ~ member(regular(intersection(X0,X1)),singleton_relation)
        | ~ subclass(X1,compose(element_relation,complement(identity_relation)))
        | intersection(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).

fof(f2988,plain,
    ( spl0_282
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f6180,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,X1)),singleton_relation)
        | ~ subclass(X1,compose(element_relation,complement(identity_relation)))
        | intersection(X0,X1) = y )
    | ~ spl0_282
    | ~ spl0_445 ),
    inference(resolution,[],[f6112,f2989]) ).

fof(f2989,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X1,X2)
        | intersection(X0,X1) = y )
    | ~ spl0_282 ),
    inference(avatar_component_clause,[],[f2988]) ).

fof(f54530,plain,
    ( spl0_1323
    | ~ spl0_112
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f6166,f6111,f856,f54528]) ).

fof(f54528,plain,
    ( spl0_1323
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,compose(element_relation,complement(identity_relation)))),singleton_relation)
        | y = intersection(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).

fof(f856,plain,
    ( spl0_112
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f6166,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,compose(element_relation,complement(identity_relation)))),singleton_relation)
        | y = intersection(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_112
    | ~ spl0_445 ),
    inference(resolution,[],[f6112,f857]) ).

fof(f857,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = y )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f856]) ).

fof(f54526,plain,
    ( spl0_1322
    | ~ spl0_111
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f6154,f6111,f852,f54524]) ).

fof(f54524,plain,
    ( spl0_1322
  <=> ! [X0] :
        ( ~ member(regular(intersection(compose(element_relation,complement(identity_relation)),X0)),singleton_relation)
        | y = intersection(compose(element_relation,complement(identity_relation)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).

fof(f852,plain,
    ( spl0_111
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f6154,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(compose(element_relation,complement(identity_relation)),X0)),singleton_relation)
        | y = intersection(compose(element_relation,complement(identity_relation)),X0) )
    | ~ spl0_111
    | ~ spl0_445 ),
    inference(resolution,[],[f6112,f853]) ).

fof(f853,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = y )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f852]) ).

fof(f54522,plain,
    ( spl0_1321
    | ~ spl0_160
    | ~ spl0_381 ),
    inference(avatar_split_clause,[],[f5154,f5023,f1347,f54520]) ).

fof(f54520,plain,
    ( spl0_1321
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X0)),X1),y)
        | subclass(intersection(X0,regular(X0)),X1)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).

fof(f1347,plain,
    ( spl0_160
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f5023,plain,
    ( spl0_381
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,regular(X1)),X2)
        | member(not_subclass_element(intersection(X0,regular(X1)),X2),y)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f5154,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X0)),X1),y)
        | subclass(intersection(X0,regular(X0)),X1)
        | y = X0 )
    | ~ spl0_160
    | ~ spl0_381 ),
    inference(duplicate_literal_removal,[],[f5121]) ).

fof(f5121,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X0)),X1),y)
        | subclass(intersection(X0,regular(X0)),X1)
        | y = X0
        | subclass(intersection(X0,regular(X0)),X1) )
    | ~ spl0_160
    | ~ spl0_381 ),
    inference(resolution,[],[f5024,f1348]) ).

fof(f1348,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1347]) ).

fof(f5024,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | member(not_subclass_element(intersection(X0,regular(X1)),X2),y)
        | subclass(intersection(X0,regular(X1)),X2)
        | y = X1 )
    | ~ spl0_381 ),
    inference(avatar_component_clause,[],[f5023]) ).

fof(f54518,plain,
    ( spl0_1320
    | ~ spl0_161
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f5110,f5015,f1351,f54516]) ).

fof(f54516,plain,
    ( spl0_1320
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X0),X1),y)
        | subclass(intersection(regular(X0),X0),X1)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).

fof(f1351,plain,
    ( spl0_161
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f5015,plain,
    ( spl0_379
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(regular(X0),X1),X2)
        | member(not_subclass_element(intersection(regular(X0),X1),X2),y)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f5110,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X0),X1),y)
        | subclass(intersection(regular(X0),X0),X1)
        | y = X0 )
    | ~ spl0_161
    | ~ spl0_379 ),
    inference(duplicate_literal_removal,[],[f5080]) ).

fof(f5080,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X0),X1),y)
        | subclass(intersection(regular(X0),X0),X1)
        | y = X0
        | subclass(intersection(regular(X0),X0),X1) )
    | ~ spl0_161
    | ~ spl0_379 ),
    inference(resolution,[],[f5016,f1352]) ).

fof(f1352,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1351]) ).

fof(f5016,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | member(not_subclass_element(intersection(regular(X0),X1),X2),y)
        | subclass(intersection(regular(X0),X1),X2)
        | y = X0 )
    | ~ spl0_379 ),
    inference(avatar_component_clause,[],[f5015]) ).

fof(f54514,plain,
    ( spl0_1319
    | ~ spl0_302
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f4409,f4287,f3434,f54512]) ).

fof(f54512,plain,
    ( spl0_1319
  <=> ! [X0,X1] :
        ( member(X0,y)
        | ~ member(X0,X0)
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).

fof(f3434,plain,
    ( spl0_302
  <=> ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f4287,plain,
    ( spl0_349
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,y)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f4409,plain,
    ( ! [X0,X1] :
        ( member(X0,y)
        | ~ member(X0,X0)
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 )
    | ~ spl0_302
    | ~ spl0_349 ),
    inference(duplicate_literal_removal,[],[f4363]) ).

fof(f4363,plain,
    ( ! [X0,X1] :
        ( member(X0,y)
        | ~ member(X0,X0)
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 )
    | ~ spl0_302
    | ~ spl0_349 ),
    inference(resolution,[],[f4288,f3435]) ).

fof(f3435,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_302 ),
    inference(avatar_component_clause,[],[f3434]) ).

fof(f4288,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | member(X2,y)
        | ~ member(X2,X1)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f4287]) ).

fof(f54510,plain,
    ( spl0_1318
    | ~ spl0_301
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f4355,f4283,f3430,f54508]) ).

fof(f54508,plain,
    ( spl0_1318
  <=> ! [X0,X1] :
        ( member(X0,y)
        | ~ member(X0,X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).

fof(f3430,plain,
    ( spl0_301
  <=> ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f4283,plain,
    ( spl0_348
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,y)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f4355,plain,
    ( ! [X0,X1] :
        ( member(X0,y)
        | ~ member(X0,X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_301
    | ~ spl0_348 ),
    inference(duplicate_literal_removal,[],[f4306]) ).

fof(f4306,plain,
    ( ! [X0,X1] :
        ( member(X0,y)
        | ~ member(X0,X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_301
    | ~ spl0_348 ),
    inference(resolution,[],[f4284,f3431]) ).

fof(f3431,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_301 ),
    inference(avatar_component_clause,[],[f3430]) ).

fof(f4284,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | member(X2,y)
        | ~ member(X2,X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_348 ),
    inference(avatar_component_clause,[],[f4283]) ).

fof(f54506,plain,
    ( spl0_1317
    | ~ spl0_154
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f4066,f4021,f1287,f54504]) ).

fof(f54504,plain,
    ( spl0_1317
  <=> ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),y)
        | y = X0
        | subclass(regular(X0),X1)
        | ~ subclass(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).

fof(f1287,plain,
    ( spl0_154
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f4021,plain,
    ( spl0_333
  <=> ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),y)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | y = X0
        | subclass(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f4066,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),y)
        | y = X0
        | subclass(regular(X0),X1)
        | ~ subclass(regular(X0),X0) )
    | ~ spl0_154
    | ~ spl0_333 ),
    inference(duplicate_literal_removal,[],[f4053]) ).

fof(f4053,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),y)
        | y = X0
        | subclass(regular(X0),X1)
        | ~ subclass(regular(X0),X0)
        | subclass(regular(X0),X1) )
    | ~ spl0_154
    | ~ spl0_333 ),
    inference(resolution,[],[f4022,f1288]) ).

fof(f1288,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1287]) ).

fof(f4022,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(regular(X0),X1),X0)
        | member(not_subclass_element(regular(X0),X1),y)
        | y = X0
        | subclass(regular(X0),X1) )
    | ~ spl0_333 ),
    inference(avatar_component_clause,[],[f4021]) ).

fof(f54489,plain,
    ( ~ spl0_1314
    | spl0_882
    | ~ spl0_1315
    | spl0_1316
    | ~ spl0_19
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f3975,f3826,f292,f54486,f54482,f21901,f54478]) ).

fof(f54478,plain,
    ( spl0_1314
  <=> inductive(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).

fof(f21901,plain,
    ( spl0_882
  <=> omega = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).

fof(f54482,plain,
    ( spl0_1315
  <=> member(regular(omega),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).

fof(f54486,plain,
    ( spl0_1316
  <=> member(regular(omega),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).

fof(f292,plain,
    ( spl0_19
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f3826,plain,
    ( spl0_331
  <=> ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f3975,plain,
    ( member(regular(omega),identity_relation)
    | ~ member(regular(omega),subset_relation)
    | omega = y
    | ~ inductive(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_19
    | ~ spl0_331 ),
    inference(resolution,[],[f3827,f293]) ).

fof(f293,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f292]) ).

fof(f3827,plain,
    ( ! [X0] :
        ( ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | member(regular(X0),identity_relation)
        | ~ member(regular(X0),subset_relation)
        | y = X0 )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f3826]) ).

fof(f54463,plain,
    ( ~ spl0_1311
    | spl0_882
    | ~ spl0_1312
    | spl0_1313
    | ~ spl0_19
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3970,f3822,f292,f54460,f54456,f21901,f54452]) ).

fof(f54452,plain,
    ( spl0_1311
  <=> inductive(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).

fof(f54456,plain,
    ( spl0_1312
  <=> member(regular(omega),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).

fof(f54460,plain,
    ( spl0_1313
  <=> member(regular(omega),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).

fof(f3822,plain,
    ( spl0_330
  <=> ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f3970,plain,
    ( member(regular(omega),singleton_relation)
    | ~ member(regular(omega),element_relation)
    | omega = y
    | ~ inductive(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_19
    | ~ spl0_330 ),
    inference(resolution,[],[f3823,f293]) ).

fof(f3823,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | member(regular(X0),singleton_relation)
        | ~ member(regular(X0),element_relation)
        | y = X0 )
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f3822]) ).

fof(f54450,plain,
    ( spl0_1310
    | ~ spl0_109
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3889,f3810,f831,f54448]) ).

fof(f54448,plain,
    ( spl0_1310
  <=> ! [X0,X1] :
        ( member(regular(X0),y)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | y = X0
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).

fof(f831,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f3810,plain,
    ( spl0_327
  <=> ! [X0,X1] :
        ( member(regular(X0),y)
        | ~ member(regular(X0),X1)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f3889,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),y)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | y = X0
        | ~ subclass(X0,X1) )
    | ~ spl0_109
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3833]) ).

fof(f3833,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),y)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | y = X0
        | ~ subclass(X0,X1)
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_327 ),
    inference(resolution,[],[f3811,f832]) ).

fof(f832,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | y = X0 )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f831]) ).

fof(f3811,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | member(regular(X0),y)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | y = X0 )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f3810]) ).

fof(f54433,plain,
    ( spl0_1258
    | spl0_1309
    | ~ spl0_245
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3876,f3810,f2422,f54431,f49612]) ).

fof(f49612,plain,
    ( spl0_1258
  <=> element_relation = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).

fof(f54431,plain,
    ( spl0_1309
  <=> ! [X0] :
        ( member(regular(X0),y)
        | ~ subclass(X0,singleton_relation)
        | y = X0
        | ~ subclass(X0,regular(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).

fof(f2422,plain,
    ( spl0_245
  <=> ! [X0] :
        ( member(regular(X0),element_relation)
        | ~ subclass(X0,singleton_relation)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f3876,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | element_relation = y
        | ~ subclass(X0,regular(element_relation))
        | y = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_245
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3851]) ).

fof(f3851,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | element_relation = y
        | ~ subclass(X0,regular(element_relation))
        | y = X0
        | ~ subclass(X0,singleton_relation)
        | y = X0 )
    | ~ spl0_245
    | ~ spl0_327 ),
    inference(resolution,[],[f3811,f2423]) ).

fof(f2423,plain,
    ( ! [X0] :
        ( member(regular(X0),element_relation)
        | ~ subclass(X0,singleton_relation)
        | y = X0 )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f2422]) ).

fof(f54232,plain,
    ( spl0_168
    | ~ spl0_1217
    | ~ spl0_1291 ),
    inference(avatar_split_clause,[],[f54045,f53890,f37756,f1428]) ).

fof(f1428,plain,
    ( spl0_168
  <=> singleton_relation = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f37756,plain,
    ( spl0_1217
  <=> ! [X0] : singleton_relation = cross_product(singleton_relation,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f54045,plain,
    ( singleton_relation = y
    | ~ spl0_1217
    | ~ spl0_1291 ),
    inference(superposition,[],[f53891,f37757]) ).

fof(f37757,plain,
    ( ! [X0] : singleton_relation = cross_product(singleton_relation,X0)
    | ~ spl0_1217 ),
    inference(avatar_component_clause,[],[f37756]) ).

fof(f54229,plain,
    ( spl0_238
    | spl0_1308
    | ~ spl0_246
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3873,f3810,f2426,f54227,f2279]) ).

fof(f2279,plain,
    ( spl0_238
  <=> subset_relation = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f54227,plain,
    ( spl0_1308
  <=> ! [X0] :
        ( member(regular(X0),y)
        | ~ subclass(X0,identity_relation)
        | y = X0
        | ~ subclass(X0,regular(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).

fof(f2426,plain,
    ( spl0_246
  <=> ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ subclass(X0,identity_relation)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f3873,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | subset_relation = y
        | ~ subclass(X0,regular(subset_relation))
        | y = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_246
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3864]) ).

fof(f3864,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | subset_relation = y
        | ~ subclass(X0,regular(subset_relation))
        | y = X0
        | ~ subclass(X0,identity_relation)
        | y = X0 )
    | ~ spl0_246
    | ~ spl0_327 ),
    inference(resolution,[],[f3811,f2427]) ).

fof(f2427,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ subclass(X0,identity_relation)
        | y = X0 )
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f2426]) ).

fof(f54222,plain,
    ( spl0_1307
    | ~ spl0_160
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3799,f3634,f1347,f54220]) ).

fof(f54220,plain,
    ( spl0_1307
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(regular(X0),X1),y),X0)
        | subclass(intersection(regular(X0),X1),y)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).

fof(f3634,plain,
    ( spl0_323
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,y),regular(X0))
        | ~ member(not_subclass_element(X1,y),X0)
        | subclass(X1,y)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f3799,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(regular(X0),X1),y),X0)
        | subclass(intersection(regular(X0),X1),y)
        | y = X0 )
    | ~ spl0_160
    | ~ spl0_323 ),
    inference(duplicate_literal_removal,[],[f3782]) ).

fof(f3782,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(regular(X0),X1),y),X0)
        | subclass(intersection(regular(X0),X1),y)
        | y = X0
        | subclass(intersection(regular(X0),X1),y) )
    | ~ spl0_160
    | ~ spl0_323 ),
    inference(resolution,[],[f3635,f1348]) ).

fof(f3635,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,y),regular(X0))
        | ~ member(not_subclass_element(X1,y),X0)
        | subclass(X1,y)
        | y = X0 )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f3634]) ).

fof(f54215,plain,
    ( spl0_1306
    | ~ spl0_161
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3798,f3634,f1351,f54213]) ).

fof(f54213,plain,
    ( spl0_1306
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,regular(X1)),y),X1)
        | subclass(intersection(X0,regular(X1)),y)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).

fof(f3798,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,regular(X1)),y),X1)
        | subclass(intersection(X0,regular(X1)),y)
        | y = X1 )
    | ~ spl0_161
    | ~ spl0_323 ),
    inference(duplicate_literal_removal,[],[f3783]) ).

fof(f3783,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,regular(X1)),y),X1)
        | subclass(intersection(X0,regular(X1)),y)
        | y = X1
        | subclass(intersection(X0,regular(X1)),y) )
    | ~ spl0_161
    | ~ spl0_323 ),
    inference(resolution,[],[f3635,f1352]) ).

fof(f54210,plain,
    ( spl0_1305
    | ~ spl0_39
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3401,f3235,f381,f54208]) ).

fof(f54208,plain,
    ( spl0_1305
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(X0,y),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).

fof(f381,plain,
    ( spl0_39
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f3235,plain,
    ( spl0_298
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | member(not_subclass_element(intersection(X0,y),X1),X2)
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f3401,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(X0,y),X1),X2) )
    | ~ spl0_39
    | ~ spl0_298 ),
    inference(resolution,[],[f3236,f382]) ).

fof(f382,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f381]) ).

fof(f3236,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,y),X1),X2)
        | subclass(intersection(X0,y),X1)
        | y = X2 )
    | ~ spl0_298 ),
    inference(avatar_component_clause,[],[f3235]) ).

fof(f54205,plain,
    ( spl0_1304
    | ~ spl0_40
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3400,f3235,f385,f54203]) ).

fof(f54203,plain,
    ( spl0_1304
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(X0,y),X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).

fof(f385,plain,
    ( spl0_40
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f3400,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(X0,y),X1),X3) )
    | ~ spl0_40
    | ~ spl0_298 ),
    inference(resolution,[],[f3236,f386]) ).

fof(f386,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f385]) ).

fof(f54200,plain,
    ( spl0_1303
    | ~ spl0_39
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f3372,f3231,f381,f54198]) ).

fof(f54198,plain,
    ( spl0_1303
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(y,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).

fof(f3231,plain,
    ( spl0_297
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | member(not_subclass_element(intersection(y,X0),X1),X2)
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f3372,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(y,X0),X1),X2) )
    | ~ spl0_39
    | ~ spl0_297 ),
    inference(resolution,[],[f3232,f382]) ).

fof(f3232,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(y,X0),X1),X2)
        | subclass(intersection(y,X0),X1)
        | y = X2 )
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f3231]) ).

fof(f54195,plain,
    ( spl0_1302
    | ~ spl0_40
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f3371,f3231,f385,f54193]) ).

fof(f54193,plain,
    ( spl0_1302
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(y,X0),X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).

fof(f3371,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = intersection(X2,X3)
        | member(not_subclass_element(intersection(y,X0),X1),X3) )
    | ~ spl0_40
    | ~ spl0_297 ),
    inference(resolution,[],[f3232,f386]) ).

fof(f54190,plain,
    ( spl0_1301
    | ~ spl0_29
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3334,f3209,f334,f54188]) ).

fof(f54188,plain,
    ( spl0_1301
  <=> ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(complement(X1),X2))
        | ~ member(regular(intersection(X0,intersection(complement(X1),X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).

fof(f334,plain,
    ( spl0_29
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f3209,plain,
    ( spl0_292
  <=> ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f3334,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(complement(X1),X2))
        | ~ member(regular(intersection(X0,intersection(complement(X1),X2))),X1) )
    | ~ spl0_29
    | ~ spl0_292 ),
    inference(resolution,[],[f3210,f335]) ).

fof(f335,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f334]) ).

fof(f3210,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X1)
        | y = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f3209]) ).

fof(f54185,plain,
    ( spl0_1300
    | ~ spl0_29
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f3305,f3205,f334,f54183]) ).

fof(f54183,plain,
    ( spl0_1300
  <=> ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,complement(X2)))
        | ~ member(regular(intersection(X0,intersection(X1,complement(X2)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).

fof(f3205,plain,
    ( spl0_291
  <=> ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f3305,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,complement(X2)))
        | ~ member(regular(intersection(X0,intersection(X1,complement(X2)))),X2) )
    | ~ spl0_29
    | ~ spl0_291 ),
    inference(resolution,[],[f3206,f335]) ).

fof(f3206,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X2)
        | y = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f3205]) ).

fof(f54180,plain,
    ( spl0_1299
    | ~ spl0_29
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3276,f3201,f334,f54178]) ).

fof(f54178,plain,
    ( spl0_1299
  <=> ! [X2,X0,X1] :
        ( y = intersection(intersection(complement(X0),X1),X2)
        | ~ member(regular(intersection(intersection(complement(X0),X1),X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).

fof(f3201,plain,
    ( spl0_290
  <=> ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f3276,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(complement(X0),X1),X2)
        | ~ member(regular(intersection(intersection(complement(X0),X1),X2)),X0) )
    | ~ spl0_29
    | ~ spl0_290 ),
    inference(resolution,[],[f3202,f335]) ).

fof(f3202,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X0)
        | y = intersection(intersection(X0,X1),X2) )
    | ~ spl0_290 ),
    inference(avatar_component_clause,[],[f3201]) ).

fof(f54044,plain,
    ( spl0_1298
    | ~ spl0_29
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f3247,f3197,f334,f54042]) ).

fof(f54042,plain,
    ( spl0_1298
  <=> ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,complement(X1)),X2)
        | ~ member(regular(intersection(intersection(X0,complement(X1)),X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).

fof(f3197,plain,
    ( spl0_289
  <=> ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f3247,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,complement(X1)),X2)
        | ~ member(regular(intersection(intersection(X0,complement(X1)),X2)),X1) )
    | ~ spl0_29
    | ~ spl0_289 ),
    inference(resolution,[],[f3198,f335]) ).

fof(f3198,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X1)
        | y = intersection(intersection(X0,X1),X2) )
    | ~ spl0_289 ),
    inference(avatar_component_clause,[],[f3197]) ).

fof(f54040,plain,
    ( spl0_1297
    | ~ spl0_46
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3148,f3019,f424,f54038]) ).

fof(f54038,plain,
    ( spl0_1297
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,X0)
        | y = cross_product(X1,X2)
        | ~ subclass(X0,X3)
        | member(regular(cross_product(X1,X2)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).

fof(f424,plain,
    ( spl0_46
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f3019,plain,
    ( spl0_286
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f3148,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | y = cross_product(X1,X2)
        | ~ subclass(X0,X3)
        | member(regular(cross_product(X1,X2)),X3) )
    | ~ spl0_46
    | ~ spl0_286 ),
    inference(resolution,[],[f3020,f425]) ).

fof(f425,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f424]) ).

fof(f3020,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = y )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f3019]) ).

fof(f54036,plain,
    ( spl0_1296
    | ~ spl0_46
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3091,f2988,f424,f54034]) ).

fof(f54034,plain,
    ( spl0_1296
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X2,X0)
        | ~ subclass(X1,X3)
        | member(regular(intersection(X2,X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).

fof(f3091,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X2,X0)
        | ~ subclass(X1,X3)
        | member(regular(intersection(X2,X0)),X3) )
    | ~ spl0_46
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f425]) ).

fof(f54032,plain,
    ( spl0_1295
    | ~ spl0_46
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3038,f2980,f424,f54030]) ).

fof(f54030,plain,
    ( spl0_1295
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,X2)
        | ~ subclass(X1,X3)
        | member(regular(intersection(X0,X2)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).

fof(f3038,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,X2)
        | ~ subclass(X1,X3)
        | member(regular(intersection(X0,X2)),X3) )
    | ~ spl0_46
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f425]) ).

fof(f54028,plain,
    ( spl0_1294
    | ~ spl0_139
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2950,f2838,f1089,f54026]) ).

fof(f54026,plain,
    ( spl0_1294
  <=> ! [X0] :
        ( y = intersection(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).

fof(f1089,plain,
    ( spl0_139
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f2838,plain,
    ( spl0_275
  <=> ! [X0,X1] :
        ( y = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f2950,plain,
    ( ! [X0] :
        ( y = intersection(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) )
    | ~ spl0_139
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f1090]) ).

fof(f1090,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1089]) ).

fof(f2839,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,complement(X1))),X1)
        | y = intersection(X0,complement(X1)) )
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2838]) ).

fof(f54024,plain,
    ( spl0_1293
    | ~ spl0_139
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2922,f2834,f1089,f54022]) ).

fof(f54022,plain,
    ( spl0_1293
  <=> ! [X0] :
        ( y = intersection(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).

fof(f2834,plain,
    ( spl0_274
  <=> ! [X0,X1] :
        ( y = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f2922,plain,
    ( ! [X0] :
        ( y = intersection(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) )
    | ~ spl0_139
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f1090]) ).

fof(f2835,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(complement(X0),X1)),X0)
        | y = intersection(complement(X0),X1) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2834]) ).

fof(f54020,plain,
    ( spl0_1292
    | ~ spl0_56
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2661,f2450,f496,f54018]) ).

fof(f54018,plain,
    ( spl0_1292
  <=> ! [X2,X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(intersection(X1,X2)))
        | ~ member(regular(X0),X2)
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).

fof(f496,plain,
    ( spl0_56
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f2450,plain,
    ( spl0_248
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f2661,plain,
    ( ! [X2,X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(intersection(X1,X2)))
        | ~ member(regular(X0),X2)
        | ~ member(regular(X0),X1) )
    | ~ spl0_56
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f497]) ).

fof(f497,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f496]) ).

fof(f2451,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | y = X0
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f2450]) ).

fof(f53892,plain,
    ( spl0_1291
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1105 ),
    inference(avatar_split_clause,[],[f46544,f33974,f9421,f8731,f53890]) ).

fof(f8731,plain,
    ( spl0_550
  <=> ! [X0] : ~ member(X0,domain_of(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f33974,plain,
    ( spl0_1105
  <=> ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f46544,plain,
    ( ! [X0] : y = cross_product(X0,y)
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1105 ),
    inference(forward_demodulation,[],[f46516,f9423]) ).

fof(f9423,plain,
    ( y = domain_of(y)
    | ~ spl0_567 ),
    inference(avatar_component_clause,[],[f9421]) ).

fof(f46516,plain,
    ( ! [X0] : y = cross_product(X0,domain_of(y))
    | ~ spl0_550
    | ~ spl0_1105 ),
    inference(resolution,[],[f33975,f8732]) ).

fof(f8732,plain,
    ( ! [X0] : ~ member(X0,domain_of(y))
    | ~ spl0_550 ),
    inference(avatar_component_clause,[],[f8731]) ).

fof(f33975,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = y )
    | ~ spl0_1105 ),
    inference(avatar_component_clause,[],[f33974]) ).

fof(f53603,plain,
    ( spl0_1290
    | ~ spl0_10
    | ~ spl0_639 ),
    inference(avatar_split_clause,[],[f17595,f11827,f251,f53601]) ).

fof(f53601,plain,
    ( spl0_1290
  <=> ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = subset_relation
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).

fof(f251,plain,
    ( spl0_10
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f11827,plain,
    ( spl0_639
  <=> ! [X2,X0,X1] :
        ( unordered_pair(X0,X1) = subset_relation
        | member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f17595,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = subset_relation
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_10
    | ~ spl0_639 ),
    inference(resolution,[],[f11828,f252]) ).

fof(f252,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f251]) ).

fof(f11828,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | unordered_pair(X0,X1) = subset_relation
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_639 ),
    inference(avatar_component_clause,[],[f11827]) ).

fof(f53461,plain,
    ( spl0_1288
    | spl0_1258
    | spl0_1289
    | ~ spl0_252
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f4885,f4449,f2522,f53458,f49612,f53454]) ).

fof(f53454,plain,
    ( spl0_1288
  <=> y = intersection(singleton_relation,regular(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).

fof(f53458,plain,
    ( spl0_1289
  <=> member(regular(intersection(singleton_relation,regular(element_relation))),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).

fof(f2522,plain,
    ( spl0_252
  <=> ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | y = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f4449,plain,
    ( spl0_358
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),y)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | y = X1
        | y = intersection(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f4885,plain,
    ( member(regular(intersection(singleton_relation,regular(element_relation))),y)
    | element_relation = y
    | y = intersection(singleton_relation,regular(element_relation))
    | ~ spl0_252
    | ~ spl0_358 ),
    inference(duplicate_literal_removal,[],[f4851]) ).

fof(f4851,plain,
    ( member(regular(intersection(singleton_relation,regular(element_relation))),y)
    | element_relation = y
    | y = intersection(singleton_relation,regular(element_relation))
    | y = intersection(singleton_relation,regular(element_relation))
    | ~ spl0_252
    | ~ spl0_358 ),
    inference(resolution,[],[f4450,f2523]) ).

fof(f2523,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | y = intersection(singleton_relation,X0) )
    | ~ spl0_252 ),
    inference(avatar_component_clause,[],[f2522]) ).

fof(f4450,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,regular(X1))),X1)
        | member(regular(intersection(X0,regular(X1))),y)
        | y = X1
        | y = intersection(X0,regular(X1)) )
    | ~ spl0_358 ),
    inference(avatar_component_clause,[],[f4449]) ).

fof(f53307,plain,
    ( spl0_1286
    | spl0_238
    | spl0_1287
    | ~ spl0_254
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f4883,f4449,f2532,f53304,f2279,f53300]) ).

fof(f53300,plain,
    ( spl0_1286
  <=> y = intersection(identity_relation,regular(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).

fof(f53304,plain,
    ( spl0_1287
  <=> member(regular(intersection(identity_relation,regular(subset_relation))),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).

fof(f2532,plain,
    ( spl0_254
  <=> ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | y = intersection(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f4883,plain,
    ( member(regular(intersection(identity_relation,regular(subset_relation))),y)
    | subset_relation = y
    | y = intersection(identity_relation,regular(subset_relation))
    | ~ spl0_254
    | ~ spl0_358 ),
    inference(duplicate_literal_removal,[],[f4860]) ).

fof(f4860,plain,
    ( member(regular(intersection(identity_relation,regular(subset_relation))),y)
    | subset_relation = y
    | y = intersection(identity_relation,regular(subset_relation))
    | y = intersection(identity_relation,regular(subset_relation))
    | ~ spl0_254
    | ~ spl0_358 ),
    inference(resolution,[],[f4450,f2533]) ).

fof(f2533,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | y = intersection(identity_relation,X0) )
    | ~ spl0_254 ),
    inference(avatar_component_clause,[],[f2532]) ).

fof(f53298,plain,
    ( spl0_1285
    | ~ spl0_112
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f4840,f4445,f856,f53296]) ).

fof(f53296,plain,
    ( spl0_1285
  <=> ! [X0] :
        ( member(regular(intersection(regular(X0),X0)),y)
        | y = X0
        | y = intersection(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).

fof(f4445,plain,
    ( spl0_357
  <=> ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),y)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | y = X0
        | y = intersection(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f4840,plain,
    ( ! [X0] :
        ( member(regular(intersection(regular(X0),X0)),y)
        | y = X0
        | y = intersection(regular(X0),X0) )
    | ~ spl0_112
    | ~ spl0_357 ),
    inference(duplicate_literal_removal,[],[f4791]) ).

fof(f4791,plain,
    ( ! [X0] :
        ( member(regular(intersection(regular(X0),X0)),y)
        | y = X0
        | y = intersection(regular(X0),X0)
        | y = intersection(regular(X0),X0) )
    | ~ spl0_112
    | ~ spl0_357 ),
    inference(resolution,[],[f4446,f857]) ).

fof(f4446,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(regular(X0),X1)),X0)
        | member(regular(intersection(regular(X0),X1)),y)
        | y = X0
        | y = intersection(regular(X0),X1) )
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f4445]) ).

fof(f53158,plain,
    ( spl0_1283
    | spl0_1258
    | spl0_1284
    | ~ spl0_253
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f4832,f4445,f2527,f53155,f49612,f53151]) ).

fof(f53151,plain,
    ( spl0_1283
  <=> y = intersection(regular(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).

fof(f53155,plain,
    ( spl0_1284
  <=> member(regular(intersection(regular(element_relation),singleton_relation)),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).

fof(f2527,plain,
    ( spl0_253
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | y = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f4832,plain,
    ( member(regular(intersection(regular(element_relation),singleton_relation)),y)
    | element_relation = y
    | y = intersection(regular(element_relation),singleton_relation)
    | ~ spl0_253
    | ~ spl0_357 ),
    inference(duplicate_literal_removal,[],[f4800]) ).

fof(f4800,plain,
    ( member(regular(intersection(regular(element_relation),singleton_relation)),y)
    | element_relation = y
    | y = intersection(regular(element_relation),singleton_relation)
    | y = intersection(regular(element_relation),singleton_relation)
    | ~ spl0_253
    | ~ spl0_357 ),
    inference(resolution,[],[f4446,f2528]) ).

fof(f2528,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | y = intersection(X0,singleton_relation) )
    | ~ spl0_253 ),
    inference(avatar_component_clause,[],[f2527]) ).

fof(f53004,plain,
    ( spl0_1281
    | spl0_238
    | spl0_1282
    | ~ spl0_255
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f4830,f4445,f2537,f53001,f2279,f52997]) ).

fof(f52997,plain,
    ( spl0_1281
  <=> y = intersection(regular(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).

fof(f53001,plain,
    ( spl0_1282
  <=> member(regular(intersection(regular(subset_relation),identity_relation)),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).

fof(f2537,plain,
    ( spl0_255
  <=> ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),subset_relation)
        | y = intersection(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f4830,plain,
    ( member(regular(intersection(regular(subset_relation),identity_relation)),y)
    | subset_relation = y
    | y = intersection(regular(subset_relation),identity_relation)
    | ~ spl0_255
    | ~ spl0_357 ),
    inference(duplicate_literal_removal,[],[f4809]) ).

fof(f4809,plain,
    ( member(regular(intersection(regular(subset_relation),identity_relation)),y)
    | subset_relation = y
    | y = intersection(regular(subset_relation),identity_relation)
    | y = intersection(regular(subset_relation),identity_relation)
    | ~ spl0_255
    | ~ spl0_357 ),
    inference(resolution,[],[f4446,f2538]) ).

fof(f2538,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),subset_relation)
        | y = intersection(X0,identity_relation) )
    | ~ spl0_255 ),
    inference(avatar_component_clause,[],[f2537]) ).

fof(f52995,plain,
    ( spl0_1280
    | ~ spl0_109
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3660,f3596,f831,f52993]) ).

fof(f52993,plain,
    ( spl0_1280
  <=> ! [X0] :
        ( member(regular(regular(X0)),y)
        | y = X0
        | regular(X0) = y
        | ~ subclass(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).

fof(f3596,plain,
    ( spl0_315
  <=> ! [X0] :
        ( member(regular(regular(X0)),y)
        | ~ member(regular(regular(X0)),X0)
        | y = X0
        | regular(X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f3660,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),y)
        | y = X0
        | regular(X0) = y
        | ~ subclass(regular(X0),X0) )
    | ~ spl0_109
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3643]) ).

fof(f3643,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),y)
        | y = X0
        | regular(X0) = y
        | ~ subclass(regular(X0),X0)
        | regular(X0) = y )
    | ~ spl0_109
    | ~ spl0_315 ),
    inference(resolution,[],[f3597,f832]) ).

fof(f3597,plain,
    ( ! [X0] :
        ( ~ member(regular(regular(X0)),X0)
        | member(regular(regular(X0)),y)
        | y = X0
        | regular(X0) = y )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3596]) ).

fof(f52991,plain,
    ( ~ spl0_1277
    | spl0_1278
    | spl0_1258
    | spl0_1279
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3659,f3596,f2422,f52988,f49612,f52984,f52980]) ).

fof(f52980,plain,
    ( spl0_1277
  <=> subclass(regular(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).

fof(f52984,plain,
    ( spl0_1278
  <=> y = regular(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).

fof(f52988,plain,
    ( spl0_1279
  <=> member(regular(regular(element_relation)),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).

fof(f3659,plain,
    ( member(regular(regular(element_relation)),y)
    | element_relation = y
    | y = regular(element_relation)
    | ~ subclass(regular(element_relation),singleton_relation)
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3645]) ).

fof(f3645,plain,
    ( member(regular(regular(element_relation)),y)
    | element_relation = y
    | y = regular(element_relation)
    | ~ subclass(regular(element_relation),singleton_relation)
    | y = regular(element_relation)
    | ~ spl0_245
    | ~ spl0_315 ),
    inference(resolution,[],[f3597,f2423]) ).

fof(f52978,plain,
    ( ~ spl0_1274
    | spl0_1275
    | spl0_238
    | spl0_1276
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3658,f3596,f2426,f52975,f2279,f52971,f52967]) ).

fof(f52967,plain,
    ( spl0_1274
  <=> subclass(regular(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).

fof(f52971,plain,
    ( spl0_1275
  <=> y = regular(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).

fof(f52975,plain,
    ( spl0_1276
  <=> member(regular(regular(subset_relation)),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).

fof(f3658,plain,
    ( member(regular(regular(subset_relation)),y)
    | subset_relation = y
    | y = regular(subset_relation)
    | ~ subclass(regular(subset_relation),identity_relation)
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3653]) ).

fof(f3653,plain,
    ( member(regular(regular(subset_relation)),y)
    | subset_relation = y
    | y = regular(subset_relation)
    | ~ subclass(regular(subset_relation),identity_relation)
    | y = regular(subset_relation)
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(resolution,[],[f3597,f2427]) ).

fof(f52965,plain,
    ( spl0_1273
    | ~ spl0_109
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f3640,f3592,f831,f52963]) ).

fof(f52963,plain,
    ( spl0_1273
  <=> ! [X0] :
        ( member(regular(complement(complement(X0))),X0)
        | y = complement(complement(X0))
        | ~ subclass(complement(complement(X0)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).

fof(f3592,plain,
    ( spl0_314
  <=> ! [X0] :
        ( y = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f3640,plain,
    ( ! [X0] :
        ( member(regular(complement(complement(X0))),X0)
        | y = complement(complement(X0))
        | ~ subclass(complement(complement(X0)),universal_class) )
    | ~ spl0_109
    | ~ spl0_314 ),
    inference(duplicate_literal_removal,[],[f3638]) ).

fof(f3638,plain,
    ( ! [X0] :
        ( member(regular(complement(complement(X0))),X0)
        | y = complement(complement(X0))
        | ~ subclass(complement(complement(X0)),universal_class)
        | y = complement(complement(X0)) )
    | ~ spl0_109
    | ~ spl0_314 ),
    inference(resolution,[],[f3593,f832]) ).

fof(f3593,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(complement(X0))),universal_class)
        | member(regular(complement(complement(X0))),X0)
        | y = complement(complement(X0)) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f3592]) ).

fof(f52961,plain,
    ( spl0_321
    | ~ spl0_1272
    | ~ spl0_109
    | spl0_322 ),
    inference(avatar_split_clause,[],[f3632,f3627,f831,f52958,f3623]) ).

fof(f3623,plain,
    ( spl0_321
  <=> y = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f52958,plain,
    ( spl0_1272
  <=> subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).

fof(f3627,plain,
    ( spl0_322
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f3632,plain,
    ( ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | y = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_109
    | spl0_322 ),
    inference(resolution,[],[f3629,f832]) ).

fof(f3629,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | spl0_322 ),
    inference(avatar_component_clause,[],[f3627]) ).

fof(f52956,plain,
    ( spl0_319
    | ~ spl0_1271
    | ~ spl0_109
    | spl0_320 ),
    inference(avatar_split_clause,[],[f3621,f3616,f831,f52953,f3612]) ).

fof(f3612,plain,
    ( spl0_319
  <=> y = complement(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f52953,plain,
    ( spl0_1271
  <=> subclass(complement(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).

fof(f3616,plain,
    ( spl0_320
  <=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f3621,plain,
    ( ~ subclass(complement(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | y = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_109
    | spl0_320 ),
    inference(resolution,[],[f3618,f832]) ).

fof(f3618,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | spl0_320 ),
    inference(avatar_component_clause,[],[f3616]) ).

fof(f52950,plain,
    ( spl0_1270
    | ~ spl0_29
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3403,f3235,f334,f52948]) ).

fof(f52948,plain,
    ( spl0_1270
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = complement(X2)
        | ~ member(not_subclass_element(intersection(X0,y),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).

fof(f3403,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = complement(X2)
        | ~ member(not_subclass_element(intersection(X0,y),X1),X2) )
    | ~ spl0_29
    | ~ spl0_298 ),
    inference(resolution,[],[f3236,f335]) ).

fof(f52946,plain,
    ( ~ spl0_1269
    | spl0_1010
    | ~ spl0_1217 ),
    inference(avatar_split_clause,[],[f52734,f37756,f32244,f52943]) ).

fof(f52943,plain,
    ( spl0_1269
  <=> operation(domain_of(flip(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).

fof(f32244,plain,
    ( spl0_1010
  <=> operation(domain_of(flip(cross_product(singleton_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f52734,plain,
    ( ~ operation(domain_of(flip(singleton_relation)))
    | spl0_1010
    | ~ spl0_1217 ),
    inference(superposition,[],[f32246,f37757]) ).

fof(f32246,plain,
    ( ~ operation(domain_of(flip(cross_product(singleton_relation,universal_class))))
    | spl0_1010 ),
    inference(avatar_component_clause,[],[f32244]) ).

fof(f52940,plain,
    ( spl0_1268
    | ~ spl0_29
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f3374,f3231,f334,f52938]) ).

fof(f52938,plain,
    ( spl0_1268
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = complement(X2)
        | ~ member(not_subclass_element(intersection(y,X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).

fof(f3374,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = complement(X2)
        | ~ member(not_subclass_element(intersection(y,X0),X1),X2) )
    | ~ spl0_29
    | ~ spl0_297 ),
    inference(resolution,[],[f3232,f335]) ).

fof(f52936,plain,
    ( spl0_1267
    | ~ spl0_39
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3152,f3019,f381,f52934]) ).

fof(f52934,plain,
    ( spl0_1267
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | y = cross_product(X2,X3)
        | member(regular(cross_product(X2,X3)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).

fof(f3152,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | y = cross_product(X2,X3)
        | member(regular(cross_product(X2,X3)),X0) )
    | ~ spl0_39
    | ~ spl0_286 ),
    inference(resolution,[],[f3020,f382]) ).

fof(f52932,plain,
    ( spl0_1266
    | ~ spl0_40
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3151,f3019,f385,f52930]) ).

fof(f52930,plain,
    ( spl0_1266
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | y = cross_product(X2,X3)
        | member(regular(cross_product(X2,X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).

fof(f3151,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | y = cross_product(X2,X3)
        | member(regular(cross_product(X2,X3)),X1) )
    | ~ spl0_40
    | ~ spl0_286 ),
    inference(resolution,[],[f3020,f386]) ).

fof(f52928,plain,
    ( spl0_1265
    | ~ spl0_39
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3095,f2988,f381,f52926]) ).

fof(f52926,plain,
    ( spl0_1265
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X3,X0)
        | member(regular(intersection(X3,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).

fof(f3095,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X3,X0)
        | member(regular(intersection(X3,X0)),X1) )
    | ~ spl0_39
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f382]) ).

fof(f52924,plain,
    ( spl0_1264
    | ~ spl0_40
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3094,f2988,f385,f52922]) ).

fof(f52922,plain,
    ( spl0_1264
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X3,X0)
        | member(regular(intersection(X3,X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).

fof(f3094,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X3,X0)
        | member(regular(intersection(X3,X0)),X2) )
    | ~ spl0_40
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f386]) ).

fof(f52920,plain,
    ( spl0_1263
    | ~ spl0_39
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3042,f2980,f381,f52918]) ).

fof(f52918,plain,
    ( spl0_1263
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X0,X3)
        | member(regular(intersection(X0,X3)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).

fof(f3042,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X0,X3)
        | member(regular(intersection(X0,X3)),X1) )
    | ~ spl0_39
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f382]) ).

fof(f52916,plain,
    ( spl0_1262
    | ~ spl0_40
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3041,f2980,f385,f52914]) ).

fof(f52914,plain,
    ( spl0_1262
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X0,X3)
        | member(regular(intersection(X0,X3)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).

fof(f3041,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = intersection(X0,X3)
        | member(regular(intersection(X0,X3)),X2) )
    | ~ spl0_40
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f386]) ).

fof(f52912,plain,
    ( spl0_1261
    | ~ spl0_51
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2664,f2450,f472,f52910]) ).

fof(f52910,plain,
    ( spl0_1261
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(complement(X1)))
        | member(regular(X0),X1)
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).

fof(f472,plain,
    ( spl0_51
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f2664,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(complement(X1)))
        | member(regular(X0),X1)
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_51
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f473]) ).

fof(f473,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f472]) ).

fof(f52850,plain,
    ( spl0_1163
    | ~ spl0_1217 ),
    inference(avatar_contradiction_clause,[],[f52849]) ).

fof(f52849,plain,
    ( $false
    | spl0_1163
    | ~ spl0_1217 ),
    inference(trivial_inequality_removal,[],[f52739]) ).

fof(f52739,plain,
    ( singleton_relation != singleton_relation
    | spl0_1163
    | ~ spl0_1217 ),
    inference(superposition,[],[f35279,f37757]) ).

fof(f35279,plain,
    ( singleton_relation != cross_product(singleton_relation,universal_class)
    | spl0_1163 ),
    inference(avatar_component_clause,[],[f35277]) ).

fof(f35277,plain,
    ( spl0_1163
  <=> singleton_relation = cross_product(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f52730,plain,
    ( spl0_1200
    | ~ spl0_130
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f44100,f3205,f1005,f37632]) ).

fof(f37632,plain,
    ( spl0_1200
  <=> ! [X0,X1] :
        ( y = intersection(X0,intersection(X1,singleton_relation))
        | member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).

fof(f1005,plain,
    ( spl0_130
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f44100,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation)
        | y = intersection(X0,intersection(X1,singleton_relation)) )
    | ~ spl0_130
    | ~ spl0_291 ),
    inference(resolution,[],[f1006,f3206]) ).

fof(f1006,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1005]) ).

fof(f52693,plain,
    ( spl0_1192
    | ~ spl0_130
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f44081,f3197,f1005,f37068]) ).

fof(f37068,plain,
    ( spl0_1192
  <=> ! [X0,X1] :
        ( y = intersection(intersection(X0,singleton_relation),X1)
        | member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

fof(f44081,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation)
        | y = intersection(intersection(X0,singleton_relation),X1) )
    | ~ spl0_130
    | ~ spl0_289 ),
    inference(resolution,[],[f1006,f3198]) ).

fof(f51469,plain,
    ( spl0_1001
    | ~ spl0_343
    | ~ spl0_1251 ),
    inference(avatar_split_clause,[],[f50354,f46479,f4186,f31968]) ).

fof(f31968,plain,
    ( spl0_1001
  <=> ! [X0] : subclass(singleton_relation,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f4186,plain,
    ( spl0_343
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f46479,plain,
    ( spl0_1251
  <=> ! [X0] : singleton_relation = intersection(X0,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).

fof(f50354,plain,
    ( ! [X0] : subclass(singleton_relation,X0)
    | ~ spl0_343
    | ~ spl0_1251 ),
    inference(superposition,[],[f4187,f46480]) ).

fof(f46480,plain,
    ( ! [X0] : singleton_relation = intersection(X0,y)
    | ~ spl0_1251 ),
    inference(avatar_component_clause,[],[f46479]) ).

fof(f4187,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_343 ),
    inference(avatar_component_clause,[],[f4186]) ).

fof(f49809,plain,
    ( spl0_1260
    | ~ spl0_152
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2665,f2450,f1260,f49807]) ).

fof(f49807,plain,
    ( spl0_1260
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(regular(X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).

fof(f1260,plain,
    ( spl0_152
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f2665,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(regular(X0),singleton_relation) )
    | ~ spl0_152
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f1261]) ).

fof(f1261,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1260]) ).

fof(f49747,plain,
    ( spl0_1145
    | ~ spl0_130
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f44099,f2980,f1005,f35129]) ).

fof(f35129,plain,
    ( spl0_1145
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = y
        | member(regular(intersection(X0,X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f44099,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),element_relation)
        | ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = y )
    | ~ spl0_130
    | ~ spl0_280 ),
    inference(resolution,[],[f1006,f2981]) ).

fof(f49696,plain,
    ( spl0_1149
    | ~ spl0_130
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f44098,f2988,f1005,f35149]) ).

fof(f35149,plain,
    ( spl0_1149
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | y = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f44098,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),element_relation)
        | ~ subclass(X1,singleton_relation)
        | intersection(X0,X1) = y )
    | ~ spl0_130
    | ~ spl0_282 ),
    inference(resolution,[],[f1006,f2989]) ).

fof(f49661,plain,
    ( spl0_1140
    | ~ spl0_31
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f42016,f2826,f342,f35104]) ).

fof(f35104,plain,
    ( spl0_1140
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f342,plain,
    ( spl0_31
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f2826,plain,
    ( spl0_272
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f42016,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | y = X1
        | ~ subclass(X1,X0)
        | member(regular(X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_31
    | ~ spl0_272 ),
    inference(resolution,[],[f343,f2827]) ).

fof(f2827,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X1,X2)
        | y = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),X2) )
    | ~ spl0_272 ),
    inference(avatar_component_clause,[],[f2826]) ).

fof(f343,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f342]) ).

fof(f49619,plain,
    ( spl0_168
    | ~ spl0_1257
    | spl0_1258
    | spl0_1259
    | ~ spl0_169
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f41445,f3810,f1432,f49616,f49612,f49608,f1428]) ).

fof(f49608,plain,
    ( spl0_1257
  <=> subclass(singleton_relation,regular(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).

fof(f49616,plain,
    ( spl0_1259
  <=> member(regular(singleton_relation),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).

fof(f1432,plain,
    ( spl0_169
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f41445,plain,
    ( member(regular(singleton_relation),y)
    | element_relation = y
    | ~ subclass(singleton_relation,regular(element_relation))
    | singleton_relation = y
    | ~ spl0_169
    | ~ spl0_327 ),
    inference(resolution,[],[f1434,f3811]) ).

fof(f1434,plain,
    ( member(regular(singleton_relation),element_relation)
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f1432]) ).

fof(f49210,plain,
    ( spl0_1001
    | ~ spl0_344
    | ~ spl0_1250 ),
    inference(avatar_split_clause,[],[f48057,f46128,f4190,f31968]) ).

fof(f4190,plain,
    ( spl0_344
  <=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f46128,plain,
    ( spl0_1250
  <=> ! [X0] : singleton_relation = intersection(y,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).

fof(f48057,plain,
    ( ! [X0] : subclass(singleton_relation,X0)
    | ~ spl0_344
    | ~ spl0_1250 ),
    inference(superposition,[],[f4191,f46129]) ).

fof(f46129,plain,
    ( ! [X0] : singleton_relation = intersection(y,X0)
    | ~ spl0_1250 ),
    inference(avatar_component_clause,[],[f46128]) ).

fof(f4191,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_344 ),
    inference(avatar_component_clause,[],[f4190]) ).

fof(f47449,plain,
    ( spl0_168
    | ~ spl0_585
    | ~ spl0_1106
    | ~ spl0_1116 ),
    inference(avatar_split_clause,[],[f46658,f34034,f33979,f9669,f1428]) ).

fof(f9669,plain,
    ( spl0_585
  <=> ! [X0] : ~ member(X0,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f33979,plain,
    ( spl0_1106
  <=> ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f34034,plain,
    ( spl0_1116
  <=> ! [X0,X1] :
        ( cross_product(X0,X1) = singleton_relation
        | member(first(regular(cross_product(X0,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f46658,plain,
    ( singleton_relation = y
    | ~ spl0_585
    | ~ spl0_1106
    | ~ spl0_1116 ),
    inference(forward_demodulation,[],[f46599,f34585]) ).

fof(f34585,plain,
    ( ! [X0] : singleton_relation = cross_product(y,X0)
    | ~ spl0_585
    | ~ spl0_1116 ),
    inference(resolution,[],[f34035,f9670]) ).

fof(f9670,plain,
    ( ! [X0] : ~ member(X0,y)
    | ~ spl0_585 ),
    inference(avatar_component_clause,[],[f9669]) ).

fof(f34035,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = singleton_relation )
    | ~ spl0_1116 ),
    inference(avatar_component_clause,[],[f34034]) ).

fof(f46599,plain,
    ( ! [X0] : y = cross_product(y,X0)
    | ~ spl0_585
    | ~ spl0_1106 ),
    inference(resolution,[],[f33980,f9670]) ).

fof(f33980,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = y )
    | ~ spl0_1106 ),
    inference(avatar_component_clause,[],[f33979]) ).

fof(f46702,plain,
    ( spl0_168
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_585
    | ~ spl0_1105
    | ~ spl0_1115 ),
    inference(avatar_split_clause,[],[f46545,f34030,f33974,f9669,f9421,f8731,f1428]) ).

fof(f34030,plain,
    ( spl0_1115
  <=> ! [X0,X1] :
        ( cross_product(X0,X1) = singleton_relation
        | member(second(regular(cross_product(X0,X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f46545,plain,
    ( singleton_relation = y
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_585
    | ~ spl0_1105
    | ~ spl0_1115 ),
    inference(forward_demodulation,[],[f46544,f34513]) ).

fof(f34513,plain,
    ( ! [X0] : singleton_relation = cross_product(X0,y)
    | ~ spl0_585
    | ~ spl0_1115 ),
    inference(resolution,[],[f34031,f9670]) ).

fof(f34031,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = singleton_relation )
    | ~ spl0_1115 ),
    inference(avatar_component_clause,[],[f34030]) ).

fof(f46700,plain,
    ( spl0_1256
    | ~ spl0_109
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f6165,f6111,f831,f46698]) ).

fof(f46698,plain,
    ( spl0_1256
  <=> ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).

fof(f6165,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_445 ),
    inference(resolution,[],[f6112,f832]) ).

fof(f46691,plain,
    ( ~ spl0_1255
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_585
    | ~ spl0_1105
    | ~ spl0_1115
    | spl0_1253 ),
    inference(avatar_split_clause,[],[f46686,f46678,f34030,f33974,f9669,f9421,f8731,f46688]) ).

fof(f46688,plain,
    ( spl0_1255
  <=> compose(element_relation,complement(identity_relation)) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).

fof(f46678,plain,
    ( spl0_1253
  <=> compose(element_relation,complement(identity_relation)) = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).

fof(f46686,plain,
    ( compose(element_relation,complement(identity_relation)) != singleton_relation
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_585
    | ~ spl0_1105
    | ~ spl0_1115
    | spl0_1253 ),
    inference(forward_demodulation,[],[f46679,f46545]) ).

fof(f46679,plain,
    ( compose(element_relation,complement(identity_relation)) != y
    | spl0_1253 ),
    inference(avatar_component_clause,[],[f46678]) ).

fof(f46685,plain,
    ( spl0_1253
    | ~ spl0_1254
    | ~ spl0_2
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f6153,f6111,f213,f46682,f46678]) ).

fof(f46682,plain,
    ( spl0_1254
  <=> member(regular(compose(element_relation,complement(identity_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).

fof(f213,plain,
    ( spl0_2
  <=> ! [X0] :
        ( y = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f6153,plain,
    ( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
    | compose(element_relation,complement(identity_relation)) = y
    | ~ spl0_2
    | ~ spl0_445 ),
    inference(resolution,[],[f6112,f214]) ).

fof(f214,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | y = X0 )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f213]) ).

fof(f46670,plain,
    ( spl0_1252
    | ~ spl0_49
    | ~ spl0_344 ),
    inference(avatar_split_clause,[],[f4229,f4190,f436,f46667]) ).

fof(f46667,plain,
    ( spl0_1252
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).

fof(f436,plain,
    ( spl0_49
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f4229,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_49
    | ~ spl0_344 ),
    inference(superposition,[],[f4191,f438]) ).

fof(f438,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f436]) ).

fof(f46481,plain,
    ( spl0_1251
    | ~ spl0_8
    | ~ spl0_236
    | ~ spl0_1062 ),
    inference(avatar_split_clause,[],[f33521,f33336,f2269,f242,f46479]) ).

fof(f242,plain,
    ( spl0_8
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f2269,plain,
    ( spl0_236
  <=> y = complement(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f33336,plain,
    ( spl0_1062
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X1,complement(X0))
        | ~ subclass(complement(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f33521,plain,
    ( ! [X0] : singleton_relation = intersection(X0,y)
    | ~ spl0_8
    | ~ spl0_236
    | ~ spl0_1062 ),
    inference(forward_demodulation,[],[f33516,f2271]) ).

fof(f2271,plain,
    ( y = complement(universal_class)
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f2269]) ).

fof(f33516,plain,
    ( ! [X0] : singleton_relation = intersection(X0,complement(universal_class))
    | ~ spl0_8
    | ~ spl0_1062 ),
    inference(resolution,[],[f33337,f243]) ).

fof(f243,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f242]) ).

fof(f33337,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | singleton_relation = intersection(X1,complement(X0)) )
    | ~ spl0_1062 ),
    inference(avatar_component_clause,[],[f33336]) ).

fof(f46130,plain,
    ( spl0_1250
    | ~ spl0_8
    | ~ spl0_236
    | ~ spl0_1061 ),
    inference(avatar_split_clause,[],[f33511,f33332,f2269,f242,f46128]) ).

fof(f33332,plain,
    ( spl0_1061
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(complement(X0),X1)
        | ~ subclass(complement(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f33511,plain,
    ( ! [X0] : singleton_relation = intersection(y,X0)
    | ~ spl0_8
    | ~ spl0_236
    | ~ spl0_1061 ),
    inference(forward_demodulation,[],[f33506,f2271]) ).

fof(f33506,plain,
    ( ! [X0] : singleton_relation = intersection(complement(universal_class),X0)
    | ~ spl0_8
    | ~ spl0_1061 ),
    inference(resolution,[],[f33333,f243]) ).

fof(f33333,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | singleton_relation = intersection(complement(X0),X1) )
    | ~ spl0_1061 ),
    inference(avatar_component_clause,[],[f33332]) ).

fof(f45899,plain,
    ( ~ spl0_1249
    | spl0_168
    | ~ spl0_248
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f2663,f2454,f2450,f1428,f45896]) ).

fof(f45896,plain,
    ( spl0_1249
  <=> subclass(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).

fof(f2454,plain,
    ( spl0_249
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f2663,plain,
    ( singleton_relation = y
    | ~ subclass(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation)))))
    | ~ spl0_248
    | ~ spl0_249 ),
    inference(resolution,[],[f2451,f2456]) ).

fof(f2456,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_249 ),
    inference(avatar_component_clause,[],[f2454]) ).

fof(f45159,plain,
    ( spl0_412
    | ~ spl0_34
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f44045,f1005,f361,f5648]) ).

fof(f5648,plain,
    ( spl0_412
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f361,plain,
    ( spl0_34
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f44045,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_34
    | ~ spl0_130 ),
    inference(resolution,[],[f1006,f362]) ).

fof(f362,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f361]) ).

fof(f45148,plain,
    ( spl0_168
    | ~ spl0_375
    | spl0_1248
    | ~ spl0_49
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f23050,f1139,f436,f45145,f4993,f1428]) ).

fof(f4993,plain,
    ( spl0_375
  <=> member(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f45145,plain,
    ( spl0_1248
  <=> 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))))))),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).

fof(f1139,plain,
    ( spl0_140
  <=> ! [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)
        | ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f23050,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))))))),complement(compose(element_relation,complement(identity_relation))))
    | ~ member(singleton_relation,universal_class)
    | singleton_relation = y
    | ~ spl0_49
    | ~ spl0_140 ),
    inference(superposition,[],[f1140,f438]) ).

fof(f1140,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)
        | ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1139]) ).

fof(f45074,plain,
    ( spl0_168
    | ~ spl0_1022
    | ~ spl0_1037 ),
    inference(avatar_split_clause,[],[f40087,f32492,f32367,f1428]) ).

fof(f32367,plain,
    ( spl0_1022
  <=> ! [X0,X1] : y = intersection(complement(X0),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f32492,plain,
    ( spl0_1037
  <=> ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f40087,plain,
    ( singleton_relation = y
    | ~ spl0_1022
    | ~ spl0_1037 ),
    inference(forward_demodulation,[],[f32368,f32493]) ).

fof(f32493,plain,
    ( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_1037 ),
    inference(avatar_component_clause,[],[f32492]) ).

fof(f32368,plain,
    ( ! [X0,X1] : y = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_1022 ),
    inference(avatar_component_clause,[],[f32367]) ).

fof(f45066,plain,
    ( spl0_168
    | ~ spl0_1021
    | ~ spl0_1036 ),
    inference(avatar_split_clause,[],[f40088,f32486,f32362,f1428]) ).

fof(f32362,plain,
    ( spl0_1021
  <=> ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f32486,plain,
    ( spl0_1036
  <=> ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f40088,plain,
    ( singleton_relation = y
    | ~ spl0_1021
    | ~ spl0_1036 ),
    inference(forward_demodulation,[],[f32363,f32487]) ).

fof(f32487,plain,
    ( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_1036 ),
    inference(avatar_component_clause,[],[f32486]) ).

fof(f32363,plain,
    ( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_1021 ),
    inference(avatar_component_clause,[],[f32362]) ).

fof(f45033,plain,
    ( spl0_168
    | ~ spl0_343
    | ~ spl0_1023
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f45000,f33180,f32372,f4186,f1428]) ).

fof(f32372,plain,
    ( spl0_1023
  <=> ! [X0,X1] : y = intersection(complement(X0),intersection(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f33180,plain,
    ( spl0_1048
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(complement(X1),X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f45000,plain,
    ( singleton_relation = y
    | ~ spl0_343
    | ~ spl0_1023
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f32373,f33233]) ).

fof(f33233,plain,
    ( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_343
    | ~ spl0_1048 ),
    inference(resolution,[],[f33181,f4187]) ).

fof(f33181,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | singleton_relation = intersection(complement(X1),X0) )
    | ~ spl0_1048 ),
    inference(avatar_component_clause,[],[f33180]) ).

fof(f32373,plain,
    ( ! [X0,X1] : y = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_1023 ),
    inference(avatar_component_clause,[],[f32372]) ).

fof(f44999,plain,
    ( spl0_168
    | ~ spl0_344
    | ~ spl0_1020
    | ~ spl0_1047 ),
    inference(avatar_split_clause,[],[f44964,f33176,f32357,f4190,f1428]) ).

fof(f32357,plain,
    ( spl0_1020
  <=> ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f33176,plain,
    ( spl0_1047
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X0,complement(X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f44964,plain,
    ( singleton_relation = y
    | ~ spl0_344
    | ~ spl0_1020
    | ~ spl0_1047 ),
    inference(forward_demodulation,[],[f32358,f33194]) ).

fof(f33194,plain,
    ( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_344
    | ~ spl0_1047 ),
    inference(resolution,[],[f33177,f4191]) ).

fof(f33177,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | singleton_relation = intersection(X0,complement(X1)) )
    | ~ spl0_1047 ),
    inference(avatar_component_clause,[],[f33176]) ).

fof(f32358,plain,
    ( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_1020 ),
    inference(avatar_component_clause,[],[f32357]) ).

fof(f44947,plain,
    ( spl0_168
    | ~ spl0_1023
    | ~ spl0_1038 ),
    inference(avatar_split_clause,[],[f40086,f32496,f32372,f1428]) ).

fof(f32496,plain,
    ( spl0_1038
  <=> ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f40086,plain,
    ( singleton_relation = y
    | ~ spl0_1023
    | ~ spl0_1038 ),
    inference(forward_demodulation,[],[f32373,f32497]) ).

fof(f32497,plain,
    ( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_1038 ),
    inference(avatar_component_clause,[],[f32496]) ).

fof(f44528,plain,
    ( spl0_168
    | ~ spl0_1020
    | ~ spl0_1035 ),
    inference(avatar_split_clause,[],[f40089,f32482,f32357,f1428]) ).

fof(f32482,plain,
    ( spl0_1035
  <=> ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f40089,plain,
    ( singleton_relation = y
    | ~ spl0_1020
    | ~ spl0_1035 ),
    inference(forward_demodulation,[],[f32358,f32483]) ).

fof(f32483,plain,
    ( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_1035 ),
    inference(avatar_component_clause,[],[f32482]) ).

fof(f44360,plain,
    ( spl0_1247
    | ~ spl0_939
    | ~ spl0_1217 ),
    inference(avatar_split_clause,[],[f41265,f37756,f28126,f44358]) ).

fof(f44358,plain,
    ( spl0_1247
  <=> ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).

fof(f28126,plain,
    ( spl0_939
  <=> ! [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(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f41265,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = y )
    | ~ spl0_939
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f28127,f37757]) ).

fof(f28127,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(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = y )
    | ~ spl0_939 ),
    inference(avatar_component_clause,[],[f28126]) ).

fof(f44331,plain,
    ( spl0_551
    | ~ spl0_116
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f42269,f1746,f912,f8860]) ).

fof(f8860,plain,
    ( spl0_551
  <=> ! [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)
        | y = 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_551])]) ).

fof(f912,plain,
    ( spl0_116
  <=> ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1746,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

fof(f42269,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)
        | y = 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_116
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f913]) ).

fof(f913,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f912]) ).

fof(f1747,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_196 ),
    inference(avatar_component_clause,[],[f1746]) ).

fof(f44127,plain,
    ( spl0_439
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f42273,f1746,f888,f5872]) ).

fof(f5872,plain,
    ( spl0_439
  <=> ! [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)))),y)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f888,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( member(X1,y)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f42273,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)))),y)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | y = X1 )
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f889]) ).

fof(f889,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,y)
        | ~ member(X1,X0)
        | y = X0 )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f888]) ).

fof(f44121,plain,
    ( spl0_339
    | ~ spl0_31
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f42047,f953,f342,f4092]) ).

fof(f4092,plain,
    ( spl0_339
  <=> ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ function(domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f953,plain,
    ( spl0_119
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X0),X1)
        | member(X2,X1)
        | ~ member(X2,universal_class)
        | y = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f42047,plain,
    ( ! [X0,X1] :
        ( ~ function(domain_of(X0))
        | member(X1,cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | y = intersection(cross_product(unordered_pair(X1,X1),universal_class),X0) )
    | ~ spl0_31
    | ~ spl0_119 ),
    inference(resolution,[],[f343,f954]) ).

fof(f954,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X0),X1)
        | member(X2,X1)
        | ~ member(X2,universal_class)
        | y = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f953]) ).

fof(f42667,plain,
    ( spl0_1001
    | ~ spl0_343
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f37130,f36096,f4186,f31968]) ).

fof(f36096,plain,
    ( spl0_1184
  <=> ! [X0] : singleton_relation = intersection(X0,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f37130,plain,
    ( ! [X0] : subclass(singleton_relation,X0)
    | ~ spl0_343
    | ~ spl0_1184 ),
    inference(superposition,[],[f4187,f36097]) ).

fof(f36097,plain,
    ( ! [X0] : singleton_relation = intersection(X0,singleton_relation)
    | ~ spl0_1184 ),
    inference(avatar_component_clause,[],[f36096]) ).

fof(f42531,plain,
    ( spl0_1246
    | ~ spl0_531
    | ~ spl0_551
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f41865,f36096,f8860,f8328,f42529]) ).

fof(f42529,plain,
    ( spl0_1246
  <=> ! [X0,X1] :
        ( singleton_relation = 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)
        | ~ 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))))
        | ~ function(X0)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f8328,plain,
    ( spl0_531
  <=> ! [X0] : y = intersection(y,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f41865,plain,
    ( ! [X0,X1] :
        ( singleton_relation = 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)
        | ~ 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))))
        | ~ function(X0)
        | ~ member(X1,universal_class) )
    | ~ spl0_531
    | ~ spl0_551
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f8861,f37352]) ).

fof(f37352,plain,
    ( singleton_relation = y
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(superposition,[],[f8329,f36097]) ).

fof(f8329,plain,
    ( ! [X0] : y = intersection(y,X0)
    | ~ spl0_531 ),
    inference(avatar_component_clause,[],[f8328]) ).

fof(f8861,plain,
    ( ! [X0,X1] :
        ( ~ 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))))
        | ~ function(X0)
        | ~ member(X1,universal_class)
        | y = 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_551 ),
    inference(avatar_component_clause,[],[f8860]) ).

fof(f42337,plain,
    ( spl0_1001
    | ~ spl0_344
    | ~ spl0_1183 ),
    inference(avatar_split_clause,[],[f36784,f35368,f4190,f31968]) ).

fof(f35368,plain,
    ( spl0_1183
  <=> ! [X0] : singleton_relation = intersection(singleton_relation,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f36784,plain,
    ( ! [X0] : subclass(singleton_relation,X0)
    | ~ spl0_344
    | ~ spl0_1183 ),
    inference(superposition,[],[f4191,f35369]) ).

fof(f35369,plain,
    ( ! [X0] : singleton_relation = intersection(singleton_relation,X0)
    | ~ spl0_1183 ),
    inference(avatar_component_clause,[],[f35368]) ).

fof(f42336,plain,
    ( spl0_1245
    | ~ spl0_439
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f41823,f36096,f8328,f5872,f42334]) ).

fof(f42334,plain,
    ( spl0_1245
  <=> ! [X2,X0,X1] :
        ( singleton_relation = X1
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f41823,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = X1
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | ~ function(X0) )
    | ~ spl0_439
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f41822,f37352]) ).

fof(f41822,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | ~ function(X0)
        | y = X1 )
    | ~ spl0_439
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f5873,f37352]) ).

fof(f5873,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | ~ 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)))),y)
        | ~ function(X0)
        | y = X1 )
    | ~ spl0_439 ),
    inference(avatar_component_clause,[],[f5872]) ).

fof(f42324,plain,
    ( spl0_1244
    | ~ spl0_339
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f41989,f36096,f8328,f4092,f42322]) ).

fof(f42322,plain,
    ( spl0_1244
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ function(domain_of(X1))
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).

fof(f41989,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ function(domain_of(X1))
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_339
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f4093,f37352]) ).

fof(f4093,plain,
    ( ! [X0,X1] :
        ( ~ function(domain_of(X1))
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_339 ),
    inference(avatar_component_clause,[],[f4092]) ).

fof(f42137,plain,
    ( spl0_1243
    | ~ spl0_122
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f41996,f36096,f8328,f970,f42135]) ).

fof(f42135,plain,
    ( spl0_1243
  <=> ! [X0] :
        ( singleton_relation = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).

fof(f970,plain,
    ( spl0_122
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | y = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f41996,plain,
    ( ! [X0] :
        ( singleton_relation = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | ~ member(X0,universal_class) )
    | ~ spl0_122
    | ~ spl0_531
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f971,f37352]) ).

fof(f971,plain,
    ( ! [X0] :
        ( ~ function(regular(cross_product(X0,universal_class)))
        | y = cross_product(X0,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f970]) ).

fof(f41806,plain,
    ( ~ spl0_6
    | ~ spl0_1241 ),
    inference(avatar_contradiction_clause,[],[f41804]) ).

fof(f41804,plain,
    ( $false
    | ~ spl0_6
    | ~ spl0_1241 ),
    inference(resolution,[],[f41799,f235]) ).

fof(f235,plain,
    ( function(choice)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f233,plain,
    ( spl0_6
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f41799,plain,
    ( ! [X1] : ~ function(X1)
    | ~ spl0_1241 ),
    inference(avatar_component_clause,[],[f41798]) ).

fof(f41798,plain,
    ( spl0_1241
  <=> ! [X1] : ~ function(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f41803,plain,
    ( spl0_1241
    | spl0_1242
    | ~ spl0_375
    | ~ spl0_675
    | ~ spl0_1183
    | ~ spl0_1217 ),
    inference(avatar_split_clause,[],[f41669,f37756,f35368,f13560,f4993,f41801,f41798]) ).

fof(f41801,plain,
    ( spl0_1242
  <=> ! [X2,X0] :
        ( member(domain_of(domain_of(flip(singleton_relation))),X2)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).

fof(f13560,plain,
    ( spl0_675
  <=> ! [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_675])]) ).

fof(f41669,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(singleton_relation))),X2)
        | ~ subclass(universal_class,X0)
        | ~ function(X1)
        | ~ subclass(X0,X2) )
    | ~ spl0_375
    | ~ spl0_675
    | ~ spl0_1183
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41668,f37757]) ).

fof(f41668,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),X2)
        | ~ subclass(universal_class,X0)
        | ~ function(X1)
        | ~ subclass(X0,X2) )
    | ~ spl0_375
    | ~ spl0_675
    | ~ spl0_1183
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41667,f35369]) ).

fof(f41667,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(singleton_relation,X1),universal_class)))),X2)
        | ~ subclass(universal_class,X0)
        | ~ function(X1)
        | ~ subclass(X0,X2) )
    | ~ spl0_375
    | ~ spl0_675
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f29535,f37757]) ).

fof(f29535,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ function(X1)
        | ~ subclass(X0,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(singleton_relation,universal_class),X1),universal_class)))),X2) )
    | ~ spl0_375
    | ~ spl0_675 ),
    inference(resolution,[],[f4994,f13561]) ).

fof(f13561,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,universal_class)
        | ~ subclass(universal_class,X1)
        | ~ function(X0)
        | ~ subclass(X1,X3)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
    | ~ spl0_675 ),
    inference(avatar_component_clause,[],[f13560]) ).

fof(f4994,plain,
    ( member(singleton_relation,universal_class)
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f4993]) ).

fof(f41796,plain,
    ( spl0_1240
    | ~ spl0_531
    | ~ spl0_1145
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f39160,f36096,f35129,f8328,f41794]) ).

fof(f41794,plain,
    ( spl0_1240
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(X0,singleton_relation)
        | member(regular(intersection(X0,X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f39160,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(X0,singleton_relation)
        | member(regular(intersection(X0,X1)),element_relation) )
    | ~ spl0_531
    | ~ spl0_1145
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f35130,f37352]) ).

fof(f35130,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),element_relation)
        | intersection(X0,X1) = y
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_1145 ),
    inference(avatar_component_clause,[],[f35129]) ).

fof(f41776,plain,
    ( spl0_375
    | ~ spl0_8
    | ~ spl0_1011 ),
    inference(avatar_split_clause,[],[f32254,f32249,f242,f4993]) ).

fof(f32249,plain,
    ( spl0_1011
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f32254,plain,
    ( member(singleton_relation,universal_class)
    | ~ spl0_8
    | ~ spl0_1011 ),
    inference(resolution,[],[f32250,f243]) ).

fof(f32250,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(singleton_relation,X0) )
    | ~ spl0_1011 ),
    inference(avatar_component_clause,[],[f32249]) ).

fof(f41775,plain,
    ( spl0_1239
    | ~ spl0_531
    | ~ spl0_1149
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f39157,f36096,f35149,f8328,f41773]) ).

fof(f41773,plain,
    ( spl0_1239
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X1,X0)
        | ~ subclass(X0,singleton_relation)
        | member(regular(intersection(X1,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f39157,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X1,X0)
        | ~ subclass(X0,singleton_relation)
        | member(regular(intersection(X1,X0)),element_relation) )
    | ~ spl0_531
    | ~ spl0_1149
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f35150,f37352]) ).

fof(f35150,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X1,X0)),element_relation)
        | y = intersection(X1,X0)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_1149 ),
    inference(avatar_component_clause,[],[f35149]) ).

fof(f41726,plain,
    ( spl0_1238
    | ~ spl0_531
    | ~ spl0_1094
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f39656,f36096,f33921,f8328,f41724]) ).

fof(f41724,plain,
    ( spl0_1238
  <=> ! [X0] :
        ( singleton_relation = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f33921,plain,
    ( spl0_1094
  <=> ! [X0] :
        ( y = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f39656,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_531
    | ~ spl0_1094
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f33922,f37352]) ).

fof(f33922,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(complement(element_relation),X0),singleton_relation)
        | y = intersection(complement(element_relation),X0) )
    | ~ spl0_1094 ),
    inference(avatar_component_clause,[],[f33921]) ).

fof(f41722,plain,
    ( spl0_1237
    | ~ spl0_531
    | ~ spl0_1097
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f39653,f36096,f33936,f8328,f41720]) ).

fof(f41720,plain,
    ( spl0_1237
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f33936,plain,
    ( spl0_1097
  <=> ! [X0] :
        ( y = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f39653,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_531
    | ~ spl0_1097
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f33937,f37352]) ).

fof(f33937,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(X0,complement(element_relation)),singleton_relation)
        | y = intersection(X0,complement(element_relation)) )
    | ~ spl0_1097 ),
    inference(avatar_component_clause,[],[f33936]) ).

fof(f41704,plain,
    ( spl0_1236
    | ~ spl0_531
    | ~ spl0_1050
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f39822,f36096,f33271,f8328,f41702]) ).

fof(f41702,plain,
    ( spl0_1236
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f33271,plain,
    ( spl0_1050
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f39822,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_531
    | ~ spl0_1050
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f33272,f37352]) ).

fof(f33272,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(element_relation))
        | y = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_1050 ),
    inference(avatar_component_clause,[],[f33271]) ).

fof(f41665,plain,
    ( ~ spl0_22
    | spl0_375
    | ~ spl0_1006 ),
    inference(avatar_split_clause,[],[f41444,f32159,f4993,f305]) ).

fof(f305,plain,
    ( spl0_22
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f32159,plain,
    ( spl0_1006
  <=> ! [X0] :
        ( member(singleton_relation,X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f41444,plain,
    ( ~ inductive(universal_class)
    | spl0_375
    | ~ spl0_1006 ),
    inference(resolution,[],[f4995,f32160]) ).

fof(f32160,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ inductive(X0) )
    | ~ spl0_1006 ),
    inference(avatar_component_clause,[],[f32159]) ).

fof(f4995,plain,
    ( ~ member(singleton_relation,universal_class)
    | spl0_375 ),
    inference(avatar_component_clause,[],[f4993]) ).

fof(f41495,plain,
    ( ~ spl0_928
    | ~ spl0_1056 ),
    inference(avatar_contradiction_clause,[],[f41491]) ).

fof(f41491,plain,
    ( $false
    | ~ spl0_928
    | ~ spl0_1056 ),
    inference(resolution,[],[f27611,f33302]) ).

fof(f33302,plain,
    ( ! [X0] : ~ member(X0,singleton_relation)
    | ~ spl0_1056 ),
    inference(avatar_component_clause,[],[f33301]) ).

fof(f33301,plain,
    ( spl0_1056
  <=> ! [X0] : ~ member(X0,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f27611,plain,
    ( member(regular(singleton_relation),singleton_relation)
    | ~ spl0_928 ),
    inference(avatar_component_clause,[],[f27609]) ).

fof(f27609,plain,
    ( spl0_928
  <=> member(regular(singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f41468,plain,
    ( spl0_1235
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(avatar_split_clause,[],[f41108,f37756,f36096,f29875,f8328,f41466]) ).

fof(f41466,plain,
    ( spl0_1235
  <=> ! [X0,X3,X2,X1] :
        ( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f29875,plain,
    ( spl0_952
  <=> ! [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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f41108,plain,
    ( ! [X2,X3,X0,X1] :
        ( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41107,f37352]) ).

fof(f41107,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41106,f37757]) ).

fof(f41106,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41105,f37352]) ).

fof(f41105,plain,
    ( ! [X2,X3,X0,X1] :
        ( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41104,f37757]) ).

fof(f41104,plain,
    ( ! [X2,X3,X0,X1] :
        ( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41103,f37352]) ).

fof(f41103,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41102,f37757]) ).

fof(f41102,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41101,f37352]) ).

fof(f41101,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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41100,f37757]) ).

fof(f41100,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41099,f37352]) ).

fof(f41099,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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41098,f37757]) ).

fof(f41098,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_531
    | ~ spl0_952
    | ~ spl0_1184 ),
    inference(forward_demodulation,[],[f29876,f37352]) ).

fof(f29876,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_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(domain_of(domain_of(flip(cross_product(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_952 ),
    inference(avatar_component_clause,[],[f29875]) ).

fof(f41453,plain,
    ( spl0_1234
    | ~ spl0_531
    | ~ spl0_939
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(avatar_split_clause,[],[f41266,f37756,f36096,f28126,f8328,f41451]) ).

fof(f41451,plain,
    ( spl0_1234
  <=> ! [X2,X0,X1] :
        ( cross_product(X0,X1) = singleton_relation
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f41266,plain,
    ( ! [X2,X0,X1] :
        ( cross_product(X0,X1) = singleton_relation
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
        | member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class)) )
    | ~ spl0_531
    | ~ spl0_939
    | ~ spl0_1184
    | ~ spl0_1217 ),
    inference(forward_demodulation,[],[f41265,f37352]) ).

fof(f38122,plain,
    ( ~ spl0_1098
    | spl0_1017
    | ~ spl0_1184
    | ~ spl0_1208 ),
    inference(avatar_split_clause,[],[f37919,f37673,f36096,f32287,f33941]) ).

fof(f33941,plain,
    ( spl0_1098
  <=> singleton_relation = domain_of(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f32287,plain,
    ( spl0_1017
  <=> singleton_relation = domain_of(intersection(x,cross_product(singleton_relation,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f37673,plain,
    ( spl0_1208
  <=> ! [X0] : singleton_relation = cross_product(X0,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).

fof(f37919,plain,
    ( singleton_relation != domain_of(singleton_relation)
    | spl0_1017
    | ~ spl0_1184
    | ~ spl0_1208 ),
    inference(forward_demodulation,[],[f37877,f36097]) ).

fof(f37877,plain,
    ( singleton_relation != domain_of(intersection(x,singleton_relation))
    | spl0_1017
    | ~ spl0_1208 ),
    inference(superposition,[],[f32289,f37674]) ).

fof(f37674,plain,
    ( ! [X0] : singleton_relation = cross_product(X0,singleton_relation)
    | ~ spl0_1208 ),
    inference(avatar_component_clause,[],[f37673]) ).

fof(f32289,plain,
    ( singleton_relation != domain_of(intersection(x,cross_product(singleton_relation,singleton_relation)))
    | spl0_1017 ),
    inference(avatar_component_clause,[],[f32287]) ).

fof(f37943,plain,
    ( spl0_1233
    | ~ spl0_168
    | ~ spl0_1212 ),
    inference(avatar_split_clause,[],[f37736,f37732,f1428,f37941]) ).

fof(f37941,plain,
    ( spl0_1233
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f37732,plain,
    ( spl0_1212
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),y)
        | ~ subclass(X0,regular(X0))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f37736,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,regular(X0)) )
    | ~ spl0_168
    | ~ spl0_1212 ),
    inference(forward_demodulation,[],[f37735,f1430]) ).

fof(f1430,plain,
    ( singleton_relation = y
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1428]) ).

fof(f37735,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,regular(X0))
        | y = X0 )
    | ~ spl0_168
    | ~ spl0_1212 ),
    inference(forward_demodulation,[],[f37733,f1430]) ).

fof(f37733,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,regular(X0))
        | member(not_subclass_element(X0,X1),y)
        | subclass(X0,X1)
        | y = X0 )
    | ~ spl0_1212 ),
    inference(avatar_component_clause,[],[f37732]) ).

fof(f37939,plain,
    ( spl0_1232
    | ~ spl0_168
    | ~ spl0_1211 ),
    inference(avatar_split_clause,[],[f37730,f37725,f1428,f37937]) ).

fof(f37937,plain,
    ( spl0_1232
  <=> ! [X0,X1] :
        ( singleton_relation = X1
        | subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),X1)
        | ~ subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f37725,plain,
    ( spl0_1211
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,y),X1)
        | subclass(X0,y)
        | y = X1
        | ~ subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f37730,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X1
        | subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),X1)
        | ~ subclass(X0,regular(X1)) )
    | ~ spl0_168
    | ~ spl0_1211 ),
    inference(forward_demodulation,[],[f37729,f1430]) ).

fof(f37729,plain,
    ( ! [X0,X1] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),X1)
        | y = X1
        | ~ subclass(X0,regular(X1)) )
    | ~ spl0_168
    | ~ spl0_1211 ),
    inference(forward_demodulation,[],[f37728,f1430]) ).

fof(f37728,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,singleton_relation),X1)
        | subclass(X0,y)
        | y = X1
        | ~ subclass(X0,regular(X1)) )
    | ~ spl0_168
    | ~ spl0_1211 ),
    inference(forward_demodulation,[],[f37726,f1430]) ).

fof(f37726,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,y),X1)
        | subclass(X0,y)
        | y = X1
        | ~ subclass(X0,regular(X1)) )
    | ~ spl0_1211 ),
    inference(avatar_component_clause,[],[f37725]) ).

fof(f37935,plain,
    ( spl0_1231
    | ~ spl0_168
    | ~ spl0_1206 ),
    inference(avatar_split_clause,[],[f37667,f37664,f1428,f37933]) ).

fof(f37933,plain,
    ( spl0_1231
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f37664,plain,
    ( spl0_1206
  <=> ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).

fof(f37667,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_168
    | ~ spl0_1206 ),
    inference(forward_demodulation,[],[f37665,f1430]) ).

fof(f37665,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1))
        | y = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_1206 ),
    inference(avatar_component_clause,[],[f37664]) ).

fof(f37931,plain,
    ( spl0_1230
    | ~ spl0_168
    | ~ spl0_1205 ),
    inference(avatar_split_clause,[],[f37662,f37659,f1428,f37929]) ).

fof(f37929,plain,
    ( spl0_1230
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f37659,plain,
    ( spl0_1205
  <=> ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = intersection(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).

fof(f37662,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_168
    | ~ spl0_1205 ),
    inference(forward_demodulation,[],[f37660,f1430]) ).

fof(f37660,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = intersection(X0,identity_relation) )
    | ~ spl0_1205 ),
    inference(avatar_component_clause,[],[f37659]) ).

fof(f37927,plain,
    ( spl0_1229
    | ~ spl0_168
    | ~ spl0_1202 ),
    inference(avatar_split_clause,[],[f37646,f37643,f1428,f37925]) ).

fof(f37925,plain,
    ( spl0_1229
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X0,intersection(identity_relation,X1))
        | member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f37643,plain,
    ( spl0_1202
  <=> ! [X0,X1] :
        ( y = intersection(X0,intersection(identity_relation,X1))
        | member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).

fof(f37646,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X0,intersection(identity_relation,X1))
        | member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1202 ),
    inference(forward_demodulation,[],[f37644,f1430]) ).

fof(f37644,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation)
        | y = intersection(X0,intersection(identity_relation,X1)) )
    | ~ spl0_1202 ),
    inference(avatar_component_clause,[],[f37643]) ).

fof(f37923,plain,
    ( spl0_1228
    | ~ spl0_168
    | ~ spl0_1201 ),
    inference(avatar_split_clause,[],[f37641,f37638,f1428,f37921]) ).

fof(f37921,plain,
    ( spl0_1228
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f37638,plain,
    ( spl0_1201
  <=> ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).

fof(f37641,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_168
    | ~ spl0_1201 ),
    inference(forward_demodulation,[],[f37639,f1430]) ).

fof(f37639,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2))
        | y = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_1201 ),
    inference(avatar_component_clause,[],[f37638]) ).

fof(f37798,plain,
    ( spl0_1227
    | ~ spl0_168
    | ~ spl0_1199 ),
    inference(avatar_split_clause,[],[f37630,f37627,f1428,f37796]) ).

fof(f37796,plain,
    ( spl0_1227
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X0,intersection(X1,identity_relation))
        | member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f37627,plain,
    ( spl0_1199
  <=> ! [X0,X1] :
        ( y = intersection(X0,intersection(X1,identity_relation))
        | member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f37630,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X0,intersection(X1,identity_relation))
        | member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1199 ),
    inference(forward_demodulation,[],[f37628,f1430]) ).

fof(f37628,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation)
        | y = intersection(X0,intersection(X1,identity_relation)) )
    | ~ spl0_1199 ),
    inference(avatar_component_clause,[],[f37627]) ).

fof(f37794,plain,
    ( spl0_1226
    | ~ spl0_168
    | ~ spl0_1198 ),
    inference(avatar_split_clause,[],[f37625,f37622,f1428,f37792]) ).

fof(f37792,plain,
    ( spl0_1226
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f37622,plain,
    ( spl0_1198
  <=> ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f37625,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_168
    | ~ spl0_1198 ),
    inference(forward_demodulation,[],[f37623,f1430]) ).

fof(f37623,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(intersection(intersection(X0,X1),X2),complement(X0))
        | y = intersection(intersection(X0,X1),X2) )
    | ~ spl0_1198 ),
    inference(avatar_component_clause,[],[f37622]) ).

fof(f37790,plain,
    ( spl0_1225
    | ~ spl0_168
    | ~ spl0_1197 ),
    inference(avatar_split_clause,[],[f37098,f37095,f1428,f37788]) ).

fof(f37788,plain,
    ( spl0_1225
  <=> ! [X0] :
        ( singleton_relation = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f37095,plain,
    ( spl0_1197
  <=> ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = intersection(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f37098,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_168
    | ~ spl0_1197 ),
    inference(forward_demodulation,[],[f37096,f1430]) ).

fof(f37096,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = intersection(identity_relation,X0) )
    | ~ spl0_1197 ),
    inference(avatar_component_clause,[],[f37095]) ).

fof(f37786,plain,
    ( spl0_1224
    | ~ spl0_168
    | ~ spl0_1194 ),
    inference(avatar_split_clause,[],[f37082,f37079,f1428,f37784]) ).

fof(f37784,plain,
    ( spl0_1224
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(intersection(identity_relation,X0),X1)
        | member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f37079,plain,
    ( spl0_1194
  <=> ! [X0,X1] :
        ( y = intersection(intersection(identity_relation,X0),X1)
        | member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f37082,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(intersection(identity_relation,X0),X1)
        | member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1194 ),
    inference(forward_demodulation,[],[f37080,f1430]) ).

fof(f37080,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation)
        | y = intersection(intersection(identity_relation,X0),X1) )
    | ~ spl0_1194 ),
    inference(avatar_component_clause,[],[f37079]) ).

fof(f37782,plain,
    ( spl0_1223
    | ~ spl0_168
    | ~ spl0_1193 ),
    inference(avatar_split_clause,[],[f37077,f37074,f1428,f37780]) ).

fof(f37780,plain,
    ( spl0_1223
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f37074,plain,
    ( spl0_1193
  <=> ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f37077,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_168
    | ~ spl0_1193 ),
    inference(forward_demodulation,[],[f37075,f1430]) ).

fof(f37075,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(intersection(intersection(X0,X1),X2),complement(X1))
        | y = intersection(intersection(X0,X1),X2) )
    | ~ spl0_1193 ),
    inference(avatar_component_clause,[],[f37074]) ).

fof(f37778,plain,
    ( spl0_1222
    | ~ spl0_168
    | ~ spl0_1191 ),
    inference(avatar_split_clause,[],[f37066,f37063,f1428,f37776]) ).

fof(f37776,plain,
    ( spl0_1222
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(intersection(X0,identity_relation),X1)
        | member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f37063,plain,
    ( spl0_1191
  <=> ! [X0,X1] :
        ( y = intersection(intersection(X0,identity_relation),X1)
        | member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f37066,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(intersection(X0,identity_relation),X1)
        | member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1191 ),
    inference(forward_demodulation,[],[f37064,f1430]) ).

fof(f37064,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation)
        | y = intersection(intersection(X0,identity_relation),X1) )
    | ~ spl0_1191 ),
    inference(avatar_component_clause,[],[f37063]) ).

fof(f37774,plain,
    ( spl0_1221
    | ~ spl0_168
    | ~ spl0_1190 ),
    inference(avatar_split_clause,[],[f37061,f37058,f1428,f37772]) ).

fof(f37772,plain,
    ( spl0_1221
  <=> ! [X2,X0,X1] :
        ( singleton_relation = cross_product(X1,X2)
        | ~ subclass(universal_class,complement(X0))
        | ~ member(regular(cross_product(X1,X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f37058,plain,
    ( spl0_1190
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | y = cross_product(X1,X2)
        | ~ member(regular(cross_product(X1,X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f37061,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = cross_product(X1,X2)
        | ~ subclass(universal_class,complement(X0))
        | ~ member(regular(cross_product(X1,X2)),X0) )
    | ~ spl0_168
    | ~ spl0_1190 ),
    inference(forward_demodulation,[],[f37059,f1430]) ).

fof(f37059,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X1,X2)),X0)
        | y = cross_product(X1,X2)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_1190 ),
    inference(avatar_component_clause,[],[f37058]) ).

fof(f37770,plain,
    ( spl0_1220
    | ~ spl0_168
    | ~ spl0_1189 ),
    inference(avatar_split_clause,[],[f37056,f37053,f1428,f37768]) ).

fof(f37768,plain,
    ( spl0_1220
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(X2,X0)
        | ~ subclass(X0,complement(X1))
        | ~ member(regular(intersection(X2,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f37053,plain,
    ( spl0_1189
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = intersection(X2,X0)
        | ~ member(regular(intersection(X2,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f37056,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(X2,X0)
        | ~ subclass(X0,complement(X1))
        | ~ member(regular(intersection(X2,X0)),X1) )
    | ~ spl0_168
    | ~ spl0_1189 ),
    inference(forward_demodulation,[],[f37054,f1430]) ).

fof(f37054,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(intersection(X2,X0)),X1)
        | y = intersection(X2,X0)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_1189 ),
    inference(avatar_component_clause,[],[f37053]) ).

fof(f37766,plain,
    ( spl0_1219
    | ~ spl0_168
    | ~ spl0_1188 ),
    inference(avatar_split_clause,[],[f37051,f37048,f1428,f37764]) ).

fof(f37764,plain,
    ( spl0_1219
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,X2)
        | ~ subclass(X0,complement(X1))
        | ~ member(regular(intersection(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f37048,plain,
    ( spl0_1188
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = intersection(X0,X2)
        | ~ member(regular(intersection(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f37051,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,X2)
        | ~ subclass(X0,complement(X1))
        | ~ member(regular(intersection(X0,X2)),X1) )
    | ~ spl0_168
    | ~ spl0_1188 ),
    inference(forward_demodulation,[],[f37049,f1430]) ).

fof(f37049,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(intersection(X0,X2)),X1)
        | y = intersection(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_1188 ),
    inference(avatar_component_clause,[],[f37048]) ).

fof(f37762,plain,
    ( spl0_1218
    | ~ spl0_168
    | ~ spl0_1187 ),
    inference(avatar_split_clause,[],[f36752,f36749,f1428,f37760]) ).

fof(f37760,plain,
    ( spl0_1218
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,flip(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f36749,plain,
    ( spl0_1187
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,flip(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f36752,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,flip(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_168
    | ~ spl0_1187 ),
    inference(forward_demodulation,[],[f36750,f1430]) ).

fof(f36750,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,flip(X1))
        | y = X0
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_1187 ),
    inference(avatar_component_clause,[],[f36749]) ).

fof(f37758,plain,
    ( spl0_1217
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1116 ),
    inference(avatar_split_clause,[],[f34601,f34034,f9421,f8731,f1428,f37756]) ).

fof(f34601,plain,
    ( ! [X0] : singleton_relation = cross_product(singleton_relation,X0)
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1116 ),
    inference(forward_demodulation,[],[f34600,f1430]) ).

fof(f34600,plain,
    ( ! [X0] : singleton_relation = cross_product(y,X0)
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1116 ),
    inference(forward_demodulation,[],[f34576,f9423]) ).

fof(f34576,plain,
    ( ! [X0] : singleton_relation = cross_product(domain_of(y),X0)
    | ~ spl0_550
    | ~ spl0_1116 ),
    inference(resolution,[],[f34035,f8732]) ).

fof(f37754,plain,
    ( spl0_1216
    | ~ spl0_168
    | ~ spl0_1186 ),
    inference(avatar_split_clause,[],[f36747,f36744,f1428,f37752]) ).

fof(f37752,plain,
    ( spl0_1216
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,rotate(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f36744,plain,
    ( spl0_1186
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,rotate(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f36747,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,rotate(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_168
    | ~ spl0_1186 ),
    inference(forward_demodulation,[],[f36745,f1430]) ).

fof(f36745,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,rotate(X1))
        | y = X0
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_1186 ),
    inference(avatar_component_clause,[],[f36744]) ).

fof(f37750,plain,
    ( spl0_1215
    | ~ spl0_168
    | ~ spl0_1185 ),
    inference(avatar_split_clause,[],[f36742,f36739,f1428,f37748]) ).

fof(f37748,plain,
    ( spl0_1215
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(regular(X0),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f36739,plain,
    ( spl0_1185
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(regular(X0),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f36742,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(regular(X0),identity_relation) )
    | ~ spl0_168
    | ~ spl0_1185 ),
    inference(forward_demodulation,[],[f36740,f1430]) ).

fof(f36740,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | y = X0
        | ~ member(regular(X0),identity_relation) )
    | ~ spl0_1185 ),
    inference(avatar_component_clause,[],[f36739]) ).

fof(f37745,plain,
    ( spl0_1214
    | ~ spl0_16
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f8214,f8088,f278,f37743]) ).

fof(f37743,plain,
    ( spl0_1214
  <=> ! [X2,X0,X1] :
        ( member(regular(intersection(X0,cross_product(X1,X2))),universal_class)
        | y = intersection(X0,cross_product(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f278,plain,
    ( spl0_16
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f8088,plain,
    ( spl0_523
  <=> ! [X2,X0,X1] :
        ( y = 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_523])]) ).

fof(f8214,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,cross_product(X1,X2))),universal_class)
        | y = intersection(X0,cross_product(X1,X2)) )
    | ~ spl0_16
    | ~ spl0_523 ),
    inference(superposition,[],[f279,f8089]) ).

fof(f8089,plain,
    ( ! [X2,X0,X1] :
        ( 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)))))))
        | y = intersection(X0,cross_product(X1,X2)) )
    | ~ spl0_523 ),
    inference(avatar_component_clause,[],[f8088]) ).

fof(f279,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f278]) ).

fof(f37740,plain,
    ( spl0_1213
    | ~ spl0_16
    | ~ spl0_522 ),
    inference(avatar_split_clause,[],[f8145,f8084,f278,f37738]) ).

fof(f37738,plain,
    ( spl0_1213
  <=> ! [X2,X0,X1] :
        ( member(regular(intersection(cross_product(X0,X1),X2)),universal_class)
        | y = intersection(cross_product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f8084,plain,
    ( spl0_522
  <=> ! [X2,X0,X1] :
        ( y = 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_522])]) ).

fof(f8145,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(cross_product(X0,X1),X2)),universal_class)
        | y = intersection(cross_product(X0,X1),X2) )
    | ~ spl0_16
    | ~ spl0_522 ),
    inference(superposition,[],[f279,f8085]) ).

fof(f8085,plain,
    ( ! [X2,X0,X1] :
        ( 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))))))
        | y = intersection(cross_product(X0,X1),X2) )
    | ~ spl0_522 ),
    inference(avatar_component_clause,[],[f8084]) ).

fof(f37734,plain,
    ( spl0_1212
    | ~ spl0_34
    | ~ spl0_342 ),
    inference(avatar_split_clause,[],[f4184,f4104,f361,f37732]) ).

fof(f4104,plain,
    ( spl0_342
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,regular(X1))
        | subclass(X0,X2)
        | member(not_subclass_element(X0,X2),y)
        | ~ member(not_subclass_element(X0,X2),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f4184,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),y)
        | ~ subclass(X0,regular(X0))
        | y = X0 )
    | ~ spl0_34
    | ~ spl0_342 ),
    inference(duplicate_literal_removal,[],[f4153]) ).

fof(f4153,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),y)
        | ~ subclass(X0,regular(X0))
        | y = X0
        | subclass(X0,X1) )
    | ~ spl0_34
    | ~ spl0_342 ),
    inference(resolution,[],[f4105,f362]) ).

fof(f4105,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | member(not_subclass_element(X0,X2),y)
        | ~ subclass(X0,regular(X1))
        | y = X1 )
    | ~ spl0_342 ),
    inference(avatar_component_clause,[],[f4104]) ).

fof(f37727,plain,
    ( spl0_1211
    | ~ spl0_154
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3795,f3634,f1287,f37725]) ).

fof(f3795,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,y),X1)
        | subclass(X0,y)
        | y = X1
        | ~ subclass(X0,regular(X1)) )
    | ~ spl0_154
    | ~ spl0_323 ),
    inference(duplicate_literal_removal,[],[f3786]) ).

fof(f3786,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,y),X1)
        | subclass(X0,y)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | subclass(X0,y) )
    | ~ spl0_154
    | ~ spl0_323 ),
    inference(resolution,[],[f3635,f1288]) ).

fof(f37703,plain,
    ( spl0_1210
    | ~ spl0_168
    | ~ spl0_1209 ),
    inference(avatar_split_clause,[],[f37699,f37696,f1428,f37701]) ).

fof(f37701,plain,
    ( spl0_1210
  <=> ! [X2] :
        ( singleton_relation = X2
        | ~ subclass(universal_class,regular(X2))
        | ~ subclass(universal_class,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f37696,plain,
    ( spl0_1209
  <=> ! [X2] :
        ( ~ subclass(universal_class,regular(X2))
        | ~ subclass(universal_class,X2)
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).

fof(f37699,plain,
    ( ! [X2] :
        ( singleton_relation = X2
        | ~ subclass(universal_class,regular(X2))
        | ~ subclass(universal_class,X2) )
    | ~ spl0_168
    | ~ spl0_1209 ),
    inference(forward_demodulation,[],[f37697,f1430]) ).

fof(f37697,plain,
    ( ! [X2] :
        ( ~ subclass(universal_class,regular(X2))
        | ~ subclass(universal_class,X2)
        | y = X2 )
    | ~ spl0_1209 ),
    inference(avatar_component_clause,[],[f37696]) ).

fof(f37698,plain,
    ( spl0_1209
    | spl0_1102
    | ~ spl0_137
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3750,f3608,f1078,f33959,f37696]) ).

fof(f33959,plain,
    ( spl0_1102
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f1078,plain,
    ( spl0_137
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f3608,plain,
    ( spl0_318
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | member(unordered_pair(X1,X2),y)
        | ~ member(unordered_pair(X1,X2),X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f3750,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),y)
        | ~ subclass(universal_class,regular(X2))
        | y = X2
        | ~ subclass(universal_class,X2) )
    | ~ spl0_137
    | ~ spl0_318 ),
    inference(resolution,[],[f3609,f1079]) ).

fof(f1079,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1078]) ).

fof(f3609,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | member(unordered_pair(X1,X2),y)
        | ~ subclass(universal_class,regular(X0))
        | y = X0 )
    | ~ spl0_318 ),
    inference(avatar_component_clause,[],[f3608]) ).

fof(f37675,plain,
    ( spl0_1208
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1115 ),
    inference(avatar_split_clause,[],[f34535,f34030,f9421,f8731,f1428,f37673]) ).

fof(f34535,plain,
    ( ! [X0] : singleton_relation = cross_product(X0,singleton_relation)
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1115 ),
    inference(forward_demodulation,[],[f34534,f1430]) ).

fof(f34534,plain,
    ( ! [X0] : singleton_relation = cross_product(X0,y)
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1115 ),
    inference(forward_demodulation,[],[f34504,f9423]) ).

fof(f34504,plain,
    ( ! [X0] : singleton_relation = cross_product(X0,domain_of(y))
    | ~ spl0_550
    | ~ spl0_1115 ),
    inference(resolution,[],[f34031,f8732]) ).

fof(f37671,plain,
    ( spl0_1207
    | spl0_882
    | ~ spl0_19
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f3501,f3426,f292,f21901,f37669]) ).

fof(f37669,plain,
    ( spl0_1207
  <=> ! [X0,X1] :
        ( regular(omega) = X0
        | ~ inductive(unordered_pair(X0,X1))
        | regular(omega) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).

fof(f3426,plain,
    ( spl0_300
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | y = X0
        | regular(X0) = X1
        | regular(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f3501,plain,
    ( ! [X0,X1] :
        ( omega = y
        | regular(omega) = X0
        | regular(omega) = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_19
    | ~ spl0_300 ),
    inference(resolution,[],[f3427,f293]) ).

fof(f3427,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | y = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f3426]) ).

fof(f37666,plain,
    ( spl0_1206
    | ~ spl0_248
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3352,f3209,f2450,f37664]) ).

fof(f3352,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f3326]) ).

fof(f3326,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | y = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_292 ),
    inference(resolution,[],[f3210,f2451]) ).

fof(f37661,plain,
    ( spl0_1205
    | ~ spl0_50
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3349,f3209,f441,f37659]) ).

fof(f441,plain,
    ( spl0_50
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f3349,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = intersection(X0,identity_relation) )
    | ~ spl0_50
    | ~ spl0_292 ),
    inference(superposition,[],[f3210,f443]) ).

fof(f443,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f441]) ).

fof(f37656,plain,
    ( spl0_1204
    | ~ spl0_49
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3348,f3209,f436,f37654]) ).

fof(f37654,plain,
    ( spl0_1204
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
        | y = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).

fof(f3348,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
        | y = intersection(X0,singleton_relation) )
    | ~ spl0_49
    | ~ spl0_292 ),
    inference(superposition,[],[f3210,f438]) ).

fof(f37650,plain,
    ( spl0_1203
    | ~ spl0_130
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3342,f3209,f1005,f37648]) ).

fof(f37648,plain,
    ( spl0_1203
  <=> ! [X0,X1] :
        ( y = intersection(X0,intersection(singleton_relation,X1))
        | member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).

fof(f3342,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,intersection(singleton_relation,X1))
        | member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) )
    | ~ spl0_130
    | ~ spl0_292 ),
    inference(resolution,[],[f3210,f1006]) ).

fof(f37645,plain,
    ( spl0_1202
    | ~ spl0_131
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3340,f3209,f1009,f37643]) ).

fof(f1009,plain,
    ( spl0_131
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f3340,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,intersection(identity_relation,X1))
        | member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
    | ~ spl0_131
    | ~ spl0_292 ),
    inference(resolution,[],[f3210,f1010]) ).

fof(f1010,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1009]) ).

fof(f37640,plain,
    ( spl0_1201
    | ~ spl0_248
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f3323,f3205,f2450,f37638]) ).

fof(f3323,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_248
    | ~ spl0_291 ),
    inference(duplicate_literal_removal,[],[f3297]) ).

fof(f3297,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | y = intersection(X0,intersection(X1,X2))
        | ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
    | ~ spl0_248
    | ~ spl0_291 ),
    inference(resolution,[],[f3206,f2451]) ).

fof(f37634,plain,
    ( spl0_1200
    | ~ spl0_130
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f3313,f3205,f1005,f37632]) ).

fof(f3313,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,intersection(X1,singleton_relation))
        | member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) )
    | ~ spl0_130
    | ~ spl0_291 ),
    inference(resolution,[],[f3206,f1006]) ).

fof(f37629,plain,
    ( spl0_1199
    | ~ spl0_131
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f3311,f3205,f1009,f37627]) ).

fof(f3311,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,intersection(X1,identity_relation))
        | member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
    | ~ spl0_131
    | ~ spl0_291 ),
    inference(resolution,[],[f3206,f1010]) ).

fof(f37624,plain,
    ( spl0_1198
    | ~ spl0_248
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3294,f3201,f2450,f37622]) ).

fof(f3294,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_248
    | ~ spl0_290 ),
    inference(duplicate_literal_removal,[],[f3268]) ).

fof(f3268,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | y = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
    | ~ spl0_248
    | ~ spl0_290 ),
    inference(resolution,[],[f3202,f2451]) ).

fof(f37097,plain,
    ( spl0_1197
    | ~ spl0_50
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3291,f3201,f441,f37095]) ).

fof(f3291,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = intersection(identity_relation,X0) )
    | ~ spl0_50
    | ~ spl0_290 ),
    inference(superposition,[],[f3202,f443]) ).

fof(f37092,plain,
    ( spl0_1196
    | ~ spl0_49
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3290,f3201,f436,f37090]) ).

fof(f37090,plain,
    ( spl0_1196
  <=> ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
        | y = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f3290,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
        | y = intersection(singleton_relation,X0) )
    | ~ spl0_49
    | ~ spl0_290 ),
    inference(superposition,[],[f3202,f438]) ).

fof(f37086,plain,
    ( spl0_1195
    | ~ spl0_130
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3284,f3201,f1005,f37084]) ).

fof(f37084,plain,
    ( spl0_1195
  <=> ! [X0,X1] :
        ( y = intersection(intersection(singleton_relation,X0),X1)
        | member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f3284,plain,
    ( ! [X0,X1] :
        ( y = intersection(intersection(singleton_relation,X0),X1)
        | member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) )
    | ~ spl0_130
    | ~ spl0_290 ),
    inference(resolution,[],[f3202,f1006]) ).

fof(f37081,plain,
    ( spl0_1194
    | ~ spl0_131
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3282,f3201,f1009,f37079]) ).

fof(f3282,plain,
    ( ! [X0,X1] :
        ( y = intersection(intersection(identity_relation,X0),X1)
        | member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
    | ~ spl0_131
    | ~ spl0_290 ),
    inference(resolution,[],[f3202,f1010]) ).

fof(f37076,plain,
    ( spl0_1193
    | ~ spl0_248
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f3265,f3197,f2450,f37074]) ).

fof(f3265,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_289 ),
    inference(duplicate_literal_removal,[],[f3239]) ).

fof(f3239,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | y = intersection(intersection(X0,X1),X2)
        | ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_289 ),
    inference(resolution,[],[f3198,f2451]) ).

fof(f37070,plain,
    ( spl0_1192
    | ~ spl0_130
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f3255,f3197,f1005,f37068]) ).

fof(f3255,plain,
    ( ! [X0,X1] :
        ( y = intersection(intersection(X0,singleton_relation),X1)
        | member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) )
    | ~ spl0_130
    | ~ spl0_289 ),
    inference(resolution,[],[f3198,f1006]) ).

fof(f37065,plain,
    ( spl0_1191
    | ~ spl0_131
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f3253,f3197,f1009,f37063]) ).

fof(f3253,plain,
    ( ! [X0,X1] :
        ( y = intersection(intersection(X0,identity_relation),X1)
        | member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
    | ~ spl0_131
    | ~ spl0_289 ),
    inference(resolution,[],[f3198,f1010]) ).

fof(f37060,plain,
    ( spl0_1190
    | ~ spl0_29
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3154,f3019,f334,f37058]) ).

fof(f3154,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | y = cross_product(X1,X2)
        | ~ member(regular(cross_product(X1,X2)),X0) )
    | ~ spl0_29
    | ~ spl0_286 ),
    inference(resolution,[],[f3020,f335]) ).

fof(f37055,plain,
    ( spl0_1189
    | ~ spl0_29
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3097,f2988,f334,f37053]) ).

fof(f3097,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = intersection(X2,X0)
        | ~ member(regular(intersection(X2,X0)),X1) )
    | ~ spl0_29
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f335]) ).

fof(f37050,plain,
    ( spl0_1188
    | ~ spl0_29
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3044,f2980,f334,f37048]) ).

fof(f3044,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = intersection(X0,X2)
        | ~ member(regular(intersection(X0,X2)),X1) )
    | ~ spl0_29
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f335]) ).

fof(f36751,plain,
    ( spl0_1187
    | ~ spl0_42
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2882,f2826,f393,f36749]) ).

fof(f393,plain,
    ( spl0_42
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f2882,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,flip(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_42
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f394]) ).

fof(f394,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f393]) ).

fof(f36746,plain,
    ( spl0_1186
    | ~ spl0_41
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2881,f2826,f389,f36744]) ).

fof(f389,plain,
    ( spl0_41
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f2881,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,rotate(X1))
        | member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
    | ~ spl0_41
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f390]) ).

fof(f390,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f389]) ).

fof(f36741,plain,
    ( spl0_1185
    | ~ spl0_153
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2667,f2450,f1264,f36739]) ).

fof(f1264,plain,
    ( spl0_153
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f2667,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(regular(X0),identity_relation) )
    | ~ spl0_153
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f1265]) ).

fof(f1265,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1264]) ).

fof(f36098,plain,
    ( spl0_1184
    | ~ spl0_168
    | ~ spl0_539 ),
    inference(avatar_split_clause,[],[f13945,f8422,f1428,f36096]) ).

fof(f13945,plain,
    ( ! [X0] : singleton_relation = intersection(X0,singleton_relation)
    | ~ spl0_168
    | ~ spl0_539 ),
    inference(superposition,[],[f8423,f1430]) ).

fof(f35370,plain,
    ( spl0_1183
    | ~ spl0_168
    | ~ spl0_531 ),
    inference(avatar_split_clause,[],[f13944,f8328,f1428,f35368]) ).

fof(f13944,plain,
    ( ! [X0] : singleton_relation = intersection(singleton_relation,X0)
    | ~ spl0_168
    | ~ spl0_531 ),
    inference(superposition,[],[f8329,f1430]) ).

fof(f35366,plain,
    ( spl0_1182
    | ~ spl0_168
    | ~ spl0_1155 ),
    inference(avatar_split_clause,[],[f35181,f35178,f1428,f35364]) ).

fof(f35364,plain,
    ( spl0_1182
  <=> ! [X0,X1] :
        ( singleton_relation = unordered_pair(X1,X0)
        | member(X0,universal_class)
        | regular(unordered_pair(X1,X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f35178,plain,
    ( spl0_1155
  <=> ! [X0,X1] :
        ( member(X0,universal_class)
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f35181,plain,
    ( ! [X0,X1] :
        ( singleton_relation = unordered_pair(X1,X0)
        | member(X0,universal_class)
        | regular(unordered_pair(X1,X0)) = X1 )
    | ~ spl0_168
    | ~ spl0_1155 ),
    inference(forward_demodulation,[],[f35179,f1430]) ).

fof(f35179,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 )
    | ~ spl0_1155 ),
    inference(avatar_component_clause,[],[f35178]) ).

fof(f35362,plain,
    ( spl0_1181
    | ~ spl0_168
    | ~ spl0_1154 ),
    inference(avatar_split_clause,[],[f35176,f35173,f1428,f35360]) ).

fof(f35360,plain,
    ( spl0_1181
  <=> ! [X0,X1] :
        ( unordered_pair(X0,X1) = singleton_relation
        | member(X0,universal_class)
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f35173,plain,
    ( spl0_1154
  <=> ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f35176,plain,
    ( ! [X0,X1] :
        ( unordered_pair(X0,X1) = singleton_relation
        | member(X0,universal_class)
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_168
    | ~ spl0_1154 ),
    inference(forward_demodulation,[],[f35174,f1430]) ).

fof(f35174,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_1154 ),
    inference(avatar_component_clause,[],[f35173]) ).

fof(f35358,plain,
    ( spl0_1180
    | ~ spl0_168
    | ~ spl0_1151 ),
    inference(avatar_split_clause,[],[f35162,f35159,f1428,f35356]) ).

fof(f35356,plain,
    ( spl0_1180
  <=> ! [X2,X0,X1] :
        ( singleton_relation = cross_product(X1,X2)
        | ~ subclass(universal_class,X0)
        | ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f35159,plain,
    ( spl0_1151
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | y = cross_product(X1,X2)
        | ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f35162,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = cross_product(X1,X2)
        | ~ subclass(universal_class,X0)
        | ~ subclass(cross_product(X1,X2),complement(X0)) )
    | ~ spl0_168
    | ~ spl0_1151 ),
    inference(forward_demodulation,[],[f35160,f1430]) ).

fof(f35160,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(cross_product(X1,X2),complement(X0))
        | y = cross_product(X1,X2)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_1151 ),
    inference(avatar_component_clause,[],[f35159]) ).

fof(f35354,plain,
    ( spl0_1179
    | ~ spl0_168
    | ~ spl0_1150 ),
    inference(avatar_split_clause,[],[f35157,f35154,f1428,f35352]) ).

fof(f35352,plain,
    ( spl0_1179
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(X2,X0)
        | ~ subclass(X0,X1)
        | ~ subclass(intersection(X2,X0),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f35154,plain,
    ( spl0_1150
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X2,X0)
        | ~ subclass(intersection(X2,X0),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f35157,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(X2,X0)
        | ~ subclass(X0,X1)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_168
    | ~ spl0_1150 ),
    inference(forward_demodulation,[],[f35155,f1430]) ).

fof(f35155,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(intersection(X2,X0),complement(X1))
        | y = intersection(X2,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_1150 ),
    inference(avatar_component_clause,[],[f35154]) ).

fof(f35350,plain,
    ( spl0_1178
    | ~ spl0_168
    | ~ spl0_1148 ),
    inference(avatar_split_clause,[],[f35147,f35144,f1428,f35348]) ).

fof(f35348,plain,
    ( spl0_1178
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X1,X0)
        | ~ subclass(X0,identity_relation)
        | member(regular(intersection(X1,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f35144,plain,
    ( spl0_1148
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | y = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f35147,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X1,X0)
        | ~ subclass(X0,identity_relation)
        | member(regular(intersection(X1,X0)),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1148 ),
    inference(forward_demodulation,[],[f35145,f1430]) ).

fof(f35145,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X1,X0)),subset_relation)
        | y = intersection(X1,X0)
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_1148 ),
    inference(avatar_component_clause,[],[f35144]) ).

fof(f35346,plain,
    ( spl0_1177
    | ~ spl0_168
    | ~ spl0_1147 ),
    inference(avatar_split_clause,[],[f35142,f35139,f1428,f35344]) ).

fof(f35344,plain,
    ( spl0_1177
  <=> ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,X2)
        | ~ subclass(X0,X1)
        | ~ subclass(intersection(X0,X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f35139,plain,
    ( spl0_1147
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,X2)
        | ~ subclass(intersection(X0,X2),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f35142,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = intersection(X0,X2)
        | ~ subclass(X0,X1)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_168
    | ~ spl0_1147 ),
    inference(forward_demodulation,[],[f35140,f1430]) ).

fof(f35140,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(intersection(X0,X2),complement(X1))
        | y = intersection(X0,X2)
        | ~ subclass(X0,X1) )
    | ~ spl0_1147 ),
    inference(avatar_component_clause,[],[f35139]) ).

fof(f35342,plain,
    ( spl0_1176
    | ~ spl0_168
    | ~ spl0_1144 ),
    inference(avatar_split_clause,[],[f35127,f35124,f1428,f35340]) ).

fof(f35340,plain,
    ( spl0_1176
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(X0,identity_relation)
        | member(regular(intersection(X0,X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f35124,plain,
    ( spl0_1144
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | intersection(X0,X1) = y
        | member(regular(intersection(X0,X1)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f35127,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(X0,identity_relation)
        | member(regular(intersection(X0,X1)),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1144 ),
    inference(forward_demodulation,[],[f35125,f1430]) ).

fof(f35125,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),subset_relation)
        | intersection(X0,X1) = y
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_1144 ),
    inference(avatar_component_clause,[],[f35124]) ).

fof(f35338,plain,
    ( spl0_1175
    | ~ spl0_168
    | ~ spl0_1143 ),
    inference(avatar_split_clause,[],[f35122,f35119,f1428,f35336]) ).

fof(f35336,plain,
    ( spl0_1175
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f35119,plain,
    ( spl0_1143
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f35122,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_168
    | ~ spl0_1143 ),
    inference(forward_demodulation,[],[f35120,f1430]) ).

fof(f35120,plain,
    ( ! [X0] :
        ( member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ subclass(X0,application_function)
        | y = X0 )
    | ~ spl0_1143 ),
    inference(avatar_component_clause,[],[f35119]) ).

fof(f35334,plain,
    ( spl0_1174
    | ~ spl0_168
    | ~ spl0_1142 ),
    inference(avatar_split_clause,[],[f35117,f35114,f1428,f35332]) ).

fof(f35332,plain,
    ( spl0_1174
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,composition_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f35114,plain,
    ( spl0_1142
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,composition_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f35117,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,composition_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_168
    | ~ spl0_1142 ),
    inference(forward_demodulation,[],[f35115,f1430]) ).

fof(f35115,plain,
    ( ! [X0] :
        ( member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ subclass(X0,composition_function)
        | y = X0 )
    | ~ spl0_1142 ),
    inference(avatar_component_clause,[],[f35114]) ).

fof(f35330,plain,
    ( spl0_1173
    | ~ spl0_168
    | ~ spl0_1141 ),
    inference(avatar_split_clause,[],[f35112,f35109,f1428,f35328]) ).

fof(f35328,plain,
    ( spl0_1173
  <=> ! [X2,X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,compose(X1,X2))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f35109,plain,
    ( spl0_1141
  <=> ! [X2,X0,X1] :
        ( y = X0
        | ~ subclass(X0,compose(X1,X2))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f35112,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,compose(X1,X2))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1141 ),
    inference(forward_demodulation,[],[f35110,f1430]) ).

fof(f35110,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,compose(X1,X2))
        | y = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_1141 ),
    inference(avatar_component_clause,[],[f35109]) ).

fof(f35326,plain,
    ( spl0_1172
    | ~ spl0_168
    | ~ spl0_1140 ),
    inference(avatar_split_clause,[],[f35107,f35104,f1428,f35324]) ).

fof(f35324,plain,
    ( spl0_1172
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f35107,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) )
    | ~ spl0_168
    | ~ spl0_1140 ),
    inference(forward_demodulation,[],[f35105,f1430]) ).

fof(f35105,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = X0
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) )
    | ~ spl0_1140 ),
    inference(avatar_component_clause,[],[f35104]) ).

fof(f35322,plain,
    ( spl0_1171
    | ~ spl0_168
    | ~ spl0_1139 ),
    inference(avatar_split_clause,[],[f35102,f35099,f1428,f35320]) ).

fof(f35320,plain,
    ( spl0_1171
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,identity_relation)
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f35099,plain,
    ( spl0_1139
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | y = X0
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f35102,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,identity_relation)
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_168
    | ~ spl0_1139 ),
    inference(forward_demodulation,[],[f35100,f1430]) ).

fof(f35100,plain,
    ( ! [X0] :
        ( member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_1139 ),
    inference(avatar_component_clause,[],[f35099]) ).

fof(f35318,plain,
    ( spl0_1170
    | ~ spl0_168
    | ~ spl0_1137 ),
    inference(avatar_split_clause,[],[f35092,f35089,f1428,f35316]) ).

fof(f35316,plain,
    ( spl0_1170
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(X0,identity_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f35089,plain,
    ( spl0_1137
  <=> ! [X0,X1] :
        ( y = intersection(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(X0,identity_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f35092,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(X0,identity_relation)),X1) )
    | ~ spl0_168
    | ~ spl0_1137 ),
    inference(forward_demodulation,[],[f35090,f1430]) ).

fof(f35090,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,identity_relation)),X1)
        | ~ subclass(subset_relation,X1)
        | y = intersection(X0,identity_relation) )
    | ~ spl0_1137 ),
    inference(avatar_component_clause,[],[f35089]) ).

fof(f35314,plain,
    ( spl0_1169
    | ~ spl0_168
    | ~ spl0_1136 ),
    inference(avatar_split_clause,[],[f35087,f35084,f1428,f35312]) ).

fof(f35312,plain,
    ( spl0_1169
  <=> ! [X0,X1] :
        ( singleton_relation = intersection(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(identity_relation,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f35084,plain,
    ( spl0_1136
  <=> ! [X0,X1] :
        ( y = intersection(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(identity_relation,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f35087,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(identity_relation,X0)),X1) )
    | ~ spl0_168
    | ~ spl0_1136 ),
    inference(forward_demodulation,[],[f35085,f1430]) ).

fof(f35085,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(identity_relation,X0)),X1)
        | ~ subclass(subset_relation,X1)
        | y = intersection(identity_relation,X0) )
    | ~ spl0_1136 ),
    inference(avatar_component_clause,[],[f35084]) ).

fof(f35310,plain,
    ( spl0_1168
    | ~ spl0_168
    | ~ spl0_1133 ),
    inference(avatar_split_clause,[],[f35072,f35069,f1428,f35308]) ).

fof(f35308,plain,
    ( spl0_1168
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f35069,plain,
    ( spl0_1133
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f35072,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_1133 ),
    inference(forward_demodulation,[],[f35070,f1430]) ).

fof(f35070,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | y = X0
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_1133 ),
    inference(avatar_component_clause,[],[f35069]) ).

fof(f35306,plain,
    ( spl0_1167
    | ~ spl0_168
    | ~ spl0_1132 ),
    inference(avatar_split_clause,[],[f35067,f35064,f1428,f35304]) ).

fof(f35304,plain,
    ( spl0_1167
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f35064,plain,
    ( spl0_1132
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | ~ member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f35067,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_1132 ),
    inference(forward_demodulation,[],[f35065,f1430]) ).

fof(f35065,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | y = X0
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_1132 ),
    inference(avatar_component_clause,[],[f35064]) ).

fof(f35295,plain,
    ( spl0_1166
    | ~ spl0_168
    | ~ spl0_539
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1098
    | ~ spl0_1115
    | ~ spl0_1165 ),
    inference(avatar_split_clause,[],[f35291,f35286,f34030,f33941,f9421,f8731,f8422,f1428,f35293]) ).

fof(f35293,plain,
    ( spl0_1166
  <=> ! [X0,X1] :
        ( member(singleton_relation,X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f35286,plain,
    ( spl0_1165
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f35291,plain,
    ( ! [X0,X1] :
        ( member(singleton_relation,X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_168
    | ~ spl0_539
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1098
    | ~ spl0_1115
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f35290,f33943]) ).

fof(f33943,plain,
    ( singleton_relation = domain_of(singleton_relation)
    | ~ spl0_1098 ),
    inference(avatar_component_clause,[],[f33941]) ).

fof(f35290,plain,
    ( ! [X0,X1] :
        ( member(domain_of(singleton_relation),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_168
    | ~ spl0_539
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1115
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f35289,f13945]) ).

fof(f35289,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,singleton_relation)),X1)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_1115
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f35287,f34535]) ).

fof(f35287,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1) )
    | ~ spl0_1165 ),
    inference(avatar_component_clause,[],[f35286]) ).

fof(f35288,plain,
    ( spl0_1165
    | ~ spl0_375
    | ~ spl0_607 ),
    inference(avatar_split_clause,[],[f29531,f10943,f4993,f35286]) ).

fof(f10943,plain,
    ( spl0_607
  <=> ! [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_607])]) ).

fof(f29531,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1) )
    | ~ spl0_375
    | ~ spl0_607 ),
    inference(resolution,[],[f4994,f10944]) ).

fof(f10944,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,universal_class)
        | ~ subclass(universal_class,X0)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
    | ~ spl0_607 ),
    inference(avatar_component_clause,[],[f10943]) ).

fof(f35284,plain,
    ( spl0_1164
    | ~ spl0_8
    | ~ spl0_639 ),
    inference(avatar_split_clause,[],[f17596,f11827,f242,f35282]) ).

fof(f35282,plain,
    ( spl0_1164
  <=> ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = subset_relation
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f17596,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = subset_relation
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_8
    | ~ spl0_639 ),
    inference(resolution,[],[f11828,f243]) ).

fof(f35280,plain,
    ( ~ spl0_1163
    | ~ spl0_168
    | spl0_671 ),
    inference(avatar_split_clause,[],[f13959,f13527,f1428,f35277]) ).

fof(f13527,plain,
    ( spl0_671
  <=> y = cross_product(y,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f13959,plain,
    ( singleton_relation != cross_product(singleton_relation,universal_class)
    | ~ spl0_168
    | spl0_671 ),
    inference(superposition,[],[f13529,f1430]) ).

fof(f13529,plain,
    ( y != cross_product(y,universal_class)
    | spl0_671 ),
    inference(avatar_component_clause,[],[f13527]) ).

fof(f35274,plain,
    ( spl0_1162
    | ~ spl0_21
    | ~ spl0_607 ),
    inference(avatar_split_clause,[],[f10969,f10943,f301,f35272]) ).

fof(f35272,plain,
    ( spl0_1162
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,y))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f301,plain,
    ( spl0_21
  <=> member(y,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f10969,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,y))),X1) )
    | ~ spl0_21
    | ~ spl0_607 ),
    inference(resolution,[],[f10944,f302]) ).

fof(f302,plain,
    ( member(y,universal_class)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f35269,plain,
    ( spl0_1161
    | ~ spl0_297
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f7335,f7230,f3231,f35267]) ).

fof(f35267,plain,
    ( spl0_1161
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | ~ subclass(intersection(y,X0),complement(X2))
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f7230,plain,
    ( spl0_485
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f7335,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | ~ subclass(intersection(y,X0),complement(X2))
        | y = X2 )
    | ~ spl0_297
    | ~ spl0_485 ),
    inference(duplicate_literal_removal,[],[f7310]) ).

fof(f7310,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | ~ subclass(intersection(y,X0),complement(X2))
        | subclass(intersection(y,X0),X1)
        | y = X2 )
    | ~ spl0_297
    | ~ spl0_485 ),
    inference(resolution,[],[f7231,f3232]) ).

fof(f7231,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_485 ),
    inference(avatar_component_clause,[],[f7230]) ).

fof(f35264,plain,
    ( spl0_1160
    | ~ spl0_298
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f7334,f7230,f3235,f35262]) ).

fof(f35262,plain,
    ( spl0_1160
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | ~ subclass(intersection(X0,y),complement(X2))
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f7334,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | ~ subclass(intersection(X0,y),complement(X2))
        | y = X2 )
    | ~ spl0_298
    | ~ spl0_485 ),
    inference(duplicate_literal_removal,[],[f7311]) ).

fof(f7311,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | ~ subclass(intersection(X0,y),complement(X2))
        | subclass(intersection(X0,y),X1)
        | y = X2 )
    | ~ spl0_298
    | ~ spl0_485 ),
    inference(resolution,[],[f7231,f3236]) ).

fof(f35260,plain,
    ( spl0_366
    | ~ spl0_1159
    | ~ spl0_109
    | spl0_368 ),
    inference(avatar_split_clause,[],[f4504,f4496,f831,f35257,f4488]) ).

fof(f4488,plain,
    ( spl0_366
  <=> y = domain_of(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f35257,plain,
    ( spl0_1159
  <=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f4496,plain,
    ( spl0_368
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f4504,plain,
    ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | y = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_109
    | spl0_368 ),
    inference(resolution,[],[f4498,f832]) ).

fof(f4498,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
    | spl0_368 ),
    inference(avatar_component_clause,[],[f4496]) ).

fof(f35255,plain,
    ( spl0_366
    | ~ spl0_1158
    | ~ spl0_109
    | spl0_367 ),
    inference(avatar_split_clause,[],[f4501,f4492,f831,f35252,f4488]) ).

fof(f35252,plain,
    ( spl0_1158
  <=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f4492,plain,
    ( spl0_367
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f4501,plain,
    ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation)
    | y = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_109
    | spl0_367 ),
    inference(resolution,[],[f4493,f832]) ).

fof(f4493,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | spl0_367 ),
    inference(avatar_component_clause,[],[f4492]) ).

fof(f35250,plain,
    ( spl0_363
    | ~ spl0_1157
    | ~ spl0_109
    | spl0_365 ),
    inference(avatar_split_clause,[],[f4486,f4478,f831,f35247,f4470]) ).

fof(f4470,plain,
    ( spl0_363
  <=> complement(compose(element_relation,complement(identity_relation))) = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f35247,plain,
    ( spl0_1157
  <=> subclass(complement(compose(element_relation,complement(identity_relation))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f4478,plain,
    ( spl0_365
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f4486,plain,
    ( ~ subclass(complement(compose(element_relation,complement(identity_relation))),element_relation)
    | complement(compose(element_relation,complement(identity_relation))) = y
    | ~ spl0_109
    | spl0_365 ),
    inference(resolution,[],[f4480,f832]) ).

fof(f4480,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | spl0_365 ),
    inference(avatar_component_clause,[],[f4478]) ).

fof(f35186,plain,
    ( spl0_363
    | ~ spl0_1156
    | ~ spl0_109
    | spl0_364 ),
    inference(avatar_split_clause,[],[f4483,f4474,f831,f35183,f4470]) ).

fof(f35183,plain,
    ( spl0_1156
  <=> subclass(complement(compose(element_relation,complement(identity_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f4474,plain,
    ( spl0_364
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f4483,plain,
    ( ~ subclass(complement(compose(element_relation,complement(identity_relation))),singleton_relation)
    | complement(compose(element_relation,complement(identity_relation))) = y
    | ~ spl0_109
    | spl0_364 ),
    inference(resolution,[],[f4475,f832]) ).

fof(f4475,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | spl0_364 ),
    inference(avatar_component_clause,[],[f4474]) ).

fof(f35180,plain,
    ( spl0_1155
    | ~ spl0_8
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f4075,f4032,f242,f35178]) ).

fof(f4032,plain,
    ( spl0_335
  <=> ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f4075,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | y = unordered_pair(X1,X0)
        | regular(unordered_pair(X1,X0)) = X1 )
    | ~ spl0_8
    | ~ spl0_335 ),
    inference(resolution,[],[f4033,f243]) ).

fof(f4033,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f4032]) ).

fof(f35175,plain,
    ( spl0_1154
    | ~ spl0_8
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f4070,f4027,f242,f35173]) ).

fof(f4027,plain,
    ( spl0_334
  <=> ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f4070,plain,
    ( ! [X0,X1] :
        ( member(X0,universal_class)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_8
    | ~ spl0_334 ),
    inference(resolution,[],[f4028,f243]) ).

fof(f4028,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f4027]) ).

fof(f35171,plain,
    ( spl0_186
    | ~ spl0_1152
    | spl0_238
    | spl0_1153
    | ~ spl0_187
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3863,f3810,f1605,f35168,f2279,f35164,f1601]) ).

fof(f1601,plain,
    ( spl0_186
  <=> identity_relation = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f35164,plain,
    ( spl0_1152
  <=> subclass(identity_relation,regular(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f35168,plain,
    ( spl0_1153
  <=> member(regular(identity_relation),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f1605,plain,
    ( spl0_187
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f3863,plain,
    ( member(regular(identity_relation),y)
    | subset_relation = y
    | ~ subclass(identity_relation,regular(subset_relation))
    | identity_relation = y
    | ~ spl0_187
    | ~ spl0_327 ),
    inference(resolution,[],[f3811,f1607]) ).

fof(f1607,plain,
    ( member(regular(identity_relation),subset_relation)
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1605]) ).

fof(f35161,plain,
    ( spl0_1151
    | ~ spl0_248
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f3165,f3019,f2450,f35159]) ).

fof(f3165,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | y = cross_product(X1,X2)
        | ~ subclass(cross_product(X1,X2),complement(X0)) )
    | ~ spl0_248
    | ~ spl0_286 ),
    inference(duplicate_literal_removal,[],[f3146]) ).

fof(f3146,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | y = cross_product(X1,X2)
        | y = cross_product(X1,X2)
        | ~ subclass(cross_product(X1,X2),complement(X0)) )
    | ~ spl0_248
    | ~ spl0_286 ),
    inference(resolution,[],[f3020,f2451]) ).

fof(f35156,plain,
    ( spl0_1150
    | ~ spl0_248
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3114,f2988,f2450,f35154]) ).

fof(f3114,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X2,X0)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_282 ),
    inference(duplicate_literal_removal,[],[f3089]) ).

fof(f3089,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X2,X0)
        | y = intersection(X2,X0)
        | ~ subclass(intersection(X2,X0),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f2451]) ).

fof(f35151,plain,
    ( spl0_1149
    | ~ spl0_130
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3106,f2988,f1005,f35149]) ).

fof(f3106,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | y = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),element_relation) )
    | ~ spl0_130
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f1006]) ).

fof(f35146,plain,
    ( spl0_1148
    | ~ spl0_131
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3104,f2988,f1009,f35144]) ).

fof(f3104,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | y = intersection(X1,X0)
        | member(regular(intersection(X1,X0)),subset_relation) )
    | ~ spl0_131
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f1010]) ).

fof(f35141,plain,
    ( spl0_1147
    | ~ spl0_248
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3061,f2980,f2450,f35139]) ).

fof(f3061,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,X2)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_280 ),
    inference(duplicate_literal_removal,[],[f3036]) ).

fof(f3036,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,X2)
        | y = intersection(X0,X2)
        | ~ subclass(intersection(X0,X2),complement(X1)) )
    | ~ spl0_248
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f2451]) ).

fof(f35137,plain,
    ( spl0_1146
    | ~ spl0_168
    | ~ spl0_612 ),
    inference(avatar_split_clause,[],[f13955,f11087,f1428,f35134]) ).

fof(f35134,plain,
    ( spl0_1146
  <=> universal_class = complement(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f11087,plain,
    ( spl0_612
  <=> universal_class = complement(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f13955,plain,
    ( universal_class = complement(singleton_relation)
    | ~ spl0_168
    | ~ spl0_612 ),
    inference(superposition,[],[f11089,f1430]) ).

fof(f11089,plain,
    ( universal_class = complement(y)
    | ~ spl0_612 ),
    inference(avatar_component_clause,[],[f11087]) ).

fof(f35131,plain,
    ( spl0_1145
    | ~ spl0_130
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3053,f2980,f1005,f35129]) ).

fof(f3053,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | intersection(X0,X1) = y
        | member(regular(intersection(X0,X1)),element_relation) )
    | ~ spl0_130
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f1006]) ).

fof(f35126,plain,
    ( spl0_1144
    | ~ spl0_131
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3051,f2980,f1009,f35124]) ).

fof(f3051,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | intersection(X0,X1) = y
        | member(regular(intersection(X0,X1)),subset_relation) )
    | ~ spl0_131
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f1010]) ).

fof(f35121,plain,
    ( spl0_1143
    | ~ spl0_33
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2891,f2826,f352,f35119]) ).

fof(f352,plain,
    ( spl0_33
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f2891,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,application_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_33
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f354]) ).

fof(f354,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f352]) ).

fof(f35116,plain,
    ( spl0_1142
    | ~ spl0_32
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2889,f2826,f347,f35114]) ).

fof(f347,plain,
    ( spl0_32
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f2889,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,composition_function)
        | member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
    | ~ spl0_32
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f349]) ).

fof(f349,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f35111,plain,
    ( spl0_1141
    | ~ spl0_30
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2885,f2826,f338,f35109]) ).

fof(f338,plain,
    ( spl0_30
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f2885,plain,
    ( ! [X2,X0,X1] :
        ( y = X0
        | ~ subclass(X0,compose(X1,X2))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_30
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f339]) ).

fof(f339,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f338]) ).

fof(f35106,plain,
    ( spl0_1140
    | ~ spl0_31
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2875,f2826,f342,f35104]) ).

fof(f2875,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),cross_product(universal_class,universal_class))
        | ~ function(X1) )
    | ~ spl0_31
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f343]) ).

fof(f35101,plain,
    ( spl0_1139
    | ~ spl0_50
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2788,f2747,f441,f35099]) ).

fof(f2747,plain,
    ( spl0_263
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f2788,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | y = X0
        | member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_50
    | ~ spl0_263 ),
    inference(superposition,[],[f2748,f443]) ).

fof(f2748,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = X0
        | member(regular(X0),X1) )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2747]) ).

fof(f35096,plain,
    ( spl0_1138
    | ~ spl0_49
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2787,f2747,f436,f35094]) ).

fof(f35094,plain,
    ( spl0_1138
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | y = X0
        | member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f2787,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | y = X0
        | member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_49
    | ~ spl0_263 ),
    inference(superposition,[],[f2748,f438]) ).

fof(f35091,plain,
    ( spl0_1137
    | ~ spl0_46
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f2734,f2537,f424,f35089]) ).

fof(f2734,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(X0,identity_relation)),X1) )
    | ~ spl0_46
    | ~ spl0_255 ),
    inference(resolution,[],[f2538,f425]) ).

fof(f35086,plain,
    ( spl0_1136
    | ~ spl0_46
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f2727,f2532,f424,f35084]) ).

fof(f2727,plain,
    ( ! [X0,X1] :
        ( y = intersection(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(regular(intersection(identity_relation,X0)),X1) )
    | ~ spl0_46
    | ~ spl0_254 ),
    inference(resolution,[],[f2533,f425]) ).

fof(f35081,plain,
    ( spl0_1135
    | ~ spl0_46
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f2722,f2527,f424,f35079]) ).

fof(f35079,plain,
    ( spl0_1135
  <=> ! [X0,X1] :
        ( y = intersection(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(X0,singleton_relation)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f2722,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(X0,singleton_relation)),X1) )
    | ~ spl0_46
    | ~ spl0_253 ),
    inference(resolution,[],[f2528,f425]) ).

fof(f35076,plain,
    ( spl0_1134
    | ~ spl0_46
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2717,f2522,f424,f35074]) ).

fof(f35074,plain,
    ( spl0_1134
  <=> ! [X0,X1] :
        ( y = intersection(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(singleton_relation,X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f2717,plain,
    ( ! [X0,X1] :
        ( y = intersection(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(regular(intersection(singleton_relation,X0)),X1) )
    | ~ spl0_46
    | ~ spl0_252 ),
    inference(resolution,[],[f2523,f425]) ).

fof(f35071,plain,
    ( spl0_1133
    | ~ spl0_38
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2656,f2450,f377,f35069]) ).

fof(f377,plain,
    ( spl0_38
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f2656,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_38
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f378]) ).

fof(f378,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f377]) ).

fof(f35066,plain,
    ( spl0_1132
    | ~ spl0_36
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2655,f2450,f369,f35064]) ).

fof(f369,plain,
    ( spl0_36
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f2655,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
        | ~ member(regular(X0),universal_class) )
    | ~ spl0_36
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f370]) ).

fof(f370,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f369]) ).

fof(f34764,plain,
    ( spl0_1131
    | ~ spl0_168
    | ~ spl0_1125 ),
    inference(avatar_split_clause,[],[f34740,f34735,f1428,f34762]) ).

fof(f34762,plain,
    ( spl0_1131
  <=> ! [X0] :
        ( singleton_relation = X0
        | subclass(regular(X0),singleton_relation)
        | ~ member(not_subclass_element(regular(X0),singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f34735,plain,
    ( spl0_1125
  <=> ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),y),X0)
        | subclass(regular(X0),y)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f34740,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | subclass(regular(X0),singleton_relation)
        | ~ member(not_subclass_element(regular(X0),singleton_relation),X0) )
    | ~ spl0_168
    | ~ spl0_1125 ),
    inference(forward_demodulation,[],[f34739,f1430]) ).

fof(f34739,plain,
    ( ! [X0] :
        ( subclass(regular(X0),singleton_relation)
        | ~ member(not_subclass_element(regular(X0),singleton_relation),X0)
        | y = X0 )
    | ~ spl0_168
    | ~ spl0_1125 ),
    inference(forward_demodulation,[],[f34738,f1430]) ).

fof(f34738,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),singleton_relation),X0)
        | subclass(regular(X0),y)
        | y = X0 )
    | ~ spl0_168
    | ~ spl0_1125 ),
    inference(forward_demodulation,[],[f34736,f1430]) ).

fof(f34736,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),y),X0)
        | subclass(regular(X0),y)
        | y = X0 )
    | ~ spl0_1125 ),
    inference(avatar_component_clause,[],[f34735]) ).

fof(f34760,plain,
    ( spl0_1130
    | ~ spl0_168
    | ~ spl0_1124 ),
    inference(avatar_split_clause,[],[f34733,f34730,f1428,f34758]) ).

fof(f34758,plain,
    ( spl0_1130
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,subset_relation)
        | member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f34730,plain,
    ( spl0_1124
  <=> ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | y = intersection(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f34733,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,subset_relation)
        | member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1124 ),
    inference(forward_demodulation,[],[f34731,f1430]) ).

fof(f34731,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | y = intersection(X0,subset_relation) )
    | ~ spl0_1124 ),
    inference(avatar_component_clause,[],[f34730]) ).

fof(f34756,plain,
    ( spl0_1129
    | ~ spl0_168
    | ~ spl0_1123 ),
    inference(avatar_split_clause,[],[f34728,f34725,f1428,f34754]) ).

fof(f34754,plain,
    ( spl0_1129
  <=> ! [X0] :
        ( singleton_relation = intersection(subset_relation,X0)
        | member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f34725,plain,
    ( spl0_1123
  <=> ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | y = intersection(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f34728,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(subset_relation,X0)
        | member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1123 ),
    inference(forward_demodulation,[],[f34726,f1430]) ).

fof(f34726,plain,
    ( ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | y = intersection(subset_relation,X0) )
    | ~ spl0_1123 ),
    inference(avatar_component_clause,[],[f34725]) ).

fof(f34752,plain,
    ( spl0_1128
    | ~ spl0_168
    | ~ spl0_1122 ),
    inference(avatar_split_clause,[],[f34723,f34720,f1428,f34750]) ).

fof(f34750,plain,
    ( spl0_1128
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f34720,plain,
    ( spl0_1122
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f34723,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1122 ),
    inference(forward_demodulation,[],[f34721,f1430]) ).

fof(f34721,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,compose_class(X1))
        | y = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_1122 ),
    inference(avatar_component_clause,[],[f34720]) ).

fof(f34748,plain,
    ( spl0_1127
    | ~ spl0_168
    | ~ spl0_1121 ),
    inference(avatar_split_clause,[],[f34634,f34631,f1428,f34746]) ).

fof(f34746,plain,
    ( spl0_1127
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f34631,plain,
    ( spl0_1121
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f34634,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_168
    | ~ spl0_1121 ),
    inference(forward_demodulation,[],[f34632,f1430]) ).

fof(f34632,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | y = X0
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_1121 ),
    inference(avatar_component_clause,[],[f34631]) ).

fof(f34744,plain,
    ( spl0_1126
    | ~ spl0_168
    | ~ spl0_1120 ),
    inference(avatar_split_clause,[],[f34629,f34626,f1428,f34742]) ).

fof(f34742,plain,
    ( spl0_1126
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f34626,plain,
    ( spl0_1120
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | y = X0
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f34629,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_168
    | ~ spl0_1120 ),
    inference(forward_demodulation,[],[f34627,f1430]) ).

fof(f34627,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | y = X0
        | ~ subclass(subset_relation,X1)
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_1120 ),
    inference(avatar_component_clause,[],[f34626]) ).

fof(f34737,plain,
    ( spl0_1125
    | ~ spl0_34
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3800,f3634,f361,f34735]) ).

fof(f3800,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),y),X0)
        | subclass(regular(X0),y)
        | y = X0 )
    | ~ spl0_34
    | ~ spl0_323 ),
    inference(duplicate_literal_removal,[],[f3781]) ).

fof(f3781,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),y),X0)
        | subclass(regular(X0),y)
        | y = X0
        | subclass(regular(X0),y) )
    | ~ spl0_34
    | ~ spl0_323 ),
    inference(resolution,[],[f3635,f362]) ).

fof(f34732,plain,
    ( spl0_1124
    | ~ spl0_79
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3347,f3209,f642,f34730]) ).

fof(f642,plain,
    ( spl0_79
  <=> 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_79])]) ).

fof(f3347,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | y = intersection(X0,subset_relation) )
    | ~ spl0_79
    | ~ spl0_292 ),
    inference(superposition,[],[f3210,f644]) ).

fof(f644,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_79 ),
    inference(avatar_component_clause,[],[f642]) ).

fof(f34727,plain,
    ( spl0_1123
    | ~ spl0_79
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3289,f3201,f642,f34725]) ).

fof(f3289,plain,
    ( ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | y = intersection(subset_relation,X0) )
    | ~ spl0_79
    | ~ spl0_290 ),
    inference(superposition,[],[f3202,f644]) ).

fof(f34722,plain,
    ( spl0_1122
    | ~ spl0_26
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2888,f2826,f322,f34720]) ).

fof(f322,plain,
    ( spl0_26
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f2888,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_26
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f323]) ).

fof(f323,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f34633,plain,
    ( spl0_1121
    | ~ spl0_139
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2658,f2450,f1089,f34631]) ).

fof(f2658,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_139
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f1090]) ).

fof(f34628,plain,
    ( spl0_1120
    | ~ spl0_46
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2439,f2426,f424,f34626]) ).

fof(f2439,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | y = X0
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_46
    | ~ spl0_246 ),
    inference(resolution,[],[f2427,f425]) ).

fof(f34623,plain,
    ( spl0_1119
    | ~ spl0_46
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2431,f2422,f424,f34621]) ).

fof(f34621,plain,
    ( spl0_1119
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | y = X0
        | ~ subclass(element_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f2431,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | y = X0
        | ~ subclass(element_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_46
    | ~ spl0_245 ),
    inference(resolution,[],[f2423,f425]) ).

fof(f34613,plain,
    ( spl0_1118
    | ~ spl0_50
    | ~ spl0_344 ),
    inference(avatar_split_clause,[],[f4230,f4190,f441,f34610]) ).

fof(f34610,plain,
    ( spl0_1118
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f4230,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_50
    | ~ spl0_344 ),
    inference(superposition,[],[f4191,f443]) ).

fof(f34177,plain,
    ( ~ spl0_1117
    | ~ spl0_168
    | spl0_800 ),
    inference(avatar_split_clause,[],[f27703,f19436,f1428,f34174]) ).

fof(f34174,plain,
    ( spl0_1117
  <=> subclass(universal_class,flip(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f19436,plain,
    ( spl0_800
  <=> subclass(universal_class,flip(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f27703,plain,
    ( ~ subclass(universal_class,flip(singleton_relation))
    | ~ spl0_168
    | spl0_800 ),
    inference(superposition,[],[f19438,f1430]) ).

fof(f19438,plain,
    ( ~ subclass(universal_class,flip(y))
    | spl0_800 ),
    inference(avatar_component_clause,[],[f19436]) ).

fof(f34036,plain,
    ( spl0_1116
    | ~ spl0_168
    | ~ spl0_1106 ),
    inference(avatar_split_clause,[],[f33982,f33979,f1428,f34034]) ).

fof(f33982,plain,
    ( ! [X0,X1] :
        ( cross_product(X0,X1) = singleton_relation
        | member(first(regular(cross_product(X0,X1))),X0) )
    | ~ spl0_168
    | ~ spl0_1106 ),
    inference(forward_demodulation,[],[f33980,f1430]) ).

fof(f34032,plain,
    ( spl0_1115
    | ~ spl0_168
    | ~ spl0_1105 ),
    inference(avatar_split_clause,[],[f33977,f33974,f1428,f34030]) ).

fof(f33977,plain,
    ( ! [X0,X1] :
        ( cross_product(X0,X1) = singleton_relation
        | member(second(regular(cross_product(X0,X1))),X1) )
    | ~ spl0_168
    | ~ spl0_1105 ),
    inference(forward_demodulation,[],[f33975,f1430]) ).

fof(f34017,plain,
    ( spl0_1114
    | ~ spl0_168
    | ~ spl0_1092 ),
    inference(avatar_split_clause,[],[f33914,f33911,f1428,f34015]) ).

fof(f34015,plain,
    ( spl0_1114
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f33911,plain,
    ( spl0_1092
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f33914,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1092 ),
    inference(forward_demodulation,[],[f33912,f1430]) ).

fof(f33912,plain,
    ( ! [X0] :
        ( member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,domain_relation)
        | y = X0 )
    | ~ spl0_1092 ),
    inference(avatar_component_clause,[],[f33911]) ).

fof(f34013,plain,
    ( spl0_1113
    | ~ spl0_168
    | ~ spl0_1091 ),
    inference(avatar_split_clause,[],[f33909,f33906,f1428,f34011]) ).

fof(f34011,plain,
    ( spl0_1113
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f33906,plain,
    ( spl0_1091
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f33909,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) )
    | ~ spl0_168
    | ~ spl0_1091 ),
    inference(forward_demodulation,[],[f33907,f1430]) ).

fof(f33907,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,omega)
        | y = X0
        | ~ inductive(X1) )
    | ~ spl0_1091 ),
    inference(avatar_component_clause,[],[f33906]) ).

fof(f34009,plain,
    ( spl0_1112
    | ~ spl0_168
    | ~ spl0_1090 ),
    inference(avatar_split_clause,[],[f33904,f33901,f1428,f34007]) ).

fof(f34007,plain,
    ( spl0_1112
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f33901,plain,
    ( spl0_1090
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f33904,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1090 ),
    inference(forward_demodulation,[],[f33902,f1430]) ).

fof(f33902,plain,
    ( ! [X0] :
        ( member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,successor_relation)
        | y = X0 )
    | ~ spl0_1090 ),
    inference(avatar_component_clause,[],[f33901]) ).

fof(f34005,plain,
    ( spl0_1111
    | ~ spl0_168
    | ~ spl0_1089 ),
    inference(avatar_split_clause,[],[f33899,f33896,f1428,f34003]) ).

fof(f34003,plain,
    ( spl0_1111
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f33896,plain,
    ( spl0_1089
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f33899,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1089 ),
    inference(forward_demodulation,[],[f33897,f1430]) ).

fof(f33897,plain,
    ( ! [X0] :
        ( member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,element_relation)
        | y = X0 )
    | ~ spl0_1089 ),
    inference(avatar_component_clause,[],[f33896]) ).

fof(f34001,plain,
    ( spl0_1110
    | ~ spl0_168
    | ~ spl0_1086 ),
    inference(avatar_split_clause,[],[f33884,f33881,f1428,f33999]) ).

fof(f33999,plain,
    ( spl0_1110
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,subset_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f33881,plain,
    ( spl0_1086
  <=> ! [X0] :
        ( ~ subclass(X0,subset_relation)
        | y = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f33884,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,subset_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_168
    | ~ spl0_1086 ),
    inference(forward_demodulation,[],[f33882,f1430]) ).

fof(f33882,plain,
    ( ! [X0] :
        ( member(regular(X0),cross_product(universal_class,universal_class))
        | y = X0
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_1086 ),
    inference(avatar_component_clause,[],[f33881]) ).

fof(f33997,plain,
    ( ~ spl0_1109
    | ~ spl0_168
    | spl0_785 ),
    inference(avatar_split_clause,[],[f27701,f18374,f1428,f33994]) ).

fof(f33994,plain,
    ( spl0_1109
  <=> subclass(universal_class,rotate(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f18374,plain,
    ( spl0_785
  <=> subclass(universal_class,rotate(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f27701,plain,
    ( ~ subclass(universal_class,rotate(singleton_relation))
    | ~ spl0_168
    | spl0_785 ),
    inference(superposition,[],[f18376,f1430]) ).

fof(f18376,plain,
    ( ~ subclass(universal_class,rotate(y))
    | spl0_785 ),
    inference(avatar_component_clause,[],[f18374]) ).

fof(f33991,plain,
    ( spl0_1108
    | ~ spl0_297
    | ~ spl0_495 ),
    inference(avatar_split_clause,[],[f7533,f7271,f3231,f33989]) ).

fof(f33989,plain,
    ( spl0_1108
  <=> ! [X0,X1] :
        ( subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f7271,plain,
    ( spl0_495
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f7533,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
        | y = X1 )
    | ~ spl0_297
    | ~ spl0_495 ),
    inference(duplicate_literal_removal,[],[f7484]) ).

fof(f7484,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
        | subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
        | y = X1 )
    | ~ spl0_297
    | ~ spl0_495 ),
    inference(resolution,[],[f7272,f3232]) ).

fof(f7272,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_495 ),
    inference(avatar_component_clause,[],[f7271]) ).

fof(f33986,plain,
    ( spl0_1107
    | ~ spl0_298
    | ~ spl0_495 ),
    inference(avatar_split_clause,[],[f7532,f7271,f3235,f33984]) ).

fof(f33984,plain,
    ( spl0_1107
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f7532,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
        | y = X1 )
    | ~ spl0_298
    | ~ spl0_495 ),
    inference(duplicate_literal_removal,[],[f7485]) ).

fof(f7485,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
        | subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
        | y = X1 )
    | ~ spl0_298
    | ~ spl0_495 ),
    inference(resolution,[],[f7272,f3236]) ).

fof(f33981,plain,
    ( spl0_1106
    | ~ spl0_2
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f4152,f4100,f213,f33979]) ).

fof(f4100,plain,
    ( spl0_341
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f4152,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_341 ),
    inference(duplicate_literal_removal,[],[f4145]) ).

fof(f4145,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = y
        | cross_product(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_341 ),
    inference(resolution,[],[f4101,f214]) ).

fof(f4101,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) = y )
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f4100]) ).

fof(f33976,plain,
    ( spl0_1105
    | ~ spl0_2
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f4143,f4096,f213,f33974]) ).

fof(f4096,plain,
    ( spl0_340
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f4143,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_340 ),
    inference(duplicate_literal_removal,[],[f4136]) ).

fof(f4136,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = y
        | cross_product(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_340 ),
    inference(resolution,[],[f4097,f214]) ).

fof(f4097,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) = y )
    | ~ spl0_340 ),
    inference(avatar_component_clause,[],[f4096]) ).

fof(f33972,plain,
    ( spl0_1104
    | ~ spl0_40
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f4048,f3977,f385,f33969]) ).

fof(f33969,plain,
    ( spl0_1104
  <=> member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f3977,plain,
    ( spl0_332
  <=> 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_332])]) ).

fof(f4048,plain,
    ( member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_40
    | ~ spl0_332 ),
    inference(resolution,[],[f3979,f386]) ).

fof(f3979,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_332 ),
    inference(avatar_component_clause,[],[f3977]) ).

fof(f33967,plain,
    ( ~ spl0_1103
    | ~ spl0_168
    | spl0_1100 ),
    inference(avatar_split_clause,[],[f33962,f33951,f1428,f33964]) ).

fof(f33964,plain,
    ( spl0_1103
  <=> universal_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f33951,plain,
    ( spl0_1100
  <=> universal_class = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f33962,plain,
    ( universal_class != singleton_relation
    | ~ spl0_168
    | spl0_1100 ),
    inference(forward_demodulation,[],[f33952,f1430]) ).

fof(f33952,plain,
    ( universal_class != y
    | spl0_1100 ),
    inference(avatar_component_clause,[],[f33951]) ).

fof(f33961,plain,
    ( spl0_1100
    | ~ spl0_1101
    | spl0_1102
    | ~ spl0_16
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3753,f3608,f278,f33959,f33955,f33951]) ).

fof(f33955,plain,
    ( spl0_1101
  <=> subclass(universal_class,regular(universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f3753,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(X0,X1),y)
        | ~ subclass(universal_class,regular(universal_class))
        | universal_class = y )
    | ~ spl0_16
    | ~ spl0_318 ),
    inference(resolution,[],[f3609,f279]) ).

fof(f33948,plain,
    ( spl0_1099
    | ~ spl0_109
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2967,f2838,f831,f33946]) ).

fof(f33946,plain,
    ( spl0_1099
  <=> ! [X0,X1] :
        ( y = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f2967,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1) )
    | ~ spl0_109
    | ~ spl0_275 ),
    inference(duplicate_literal_removal,[],[f2949]) ).

fof(f2949,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1)
        | y = intersection(X0,complement(X1)) )
    | ~ spl0_109
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f832]) ).

fof(f33944,plain,
    ( spl0_1098
    | ~ spl0_168
    | ~ spl0_567 ),
    inference(avatar_split_clause,[],[f13948,f9421,f1428,f33941]) ).

fof(f13948,plain,
    ( singleton_relation = domain_of(singleton_relation)
    | ~ spl0_168
    | ~ spl0_567 ),
    inference(superposition,[],[f9423,f1430]) ).

fof(f33938,plain,
    ( spl0_1097
    | ~ spl0_245
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2965,f2838,f2422,f33936]) ).

fof(f2965,plain,
    ( ! [X0] :
        ( y = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_245
    | ~ spl0_275 ),
    inference(duplicate_literal_removal,[],[f2952]) ).

fof(f2952,plain,
    ( ! [X0] :
        ( y = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation)
        | y = intersection(X0,complement(element_relation)) )
    | ~ spl0_245
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f2423]) ).

fof(f33933,plain,
    ( spl0_1096
    | ~ spl0_246
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2963,f2838,f2426,f33931]) ).

fof(f33931,plain,
    ( spl0_1096
  <=> ! [X0] :
        ( y = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f2963,plain,
    ( ! [X0] :
        ( y = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
    | ~ spl0_246
    | ~ spl0_275 ),
    inference(duplicate_literal_removal,[],[f2961]) ).

fof(f2961,plain,
    ( ! [X0] :
        ( y = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation)
        | y = intersection(X0,complement(subset_relation)) )
    | ~ spl0_246
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f2427]) ).

fof(f33928,plain,
    ( spl0_1095
    | ~ spl0_109
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2941,f2834,f831,f33926]) ).

fof(f33926,plain,
    ( spl0_1095
  <=> ! [X0,X1] :
        ( y = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f2941,plain,
    ( ! [X0,X1] :
        ( y = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0) )
    | ~ spl0_109
    | ~ spl0_274 ),
    inference(duplicate_literal_removal,[],[f2921]) ).

fof(f2921,plain,
    ( ! [X0,X1] :
        ( y = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0)
        | y = intersection(complement(X0),X1) )
    | ~ spl0_109
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f832]) ).

fof(f33923,plain,
    ( spl0_1094
    | ~ spl0_245
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2939,f2834,f2422,f33921]) ).

fof(f2939,plain,
    ( ! [X0] :
        ( y = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_245
    | ~ spl0_274 ),
    inference(duplicate_literal_removal,[],[f2924]) ).

fof(f2924,plain,
    ( ! [X0] :
        ( y = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation)
        | y = intersection(complement(element_relation),X0) )
    | ~ spl0_245
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f2423]) ).

fof(f33918,plain,
    ( spl0_1093
    | ~ spl0_246
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2937,f2834,f2426,f33916]) ).

fof(f33916,plain,
    ( spl0_1093
  <=> ! [X0] :
        ( y = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f2937,plain,
    ( ! [X0] :
        ( y = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
    | ~ spl0_246
    | ~ spl0_274 ),
    inference(duplicate_literal_removal,[],[f2933]) ).

fof(f2933,plain,
    ( ! [X0] :
        ( y = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation)
        | y = intersection(complement(subset_relation),X0) )
    | ~ spl0_246
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f2427]) ).

fof(f33913,plain,
    ( spl0_1092
    | ~ spl0_20
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2890,f2826,f296,f33911]) ).

fof(f296,plain,
    ( spl0_20
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f2890,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_20
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f298]) ).

fof(f298,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f33908,plain,
    ( spl0_1091
    | ~ spl0_19
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2884,f2826,f292,f33906]) ).

fof(f2884,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) )
    | ~ spl0_19
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f293]) ).

fof(f33903,plain,
    ( spl0_1090
    | ~ spl0_18
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2883,f2826,f287,f33901]) ).

fof(f287,plain,
    ( spl0_18
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f2883,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_18
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f289]) ).

fof(f289,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f287]) ).

fof(f33898,plain,
    ( spl0_1089
    | ~ spl0_17
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2878,f2826,f282,f33896]) ).

fof(f282,plain,
    ( spl0_17
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f2878,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_17
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f284]) ).

fof(f284,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f33894,plain,
    ( spl0_276
    | ~ spl0_1088
    | ~ spl0_109
    | spl0_277 ),
    inference(avatar_split_clause,[],[f2851,f2846,f831,f33891,f2842]) ).

fof(f2842,plain,
    ( spl0_276
  <=> y = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f33891,plain,
    ( spl0_1088
  <=> subclass(complement(cross_product(universal_class,universal_class)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f2846,plain,
    ( spl0_277
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f2851,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),subset_relation)
    | y = complement(cross_product(universal_class,universal_class))
    | ~ spl0_109
    | spl0_277 ),
    inference(resolution,[],[f2848,f832]) ).

fof(f2848,plain,
    ( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | spl0_277 ),
    inference(avatar_component_clause,[],[f2846]) ).

fof(f33889,plain,
    ( spl0_276
    | ~ spl0_1087
    | ~ spl0_246
    | spl0_277 ),
    inference(avatar_split_clause,[],[f2850,f2846,f2426,f33886,f2842]) ).

fof(f33886,plain,
    ( spl0_1087
  <=> subclass(complement(cross_product(universal_class,universal_class)),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f2850,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),identity_relation)
    | y = complement(cross_product(universal_class,universal_class))
    | ~ spl0_246
    | spl0_277 ),
    inference(resolution,[],[f2848,f2427]) ).

fof(f33883,plain,
    ( spl0_1086
    | ~ spl0_79
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2786,f2747,f642,f33881]) ).

fof(f2786,plain,
    ( ! [X0] :
        ( ~ subclass(X0,subset_relation)
        | y = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_79
    | ~ spl0_263 ),
    inference(superposition,[],[f2748,f644]) ).

fof(f33681,plain,
    ( ~ spl0_1085
    | ~ spl0_168
    | spl0_326 ),
    inference(avatar_split_clause,[],[f13936,f3804,f1428,f33678]) ).

fof(f33678,plain,
    ( spl0_1085
  <=> member(second(singleton_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f3804,plain,
    ( spl0_326
  <=> member(second(y),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f13936,plain,
    ( ~ member(second(singleton_relation),universal_class)
    | ~ spl0_168
    | spl0_326 ),
    inference(superposition,[],[f3805,f1430]) ).

fof(f3805,plain,
    ( ~ member(second(y),universal_class)
    | spl0_326 ),
    inference(avatar_component_clause,[],[f3804]) ).

fof(f33676,plain,
    ( spl0_1084
    | ~ spl0_168
    | ~ spl0_1077 ),
    inference(avatar_split_clause,[],[f33637,f33633,f1428,f33674]) ).

fof(f33674,plain,
    ( spl0_1084
  <=> ! [X0] :
        ( singleton_relation = X0
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f33633,plain,
    ( spl0_1077
  <=> ! [X0] :
        ( member(regular(X0),y)
        | y = X0
        | ~ subclass(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f33637,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,regular(X0)) )
    | ~ spl0_168
    | ~ spl0_1077 ),
    inference(forward_demodulation,[],[f33636,f1430]) ).

fof(f33636,plain,
    ( ! [X0] :
        ( member(regular(X0),singleton_relation)
        | y = X0
        | ~ subclass(X0,regular(X0)) )
    | ~ spl0_168
    | ~ spl0_1077 ),
    inference(forward_demodulation,[],[f33634,f1430]) ).

fof(f33634,plain,
    ( ! [X0] :
        ( ~ subclass(X0,regular(X0))
        | y = X0
        | member(regular(X0),y) )
    | ~ spl0_1077 ),
    inference(avatar_component_clause,[],[f33633]) ).

fof(f33672,plain,
    ( spl0_1083
    | ~ spl0_168
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f33631,f33628,f1428,f33670]) ).

fof(f33670,plain,
    ( spl0_1083
  <=> ! [X0] :
        ( unordered_pair(X0,X0) = singleton_relation
        | regular(unordered_pair(X0,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f33628,plain,
    ( spl0_1076
  <=> ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f33631,plain,
    ( ! [X0] :
        ( unordered_pair(X0,X0) = singleton_relation
        | regular(unordered_pair(X0,X0)) = X0 )
    | ~ spl0_168
    | ~ spl0_1076 ),
    inference(forward_demodulation,[],[f33629,f1430]) ).

fof(f33629,plain,
    ( ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = y )
    | ~ spl0_1076 ),
    inference(avatar_component_clause,[],[f33628]) ).

fof(f33668,plain,
    ( spl0_1082
    | ~ spl0_168
    | ~ spl0_1073 ),
    inference(avatar_split_clause,[],[f33578,f33575,f1428,f33666]) ).

fof(f33666,plain,
    ( spl0_1082
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,identity_relation)
        | ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f33575,plain,
    ( spl0_1073
  <=> ! [X0] :
        ( y = intersection(X0,identity_relation)
        | ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f33578,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,identity_relation)
        | ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
    | ~ spl0_168
    | ~ spl0_1073 ),
    inference(forward_demodulation,[],[f33576,f1430]) ).

fof(f33576,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(X0,identity_relation),complement(subset_relation))
        | y = intersection(X0,identity_relation) )
    | ~ spl0_1073 ),
    inference(avatar_component_clause,[],[f33575]) ).

fof(f33664,plain,
    ( spl0_1081
    | ~ spl0_168
    | ~ spl0_1072 ),
    inference(avatar_split_clause,[],[f33573,f33570,f1428,f33662]) ).

fof(f33662,plain,
    ( spl0_1081
  <=> ! [X0] :
        ( singleton_relation = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f33570,plain,
    ( spl0_1072
  <=> ! [X0] :
        ( y = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f33573,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_168
    | ~ spl0_1072 ),
    inference(forward_demodulation,[],[f33571,f1430]) ).

fof(f33571,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(identity_relation,X0),complement(subset_relation))
        | y = intersection(identity_relation,X0) )
    | ~ spl0_1072 ),
    inference(avatar_component_clause,[],[f33570]) ).

fof(f33655,plain,
    ( spl0_1080
    | ~ spl0_168
    | ~ spl0_1066 ),
    inference(avatar_split_clause,[],[f33544,f33541,f1428,f33653]) ).

fof(f33653,plain,
    ( spl0_1080
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(intersection(X0,X1),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f33541,plain,
    ( spl0_1066
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(intersection(X0,X1),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f33544,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(intersection(X0,X1),complement(X0)) )
    | ~ spl0_168
    | ~ spl0_1066 ),
    inference(forward_demodulation,[],[f33542,f1430]) ).

fof(f33542,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(X0,X1),complement(X0))
        | intersection(X0,X1) = y )
    | ~ spl0_1066 ),
    inference(avatar_component_clause,[],[f33541]) ).

fof(f33651,plain,
    ( spl0_1079
    | ~ spl0_168
    | ~ spl0_1065 ),
    inference(avatar_split_clause,[],[f33539,f33536,f1428,f33649]) ).

fof(f33649,plain,
    ( spl0_1079
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(intersection(X0,X1),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f33536,plain,
    ( spl0_1065
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(intersection(X0,X1),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f33539,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = singleton_relation
        | ~ subclass(intersection(X0,X1),complement(X1)) )
    | ~ spl0_168
    | ~ spl0_1065 ),
    inference(forward_demodulation,[],[f33537,f1430]) ).

fof(f33537,plain,
    ( ! [X0,X1] :
        ( ~ subclass(intersection(X0,X1),complement(X1))
        | intersection(X0,X1) = y )
    | ~ spl0_1065 ),
    inference(avatar_component_clause,[],[f33536]) ).

fof(f33641,plain,
    ( spl0_1078
    | ~ spl0_2
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f6189,f6115,f213,f33639]) ).

fof(f33639,plain,
    ( spl0_1078
  <=> ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | member(regular(X0),universal_class)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f6115,plain,
    ( spl0_446
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f6189,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | member(regular(X0),universal_class)
        | y = X0 )
    | ~ spl0_2
    | ~ spl0_446 ),
    inference(resolution,[],[f6116,f214]) ).

fof(f6116,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,universal_class) )
    | ~ spl0_446 ),
    inference(avatar_component_clause,[],[f6115]) ).

fof(f33635,plain,
    ( spl0_1077
    | ~ spl0_2
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3893,f3810,f213,f33633]) ).

fof(f3893,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | y = X0
        | ~ subclass(X0,regular(X0)) )
    | ~ spl0_2
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3829]) ).

fof(f3829,plain,
    ( ! [X0] :
        ( member(regular(X0),y)
        | y = X0
        | ~ subclass(X0,regular(X0))
        | y = X0
        | y = X0 )
    | ~ spl0_2
    | ~ spl0_327 ),
    inference(resolution,[],[f3811,f214]) ).

fof(f33630,plain,
    ( spl0_1076
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f3140,f2996,f33628]) ).

fof(f2996,plain,
    ( spl0_284
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f3140,plain,
    ( ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = y )
    | ~ spl0_284 ),
    inference(equality_resolution,[],[f2997]) ).

fof(f2997,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f2996]) ).

fof(f33606,plain,
    ( spl0_1075
    | spl0_882
    | ~ spl0_19
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2782,f2747,f292,f21901,f33604]) ).

fof(f33604,plain,
    ( spl0_1075
  <=> ! [X0,X1] :
        ( member(regular(omega),X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f2782,plain,
    ( ! [X0,X1] :
        ( omega = y
        | member(regular(omega),X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_19
    | ~ spl0_263 ),
    inference(resolution,[],[f2748,f293]) ).

fof(f33582,plain,
    ( spl0_1074
    | spl0_882
    | ~ spl0_19
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f2771,f2743,f292,f21901,f33580]) ).

fof(f33580,plain,
    ( spl0_1074
  <=> ! [X0,X1] :
        ( member(regular(omega),X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f2743,plain,
    ( spl0_262
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f2771,plain,
    ( ! [X0,X1] :
        ( omega = y
        | member(regular(omega),X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_19
    | ~ spl0_262 ),
    inference(resolution,[],[f2744,f293]) ).

fof(f2744,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = X0
        | member(regular(X0),X2) )
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f2743]) ).

fof(f33577,plain,
    ( spl0_1073
    | ~ spl0_248
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f2736,f2537,f2450,f33575]) ).

fof(f2736,plain,
    ( ! [X0] :
        ( y = intersection(X0,identity_relation)
        | ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
    | ~ spl0_248
    | ~ spl0_255 ),
    inference(duplicate_literal_removal,[],[f2732]) ).

fof(f2732,plain,
    ( ! [X0] :
        ( y = intersection(X0,identity_relation)
        | y = intersection(X0,identity_relation)
        | ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
    | ~ spl0_248
    | ~ spl0_255 ),
    inference(resolution,[],[f2538,f2451]) ).

fof(f33572,plain,
    ( spl0_1072
    | ~ spl0_248
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f2729,f2532,f2450,f33570]) ).

fof(f2729,plain,
    ( ! [X0] :
        ( y = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_248
    | ~ spl0_254 ),
    inference(duplicate_literal_removal,[],[f2725]) ).

fof(f2725,plain,
    ( ! [X0] :
        ( y = intersection(identity_relation,X0)
        | y = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_248
    | ~ spl0_254 ),
    inference(resolution,[],[f2533,f2451]) ).

fof(f33567,plain,
    ( spl0_1071
    | ~ spl0_248
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f2724,f2527,f2450,f33565]) ).

fof(f33565,plain,
    ( spl0_1071
  <=> ! [X0] :
        ( y = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f2724,plain,
    ( ! [X0] :
        ( y = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_248
    | ~ spl0_253 ),
    inference(duplicate_literal_removal,[],[f2720]) ).

fof(f2720,plain,
    ( ! [X0] :
        ( y = intersection(X0,singleton_relation)
        | y = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_248
    | ~ spl0_253 ),
    inference(resolution,[],[f2528,f2451]) ).

fof(f33562,plain,
    ( spl0_1070
    | ~ spl0_248
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2719,f2522,f2450,f33560]) ).

fof(f33560,plain,
    ( spl0_1070
  <=> ! [X0] :
        ( y = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f2719,plain,
    ( ! [X0] :
        ( y = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_248
    | ~ spl0_252 ),
    inference(duplicate_literal_removal,[],[f2715]) ).

fof(f2715,plain,
    ( ! [X0] :
        ( y = intersection(singleton_relation,X0)
        | y = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_248
    | ~ spl0_252 ),
    inference(resolution,[],[f2523,f2451]) ).

fof(f33558,plain,
    ( spl0_1069
    | ~ spl0_46
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f2714,f2482,f424,f33556]) ).

fof(f33556,plain,
    ( spl0_1069
  <=> ! [X0] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | member(regular(identity_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f2482,plain,
    ( spl0_250
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f2714,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | member(regular(identity_relation),X0) )
    | ~ spl0_46
    | ~ spl0_250 ),
    inference(resolution,[],[f2484,f425]) ).

fof(f2484,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_250 ),
    inference(avatar_component_clause,[],[f2482]) ).

fof(f33554,plain,
    ( ~ spl0_1068
    | ~ spl0_168
    | spl0_745 ),
    inference(avatar_split_clause,[],[f27699,f16067,f1428,f33551]) ).

fof(f33551,plain,
    ( spl0_1068
  <=> subclass(element_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f16067,plain,
    ( spl0_745
  <=> subclass(element_relation,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f27699,plain,
    ( ~ subclass(element_relation,singleton_relation)
    | ~ spl0_168
    | spl0_745 ),
    inference(superposition,[],[f16069,f1430]) ).

fof(f16069,plain,
    ( ~ subclass(element_relation,y)
    | spl0_745 ),
    inference(avatar_component_clause,[],[f16067]) ).

fof(f33549,plain,
    ( ~ spl0_1067
    | spl0_186
    | ~ spl0_248
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f2711,f2482,f2450,f1601,f33546]) ).

fof(f33546,plain,
    ( spl0_1067
  <=> subclass(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f2711,plain,
    ( identity_relation = y
    | ~ subclass(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
    | ~ spl0_248
    | ~ spl0_250 ),
    inference(resolution,[],[f2484,f2451]) ).

fof(f33543,plain,
    ( spl0_1066
    | ~ spl0_111
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2679,f2450,f852,f33541]) ).

fof(f2679,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(intersection(X0,X1),complement(X0)) )
    | ~ spl0_111
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f2652]) ).

fof(f2652,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(intersection(X0,X1),complement(X0))
        | intersection(X0,X1) = y )
    | ~ spl0_111
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f853]) ).

fof(f33538,plain,
    ( spl0_1065
    | ~ spl0_112
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2677,f2450,f856,f33536]) ).

fof(f2677,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(intersection(X0,X1),complement(X1)) )
    | ~ spl0_112
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f2654]) ).

fof(f2654,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(intersection(X0,X1),complement(X1))
        | intersection(X0,X1) = y )
    | ~ spl0_112
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f857]) ).

fof(f33534,plain,
    ( spl0_1064
    | ~ spl0_46
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f2515,f2454,f424,f33532]) ).

fof(f33532,plain,
    ( spl0_1064
  <=> ! [X0] :
        ( ~ subclass(complement(compose(element_relation,complement(identity_relation))),X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f2515,plain,
    ( ! [X0] :
        ( ~ subclass(complement(compose(element_relation,complement(identity_relation))),X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_46
    | ~ spl0_249 ),
    inference(resolution,[],[f2456,f425]) ).

fof(f33530,plain,
    ( ~ spl0_1063
    | spl0_276
    | ~ spl0_31
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f2241,f2231,f342,f2842,f33527]) ).

fof(f33527,plain,
    ( spl0_1063
  <=> function(complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f2231,plain,
    ( spl0_230
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f2241,plain,
    ( y = complement(cross_product(universal_class,universal_class))
    | ~ function(complement(cross_product(universal_class,universal_class)))
    | ~ spl0_31
    | ~ spl0_230 ),
    inference(resolution,[],[f2232,f343]) ).

fof(f2232,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = y )
    | ~ spl0_230 ),
    inference(avatar_component_clause,[],[f2231]) ).

fof(f33338,plain,
    ( spl0_1062
    | ~ spl0_168
    | ~ spl0_1054 ),
    inference(avatar_split_clause,[],[f33294,f33291,f1428,f33336]) ).

fof(f33291,plain,
    ( spl0_1054
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(X1,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f33294,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X1,complement(X0))
        | ~ subclass(complement(X0),X0) )
    | ~ spl0_168
    | ~ spl0_1054 ),
    inference(forward_demodulation,[],[f33292,f1430]) ).

fof(f33292,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(X1,complement(X0)) )
    | ~ spl0_1054 ),
    inference(avatar_component_clause,[],[f33291]) ).

fof(f33334,plain,
    ( spl0_1061
    | ~ spl0_168
    | ~ spl0_1053 ),
    inference(avatar_split_clause,[],[f33289,f33286,f1428,f33332]) ).

fof(f33286,plain,
    ( spl0_1053
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f33289,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(complement(X0),X1)
        | ~ subclass(complement(X0),X0) )
    | ~ spl0_168
    | ~ spl0_1053 ),
    inference(forward_demodulation,[],[f33287,f1430]) ).

fof(f33287,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(complement(X0),X1) )
    | ~ spl0_1053 ),
    inference(avatar_component_clause,[],[f33286]) ).

fof(f33330,plain,
    ( spl0_1060
    | ~ spl0_168
    | ~ spl0_1052 ),
    inference(avatar_split_clause,[],[f33284,f33281,f1428,f33328]) ).

fof(f33328,plain,
    ( spl0_1060
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f33281,plain,
    ( spl0_1052
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f33284,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_1052 ),
    inference(forward_demodulation,[],[f33282,f1430]) ).

fof(f33282,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = X0
        | member(regular(X0),universal_class) )
    | ~ spl0_1052 ),
    inference(avatar_component_clause,[],[f33281]) ).

fof(f33326,plain,
    ( spl0_1059
    | ~ spl0_168
    | ~ spl0_1051 ),
    inference(avatar_split_clause,[],[f33279,f33276,f1428,f33324]) ).

fof(f33324,plain,
    ( spl0_1059
  <=> ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f33276,plain,
    ( spl0_1051
  <=> ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f33279,plain,
    ( ! [X0,X1] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_168
    | ~ spl0_1051 ),
    inference(forward_demodulation,[],[f33277,f1430]) ).

fof(f33277,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = X0
        | ~ subclass(X0,X1) )
    | ~ spl0_1051 ),
    inference(avatar_component_clause,[],[f33276]) ).

fof(f33322,plain,
    ( spl0_1058
    | ~ spl0_168
    | ~ spl0_1049 ),
    inference(avatar_split_clause,[],[f33269,f33266,f1428,f33320]) ).

fof(f33320,plain,
    ( spl0_1058
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f33266,plain,
    ( spl0_1049
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f33269,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_168
    | ~ spl0_1049 ),
    inference(forward_demodulation,[],[f33267,f1430]) ).

fof(f33267,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(subset_relation))
        | y = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_1049 ),
    inference(avatar_component_clause,[],[f33266]) ).

fof(f33318,plain,
    ( ~ spl0_1057
    | ~ spl0_168
    | spl0_572 ),
    inference(avatar_split_clause,[],[f13950,f9489,f1428,f33315]) ).

fof(f33315,plain,
    ( spl0_1057
  <=> singleton_relation = cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f9489,plain,
    ( spl0_572
  <=> y = cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f13950,plain,
    ( singleton_relation != cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class)
    | ~ spl0_168
    | spl0_572 ),
    inference(superposition,[],[f9490,f1430]) ).

fof(f9490,plain,
    ( y != cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
    | spl0_572 ),
    inference(avatar_component_clause,[],[f9489]) ).

fof(f33303,plain,
    ( spl0_1056
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567 ),
    inference(avatar_split_clause,[],[f27613,f9421,f8731,f1428,f33301]) ).

fof(f27613,plain,
    ( ! [X0] : ~ member(X0,singleton_relation)
    | ~ spl0_168
    | ~ spl0_550
    | ~ spl0_567 ),
    inference(forward_demodulation,[],[f13946,f13948]) ).

fof(f13946,plain,
    ( ! [X0] : ~ member(X0,domain_of(singleton_relation))
    | ~ spl0_168
    | ~ spl0_550 ),
    inference(superposition,[],[f8732,f1430]) ).

fof(f33299,plain,
    ( ~ spl0_239
    | spl0_1055
    | ~ spl0_203
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f4047,f3977,f1816,f33296,f2283]) ).

fof(f2283,plain,
    ( spl0_239
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f33296,plain,
    ( spl0_1055
  <=> member(regular(subset_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f1816,plain,
    ( spl0_203
  <=> ! [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_203])]) ).

fof(f4047,plain,
    ( member(regular(subset_relation),subset_relation)
    | ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_203
    | ~ spl0_332 ),
    inference(resolution,[],[f3979,f1817]) ).

fof(f1817,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_203 ),
    inference(avatar_component_clause,[],[f1816]) ).

fof(f33293,plain,
    ( spl0_1054
    | ~ spl0_275
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3115,f2988,f2838,f33291]) ).

fof(f3115,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(X1,complement(X0)) )
    | ~ spl0_275
    | ~ spl0_282 ),
    inference(duplicate_literal_removal,[],[f3088]) ).

fof(f3088,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(X1,complement(X0))
        | y = intersection(X1,complement(X0)) )
    | ~ spl0_275
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f2839]) ).

fof(f33288,plain,
    ( spl0_1053
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3063,f2980,f2834,f33286]) ).

fof(f3063,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(complement(X0),X1) )
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(duplicate_literal_removal,[],[f3034]) ).

fof(f3034,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | y = intersection(complement(X0),X1)
        | y = intersection(complement(X0),X1) )
    | ~ spl0_274
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f2835]) ).

fof(f33283,plain,
    ( spl0_1052
    | ~ spl0_8
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2873,f2826,f242,f33281]) ).

fof(f2873,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) )
    | ~ spl0_8
    | ~ spl0_272 ),
    inference(resolution,[],[f2827,f243]) ).

fof(f33278,plain,
    ( spl0_1051
    | ~ spl0_109
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2678,f2450,f831,f33276]) ).

fof(f2678,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_109
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f2653]) ).

fof(f2653,plain,
    ( ! [X0,X1] :
        ( y = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1)
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f832]) ).

fof(f33273,plain,
    ( spl0_1050
    | ~ spl0_245
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2676,f2450,f2422,f33271]) ).

fof(f2676,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_245
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f2660]) ).

fof(f2660,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation)
        | y = X0 )
    | ~ spl0_245
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f2423]) ).

fof(f33268,plain,
    ( spl0_1049
    | ~ spl0_246
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2675,f2450,f2426,f33266]) ).

fof(f2675,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_246
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f2670]) ).

fof(f2670,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation)
        | y = X0 )
    | ~ spl0_246
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f2427]) ).

fof(f33182,plain,
    ( spl0_1048
    | ~ spl0_168
    | ~ spl0_1045 ),
    inference(avatar_split_clause,[],[f33164,f33161,f1428,f33180]) ).

fof(f33161,plain,
    ( spl0_1045
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(complement(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f33164,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(complement(X1),X0)
        | ~ subclass(X0,X1) )
    | ~ spl0_168
    | ~ spl0_1045 ),
    inference(forward_demodulation,[],[f33162,f1430]) ).

fof(f33162,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(complement(X1),X0) )
    | ~ spl0_1045 ),
    inference(avatar_component_clause,[],[f33161]) ).

fof(f33178,plain,
    ( spl0_1047
    | ~ spl0_168
    | ~ spl0_1044 ),
    inference(avatar_split_clause,[],[f33159,f33156,f1428,f33176]) ).

fof(f33156,plain,
    ( spl0_1044
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f33159,plain,
    ( ! [X0,X1] :
        ( singleton_relation = intersection(X0,complement(X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_168
    | ~ spl0_1044 ),
    inference(forward_demodulation,[],[f33157,f1430]) ).

fof(f33157,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,complement(X1)) )
    | ~ spl0_1044 ),
    inference(avatar_component_clause,[],[f33156]) ).

fof(f33168,plain,
    ( spl0_1046
    | ~ spl0_168
    | ~ spl0_306 ),
    inference(avatar_split_clause,[],[f13934,f3490,f1428,f33166]) ).

fof(f33166,plain,
    ( spl0_1046
  <=> ! [X0,X1] :
        ( ~ member(singleton_relation,cross_product(X0,X1))
        | member(second(singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f3490,plain,
    ( spl0_306
  <=> ! [X0,X1] :
        ( ~ member(y,cross_product(X0,X1))
        | member(second(y),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f13934,plain,
    ( ! [X0,X1] :
        ( ~ member(singleton_relation,cross_product(X0,X1))
        | member(second(singleton_relation),X1) )
    | ~ spl0_168
    | ~ spl0_306 ),
    inference(superposition,[],[f3491,f1430]) ).

fof(f3491,plain,
    ( ! [X0,X1] :
        ( ~ member(y,cross_product(X0,X1))
        | member(second(y),X1) )
    | ~ spl0_306 ),
    inference(avatar_component_clause,[],[f3490]) ).

fof(f33163,plain,
    ( spl0_1045
    | ~ spl0_274
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f3116,f2988,f2834,f33161]) ).

fof(f3116,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(complement(X1),X0) )
    | ~ spl0_274
    | ~ spl0_282 ),
    inference(duplicate_literal_removal,[],[f3087]) ).

fof(f3087,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(complement(X1),X0)
        | y = intersection(complement(X1),X0) )
    | ~ spl0_274
    | ~ spl0_282 ),
    inference(resolution,[],[f2989,f2835]) ).

fof(f33158,plain,
    ( spl0_1044
    | ~ spl0_275
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f3062,f2980,f2838,f33156]) ).

fof(f3062,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,complement(X1)) )
    | ~ spl0_275
    | ~ spl0_280 ),
    inference(duplicate_literal_removal,[],[f3035]) ).

fof(f3035,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | y = intersection(X0,complement(X1))
        | y = intersection(X0,complement(X1)) )
    | ~ spl0_275
    | ~ spl0_280 ),
    inference(resolution,[],[f2981,f2839]) ).

fof(f33152,plain,
    ( spl0_1043
    | ~ spl0_160
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2871,f2822,f1347,f33150]) ).

fof(f33150,plain,
    ( spl0_1043
  <=> ! [X0,X1] :
        ( y = X0
        | subclass(intersection(y,X1),regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f2822,plain,
    ( spl0_271
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),y)
        | y = X1
        | subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f2871,plain,
    ( ! [X0,X1] :
        ( y = X0
        | subclass(intersection(y,X1),regular(X0)) )
    | ~ spl0_160
    | ~ spl0_271 ),
    inference(duplicate_literal_removal,[],[f2860]) ).

fof(f2860,plain,
    ( ! [X0,X1] :
        ( y = X0
        | subclass(intersection(y,X1),regular(X0))
        | subclass(intersection(y,X1),regular(X0)) )
    | ~ spl0_160
    | ~ spl0_271 ),
    inference(resolution,[],[f2823,f1348]) ).

fof(f2823,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),y)
        | y = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_271 ),
    inference(avatar_component_clause,[],[f2822]) ).

fof(f33146,plain,
    ( spl0_1042
    | ~ spl0_161
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2870,f2822,f1351,f33144]) ).

fof(f33144,plain,
    ( spl0_1042
  <=> ! [X0,X1] :
        ( y = X0
        | subclass(intersection(X1,y),regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f2870,plain,
    ( ! [X0,X1] :
        ( y = X0
        | subclass(intersection(X1,y),regular(X0)) )
    | ~ spl0_161
    | ~ spl0_271 ),
    inference(duplicate_literal_removal,[],[f2861]) ).

fof(f2861,plain,
    ( ! [X0,X1] :
        ( y = X0
        | subclass(intersection(X1,y),regular(X0))
        | subclass(intersection(X1,y),regular(X0)) )
    | ~ spl0_161
    | ~ spl0_271 ),
    inference(resolution,[],[f2823,f1352]) ).

fof(f33142,plain,
    ( ~ spl0_1041
    | spl0_238
    | ~ spl0_239
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2657,f2450,f2283,f2279,f33139]) ).

fof(f33139,plain,
    ( spl0_1041
  <=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f2657,plain,
    ( subset_relation = y
    | ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
    | ~ spl0_239
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f2285]) ).

fof(f2285,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_239 ),
    inference(avatar_component_clause,[],[f2283]) ).

fof(f33137,plain,
    ( ~ spl0_1040
    | ~ spl0_168
    | spl0_882 ),
    inference(avatar_split_clause,[],[f27706,f21901,f1428,f33134]) ).

fof(f33134,plain,
    ( spl0_1040
  <=> omega = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f27706,plain,
    ( omega != singleton_relation
    | ~ spl0_168
    | spl0_882 ),
    inference(superposition,[],[f21902,f1430]) ).

fof(f21902,plain,
    ( omega != y
    | spl0_882 ),
    inference(avatar_component_clause,[],[f21901]) ).

fof(f33132,plain,
    ( spl0_1039
    | ~ spl0_46
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f2417,f2283,f424,f33130]) ).

fof(f33130,plain,
    ( spl0_1039
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f2417,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) )
    | ~ spl0_46
    | ~ spl0_239 ),
    inference(resolution,[],[f2285,f425]) ).

fof(f32498,plain,
    ( spl0_1038
    | ~ spl0_168
    | ~ spl0_1023 ),
    inference(avatar_split_clause,[],[f32375,f32372,f1428,f32496]) ).

fof(f32375,plain,
    ( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_168
    | ~ spl0_1023 ),
    inference(forward_demodulation,[],[f32373,f1430]) ).

fof(f32494,plain,
    ( spl0_1037
    | ~ spl0_168
    | ~ spl0_1022 ),
    inference(avatar_split_clause,[],[f32370,f32367,f1428,f32492]) ).

fof(f32370,plain,
    ( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_168
    | ~ spl0_1022 ),
    inference(forward_demodulation,[],[f32368,f1430]) ).

fof(f32490,plain,
    ( ~ spl0_10
    | spl0_1013 ),
    inference(avatar_contradiction_clause,[],[f32489]) ).

fof(f32489,plain,
    ( $false
    | ~ spl0_10
    | spl0_1013 ),
    inference(resolution,[],[f32267,f252]) ).

fof(f32267,plain,
    ( ~ subclass(element_relation,element_relation)
    | spl0_1013 ),
    inference(avatar_component_clause,[],[f32265]) ).

fof(f32265,plain,
    ( spl0_1013
  <=> subclass(element_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f32488,plain,
    ( spl0_1036
    | ~ spl0_168
    | ~ spl0_1021 ),
    inference(avatar_split_clause,[],[f32365,f32362,f1428,f32486]) ).

fof(f32365,plain,
    ( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_168
    | ~ spl0_1021 ),
    inference(forward_demodulation,[],[f32363,f1430]) ).

fof(f32484,plain,
    ( spl0_1035
    | ~ spl0_168
    | ~ spl0_1020 ),
    inference(avatar_split_clause,[],[f32360,f32357,f1428,f32482]) ).

fof(f32360,plain,
    ( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_168
    | ~ spl0_1020 ),
    inference(forward_demodulation,[],[f32358,f1430]) ).

fof(f32480,plain,
    ( ~ spl0_1034
    | ~ spl0_168
    | spl0_662 ),
    inference(avatar_split_clause,[],[f27693,f13193,f1428,f32477]) ).

fof(f32477,plain,
    ( spl0_1034
  <=> singleton_relation = domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f13193,plain,
    ( spl0_662
  <=> y = domain_of(domain_of(flip(cross_product(y,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f27693,plain,
    ( singleton_relation != domain_of(domain_of(flip(cross_product(singleton_relation,universal_class))))
    | ~ spl0_168
    | spl0_662 ),
    inference(superposition,[],[f13194,f1430]) ).

fof(f13194,plain,
    ( y != domain_of(domain_of(flip(cross_product(y,universal_class))))
    | spl0_662 ),
    inference(avatar_component_clause,[],[f13193]) ).

fof(f32475,plain,
    ( ~ spl0_1033
    | ~ spl0_168
    | spl0_293 ),
    inference(avatar_split_clause,[],[f13928,f3213,f1428,f32472]) ).

fof(f32472,plain,
    ( spl0_1033
  <=> inductive(domain_of(regular(cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f3213,plain,
    ( spl0_293
  <=> inductive(domain_of(regular(cross_product(unordered_pair(y,y),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f13928,plain,
    ( ~ inductive(domain_of(regular(cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class))))
    | ~ spl0_168
    | spl0_293 ),
    inference(superposition,[],[f3215,f1430]) ).

fof(f3215,plain,
    ( ~ inductive(domain_of(regular(cross_product(unordered_pair(y,y),universal_class))))
    | spl0_293 ),
    inference(avatar_component_clause,[],[f3213]) ).

fof(f32450,plain,
    ( spl0_1031
    | spl0_1032
    | ~ spl0_332
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f12024,f6115,f3977,f32448,f32444]) ).

fof(f32444,plain,
    ( spl0_1031
  <=> member(regular(subset_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f32448,plain,
    ( spl0_1032
  <=> ! [X0] : ~ member(regular(subset_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f12024,plain,
    ( ! [X0] :
        ( ~ member(regular(subset_relation),X0)
        | member(regular(subset_relation),universal_class) )
    | ~ spl0_332
    | ~ spl0_446 ),
    inference(resolution,[],[f3979,f6116]) ).

fof(f32421,plain,
    ( spl0_1029
    | spl0_1030
    | ~ spl0_250
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f6256,f6115,f2482,f32419,f32415]) ).

fof(f32415,plain,
    ( spl0_1029
  <=> member(regular(identity_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f32419,plain,
    ( spl0_1030
  <=> ! [X0] : ~ member(regular(identity_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f6256,plain,
    ( ! [X0] :
        ( ~ member(regular(identity_relation),X0)
        | member(regular(identity_relation),universal_class) )
    | ~ spl0_250
    | ~ spl0_446 ),
    inference(resolution,[],[f6116,f2484]) ).

fof(f32397,plain,
    ( spl0_1027
    | spl0_1028
    | ~ spl0_249
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f6252,f6115,f2454,f32395,f32391]) ).

fof(f32391,plain,
    ( spl0_1027
  <=> member(regular(singleton_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f32395,plain,
    ( spl0_1028
  <=> ! [X0] : ~ member(regular(singleton_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f6252,plain,
    ( ! [X0] :
        ( ~ member(regular(singleton_relation),X0)
        | member(regular(singleton_relation),universal_class) )
    | ~ spl0_249
    | ~ spl0_446 ),
    inference(resolution,[],[f6116,f2456]) ).

fof(f32389,plain,
    ( spl0_1026
    | ~ spl0_45
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3494,f2248,f405,f32387]) ).

fof(f32387,plain,
    ( spl0_1026
  <=> ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f405,plain,
    ( spl0_45
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f2248,plain,
    ( spl0_233
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f3494,plain,
    ( ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_45
    | ~ spl0_233 ),
    inference(resolution,[],[f2249,f406]) ).

fof(f406,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f405]) ).

fof(f2249,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2248]) ).

fof(f32384,plain,
    ( spl0_1025
    | ~ spl0_35
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3419,f3235,f365,f32382]) ).

fof(f32382,plain,
    ( spl0_1025
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f365,plain,
    ( spl0_35
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f3419,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = X1 )
    | ~ spl0_35
    | ~ spl0_298 ),
    inference(duplicate_literal_removal,[],[f3391]) ).

fof(f3391,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | y = X1
        | subclass(intersection(X0,y),X1) )
    | ~ spl0_35
    | ~ spl0_298 ),
    inference(resolution,[],[f3236,f366]) ).

fof(f366,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f365]) ).

fof(f32379,plain,
    ( spl0_1024
    | ~ spl0_35
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f3390,f3231,f365,f32377]) ).

fof(f32377,plain,
    ( spl0_1024
  <=> ! [X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f3390,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = X1 )
    | ~ spl0_35
    | ~ spl0_297 ),
    inference(duplicate_literal_removal,[],[f3362]) ).

fof(f3362,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | y = X1
        | subclass(intersection(y,X0),X1) )
    | ~ spl0_35
    | ~ spl0_297 ),
    inference(resolution,[],[f3232,f366]) ).

fof(f32374,plain,
    ( spl0_1023
    | ~ spl0_274
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f3353,f3209,f2834,f32372]) ).

fof(f3353,plain,
    ( ! [X0,X1] : y = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_274
    | ~ spl0_292 ),
    inference(duplicate_literal_removal,[],[f3325]) ).

fof(f3325,plain,
    ( ! [X0,X1] :
        ( y = intersection(complement(X0),intersection(X0,X1))
        | y = intersection(complement(X0),intersection(X0,X1)) )
    | ~ spl0_274
    | ~ spl0_292 ),
    inference(resolution,[],[f3210,f2835]) ).

fof(f32369,plain,
    ( spl0_1022
    | ~ spl0_274
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f3324,f3205,f2834,f32367]) ).

fof(f3324,plain,
    ( ! [X0,X1] : y = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_274
    | ~ spl0_291 ),
    inference(duplicate_literal_removal,[],[f3296]) ).

fof(f3296,plain,
    ( ! [X0,X1] :
        ( y = intersection(complement(X0),intersection(X1,X0))
        | y = intersection(complement(X0),intersection(X1,X0)) )
    | ~ spl0_274
    | ~ spl0_291 ),
    inference(resolution,[],[f3206,f2835]) ).

fof(f32364,plain,
    ( spl0_1021
    | ~ spl0_275
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f3295,f3201,f2838,f32362]) ).

fof(f3295,plain,
    ( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_275
    | ~ spl0_290 ),
    inference(duplicate_literal_removal,[],[f3267]) ).

fof(f3267,plain,
    ( ! [X0,X1] :
        ( y = intersection(intersection(X0,X1),complement(X0))
        | y = intersection(intersection(X0,X1),complement(X0)) )
    | ~ spl0_275
    | ~ spl0_290 ),
    inference(resolution,[],[f3202,f2839]) ).

fof(f32359,plain,
    ( spl0_1020
    | ~ spl0_275
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f3266,f3197,f2838,f32357]) ).

fof(f3266,plain,
    ( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_275
    | ~ spl0_289 ),
    inference(duplicate_literal_removal,[],[f3238]) ).

fof(f3238,plain,
    ( ! [X0,X1] :
        ( y = intersection(intersection(X0,X1),complement(X1))
        | y = intersection(intersection(X0,X1),complement(X1)) )
    | ~ spl0_275
    | ~ spl0_289 ),
    inference(resolution,[],[f3198,f2839]) ).

fof(f32347,plain,
    ( spl0_700
    | ~ spl0_1001 ),
    inference(avatar_contradiction_clause,[],[f32301]) ).

fof(f32301,plain,
    ( $false
    | spl0_700
    | ~ spl0_1001 ),
    inference(resolution,[],[f31969,f14832]) ).

fof(f14832,plain,
    ( ~ subclass(singleton_relation,complement(element_relation))
    | spl0_700 ),
    inference(avatar_component_clause,[],[f14830]) ).

fof(f14830,plain,
    ( spl0_700
  <=> subclass(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f31969,plain,
    ( ! [X0] : subclass(singleton_relation,X0)
    | ~ spl0_1001 ),
    inference(avatar_component_clause,[],[f31968]) ).

fof(f32346,plain,
    ( spl0_921
    | ~ spl0_1001 ),
    inference(avatar_contradiction_clause,[],[f32302]) ).

fof(f32302,plain,
    ( $false
    | spl0_921
    | ~ spl0_1001 ),
    inference(resolution,[],[f31969,f24325]) ).

fof(f24325,plain,
    ( ~ subclass(singleton_relation,identity_relation)
    | spl0_921 ),
    inference(avatar_component_clause,[],[f24323]) ).

fof(f24323,plain,
    ( spl0_921
  <=> subclass(singleton_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f32345,plain,
    ( spl0_922
    | ~ spl0_1001 ),
    inference(avatar_contradiction_clause,[],[f32303]) ).

fof(f32303,plain,
    ( $false
    | spl0_922
    | ~ spl0_1001 ),
    inference(resolution,[],[f31969,f25004]) ).

fof(f25004,plain,
    ( ~ subclass(singleton_relation,subset_relation)
    | spl0_922 ),
    inference(avatar_component_clause,[],[f25002]) ).

fof(f25002,plain,
    ( spl0_922
  <=> subclass(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f32300,plain,
    ( spl0_1019
    | ~ spl0_187
    | ~ spl0_167
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f2712,f2482,f1424,f1605,f32297]) ).

fof(f32297,plain,
    ( spl0_1019
  <=> member(regular(identity_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f1424,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

fof(f2712,plain,
    ( ~ member(regular(identity_relation),subset_relation)
    | member(regular(identity_relation),identity_relation)
    | ~ spl0_167
    | ~ spl0_250 ),
    inference(resolution,[],[f2484,f1425]) ).

fof(f1425,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1424]) ).

fof(f32295,plain,
    ( ~ spl0_1018
    | spl0_123
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2471,f1428,f973,f32292]) ).

fof(f32292,plain,
    ( spl0_1018
  <=> member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f973,plain,
    ( spl0_123
  <=> member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f2471,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class)
    | spl0_123
    | ~ spl0_168 ),
    inference(superposition,[],[f974,f1430]) ).

fof(f974,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
    | spl0_123 ),
    inference(avatar_component_clause,[],[f973]) ).

fof(f32290,plain,
    ( ~ spl0_1017
    | spl0_4
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2466,f1428,f223,f32287]) ).

fof(f2466,plain,
    ( singleton_relation != domain_of(intersection(x,cross_product(singleton_relation,singleton_relation)))
    | spl0_4
    | ~ spl0_168 ),
    inference(superposition,[],[f225,f1430]) ).

fof(f32283,plain,
    ( ~ spl0_1016
    | ~ spl0_168
    | spl0_569 ),
    inference(avatar_split_clause,[],[f13949,f9473,f1428,f32280]) ).

fof(f32280,plain,
    ( spl0_1016
  <=> inductive(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f9473,plain,
    ( spl0_569
  <=> inductive(domain_of(domain_of(flip(cross_product(y,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f13949,plain,
    ( ~ inductive(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))))
    | ~ spl0_168
    | spl0_569 ),
    inference(superposition,[],[f9475,f1430]) ).

fof(f9475,plain,
    ( ~ inductive(domain_of(domain_of(flip(cross_product(y,universal_class)))))
    | spl0_569 ),
    inference(avatar_component_clause,[],[f9473]) ).

fof(f32278,plain,
    ( ~ spl0_1015
    | ~ spl0_168
    | spl0_294 ),
    inference(avatar_split_clause,[],[f13929,f3217,f1428,f32275]) ).

fof(f32275,plain,
    ( spl0_1015
  <=> singleton_relation = cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f3217,plain,
    ( spl0_294
  <=> y = cross_product(unordered_pair(y,y),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f13929,plain,
    ( singleton_relation != cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)
    | ~ spl0_168
    | spl0_294 ),
    inference(superposition,[],[f3218,f1430]) ).

fof(f3218,plain,
    ( y != cross_product(unordered_pair(y,y),universal_class)
    | spl0_294 ),
    inference(avatar_component_clause,[],[f3217]) ).

fof(f32273,plain,
    ( ~ spl0_1014
    | ~ spl0_168
    | spl0_241 ),
    inference(avatar_split_clause,[],[f13925,f2306,f1428,f32270]) ).

fof(f32270,plain,
    ( spl0_1014
  <=> member(singleton_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f2306,plain,
    ( spl0_241
  <=> member(y,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f13925,plain,
    ( ~ member(singleton_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_168
    | spl0_241 ),
    inference(superposition,[],[f2307,f1430]) ).

fof(f2307,plain,
    ( ~ member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_241 ),
    inference(avatar_component_clause,[],[f2306]) ).

fof(f32268,plain,
    ( ~ spl0_1013
    | spl0_169
    | ~ spl0_691 ),
    inference(avatar_split_clause,[],[f27714,f13889,f1432,f32265]) ).

fof(f13889,plain,
    ( spl0_691
  <=> ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f27714,plain,
    ( ~ subclass(element_relation,element_relation)
    | spl0_169
    | ~ spl0_691 ),
    inference(resolution,[],[f1433,f13890]) ).

fof(f13890,plain,
    ( ! [X0] :
        ( member(regular(singleton_relation),X0)
        | ~ subclass(element_relation,X0) )
    | ~ spl0_691 ),
    inference(avatar_component_clause,[],[f13889]) ).

fof(f1433,plain,
    ( ~ member(regular(singleton_relation),element_relation)
    | spl0_169 ),
    inference(avatar_component_clause,[],[f1432]) ).

fof(f32263,plain,
    ( ~ spl0_1012
    | ~ spl0_168
    | spl0_235 ),
    inference(avatar_split_clause,[],[f2475,f2263,f1428,f32260]) ).

fof(f32260,plain,
    ( spl0_1012
  <=> member(singleton_relation,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f2263,plain,
    ( spl0_235
  <=> member(y,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f2475,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_168
    | spl0_235 ),
    inference(superposition,[],[f2264,f1430]) ).

fof(f2264,plain,
    ( ~ member(y,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | spl0_235 ),
    inference(avatar_component_clause,[],[f2263]) ).

fof(f32251,plain,
    ( spl0_1011
    | ~ spl0_46
    | ~ spl0_375 ),
    inference(avatar_split_clause,[],[f29539,f4993,f424,f32249]) ).

fof(f29539,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(singleton_relation,X0) )
    | ~ spl0_46
    | ~ spl0_375 ),
    inference(resolution,[],[f4994,f425]) ).

fof(f32247,plain,
    ( ~ spl0_1010
    | ~ spl0_168
    | spl0_854 ),
    inference(avatar_split_clause,[],[f27705,f21109,f1428,f32244]) ).

fof(f21109,plain,
    ( spl0_854
  <=> operation(domain_of(flip(cross_product(y,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f27705,plain,
    ( ~ operation(domain_of(flip(cross_product(singleton_relation,universal_class))))
    | ~ spl0_168
    | spl0_854 ),
    inference(superposition,[],[f21111,f1430]) ).

fof(f21111,plain,
    ( ~ operation(domain_of(flip(cross_product(y,universal_class))))
    | spl0_854 ),
    inference(avatar_component_clause,[],[f21109]) ).

fof(f32242,plain,
    ( ~ spl0_1009
    | ~ spl0_168
    | spl0_304 ),
    inference(avatar_split_clause,[],[f13932,f3480,f1428,f32239]) ).

fof(f32239,plain,
    ( spl0_1009
  <=> second(singleton_relation) = domain_of(first(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f3480,plain,
    ( spl0_304
  <=> second(y) = domain_of(first(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f13932,plain,
    ( second(singleton_relation) != domain_of(first(singleton_relation))
    | ~ spl0_168
    | spl0_304 ),
    inference(superposition,[],[f3481,f1430]) ).

fof(f3481,plain,
    ( second(y) != domain_of(first(y))
    | spl0_304 ),
    inference(avatar_component_clause,[],[f3480]) ).

fof(f32171,plain,
    ( ~ spl0_1008
    | spl0_124
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f13920,f1428,f978,f32168]) ).

fof(f32168,plain,
    ( spl0_1008
  <=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f978,plain,
    ( spl0_124
  <=> member(y,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f13920,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | spl0_124
    | ~ spl0_168 ),
    inference(superposition,[],[f980,f1430]) ).

fof(f980,plain,
    ( ~ member(y,cross_product(universal_class,universal_class))
    | spl0_124 ),
    inference(avatar_component_clause,[],[f978]) ).

fof(f32166,plain,
    ( ~ spl0_1007
    | ~ spl0_168
    | spl0_823 ),
    inference(avatar_split_clause,[],[f27704,f19881,f1428,f32163]) ).

fof(f32163,plain,
    ( spl0_1007
  <=> member(singleton_relation,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f19881,plain,
    ( spl0_823
  <=> member(y,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f27704,plain,
    ( ~ member(singleton_relation,composition_function)
    | ~ spl0_168
    | spl0_823 ),
    inference(superposition,[],[f19883,f1430]) ).

fof(f19883,plain,
    ( ~ member(y,composition_function)
    | spl0_823 ),
    inference(avatar_component_clause,[],[f19881]) ).

fof(f32161,plain,
    ( spl0_1006
    | ~ spl0_1
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2465,f1428,f209,f32159]) ).

fof(f209,plain,
    ( spl0_1
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f2465,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ inductive(X0) )
    | ~ spl0_1
    | ~ spl0_168 ),
    inference(superposition,[],[f210,f1430]) ).

fof(f210,plain,
    ( ! [X0] :
        ( member(y,X0)
        | ~ inductive(X0) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f209]) ).

fof(f32095,plain,
    ( spl0_1005
    | ~ spl0_91
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1973,f1943,f710,f32093]) ).

fof(f32093,plain,
    ( spl0_1005
  <=> ! [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_1005])]) ).

fof(f710,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(f1943,plain,
    ( spl0_215
  <=> ! [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_215])]) ).

fof(f1973,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_215 ),
    inference(resolution,[],[f1944,f711]) ).

fof(f711,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,[],[f710]) ).

fof(f1944,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_215 ),
    inference(avatar_component_clause,[],[f1943]) ).

fof(f32091,plain,
    ( spl0_1004
    | ~ spl0_91
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1947,f1939,f710,f32089]) ).

fof(f32089,plain,
    ( spl0_1004
  <=> ! [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_1004])]) ).

fof(f1939,plain,
    ( spl0_214
  <=> ! [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_214])]) ).

fof(f1947,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_214 ),
    inference(resolution,[],[f1940,f711]) ).

fof(f1940,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_214 ),
    inference(avatar_component_clause,[],[f1939]) ).

fof(f32047,plain,
    ( spl0_1003
    | ~ spl0_139
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2207,f2203,f1089,f32045]) ).

fof(f32045,plain,
    ( spl0_1003
  <=> ! [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_1003])]) ).

fof(f2203,plain,
    ( spl0_226
  <=> ! [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_226])]) ).

fof(f2207,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_139
    | ~ spl0_226 ),
    inference(resolution,[],[f2204,f1090]) ).

fof(f2204,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_226 ),
    inference(avatar_component_clause,[],[f2203]) ).

fof(f32007,plain,
    ( spl0_1002
    | ~ spl0_103
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2011,f1999,f778,f32005]) ).

fof(f32005,plain,
    ( spl0_1002
  <=> ! [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_1002])]) ).

fof(f778,plain,
    ( spl0_103
  <=> ! [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_103])]) ).

fof(f1999,plain,
    ( spl0_216
  <=> ! [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_216])]) ).

fof(f2011,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_103
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f779]) ).

fof(f779,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_103 ),
    inference(avatar_component_clause,[],[f778]) ).

fof(f2000,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_216 ),
    inference(avatar_component_clause,[],[f1999]) ).

fof(f31970,plain,
    ( spl0_1001
    | ~ spl0_168
    | ~ spl0_427 ),
    inference(avatar_split_clause,[],[f13938,f5764,f1428,f31968]) ).

fof(f5764,plain,
    ( spl0_427
  <=> ! [X0] : subclass(y,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f13938,plain,
    ( ! [X0] : subclass(singleton_relation,X0)
    | ~ spl0_168
    | ~ spl0_427 ),
    inference(superposition,[],[f5765,f1430]) ).

fof(f5765,plain,
    ( ! [X0] : subclass(y,X0)
    | ~ spl0_427 ),
    inference(avatar_component_clause,[],[f5764]) ).

fof(f31966,plain,
    ( spl0_1000
    | ~ spl0_211
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2140,f2118,f1883,f31964]) ).

fof(f31964,plain,
    ( spl0_1000
  <=> ! [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_1000])]) ).

fof(f1883,plain,
    ( spl0_211
  <=> ! [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_211])]) ).

fof(f2118,plain,
    ( spl0_221
  <=> ! [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_221])]) ).

fof(f2140,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_211
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1884]) ).

fof(f1884,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_211 ),
    inference(avatar_component_clause,[],[f1883]) ).

fof(f2119,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_221 ),
    inference(avatar_component_clause,[],[f2118]) ).

fof(f31920,plain,
    ( spl0_999
    | ~ spl0_80
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2206,f2203,f647,f31918]) ).

fof(f31918,plain,
    ( spl0_999
  <=> ! [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_999])]) ).

fof(f647,plain,
    ( spl0_80
  <=> ! [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_80])]) ).

fof(f2206,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_80
    | ~ spl0_226 ),
    inference(resolution,[],[f2204,f648]) ).

fof(f648,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_80 ),
    inference(avatar_component_clause,[],[f647]) ).

fof(f31883,plain,
    ( spl0_998
    | ~ spl0_216
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2126,f2118,f1999,f31881]) ).

fof(f31881,plain,
    ( spl0_998
  <=> ! [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_998])]) ).

fof(f2126,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_216
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f2000]) ).

fof(f31846,plain,
    ( spl0_997
    | ~ spl0_93
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2145,f2118,f719,f31844]) ).

fof(f31844,plain,
    ( spl0_997
  <=> ! [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_997])]) ).

fof(f719,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(f2145,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_221 ),
    inference(resolution,[],[f2119,f720]) ).

fof(f720,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,[],[f719]) ).

fof(f31824,plain,
    ( spl0_996
    | ~ spl0_103
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1897,f1889,f778,f31822]) ).

fof(f31822,plain,
    ( spl0_996
  <=> ! [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_996])]) ).

fof(f1889,plain,
    ( spl0_212
  <=> ! [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_212])]) ).

fof(f1897,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_103
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f779]) ).

fof(f1890,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_212 ),
    inference(avatar_component_clause,[],[f1889]) ).

fof(f31820,plain,
    ( spl0_995
    | ~ spl0_103
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1707,f1646,f778,f31818]) ).

fof(f31818,plain,
    ( spl0_995
  <=> ! [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_995])]) ).

fof(f1646,plain,
    ( spl0_192
  <=> ! [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_192])]) ).

fof(f1707,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_103
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f779]) ).

fof(f1647,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_192 ),
    inference(avatar_component_clause,[],[f1646]) ).

fof(f31783,plain,
    ( spl0_994
    | ~ spl0_57
    | ~ spl0_103
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1285,f1264,f778,f500,f31781]) ).

fof(f31781,plain,
    ( spl0_994
  <=> ! [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_994])]) ).

fof(f500,plain,
    ( spl0_57
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1285,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_57
    | ~ spl0_103
    | ~ spl0_153 ),
    inference(forward_demodulation,[],[f1282,f501]) ).

fof(f501,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f500]) ).

fof(f1282,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_103
    | ~ spl0_153 ),
    inference(resolution,[],[f1265,f779]) ).

fof(f31779,plain,
    ( spl0_993
    | ~ spl0_103
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1096,f1078,f778,f31777]) ).

fof(f31777,plain,
    ( spl0_993
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(universal_class,domain_of(X0))
        | ~ homomorphism(X1,X0,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f1096,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_103
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f779]) ).

fof(f31611,plain,
    ( spl0_992
    | ~ spl0_96
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2016,f1999,f746,f31609]) ).

fof(f31609,plain,
    ( spl0_992
  <=> ! [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_992])]) ).

fof(f746,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(f2016,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_216 ),
    inference(resolution,[],[f2000,f747]) ).

fof(f747,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,[],[f746]) ).

fof(f31607,plain,
    ( spl0_990
    | ~ spl0_991
    | ~ spl0_101
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2018,f1999,f767,f31604,f31601]) ).

fof(f31601,plain,
    ( spl0_990
  <=> ! [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_990])]) ).

fof(f31604,plain,
    ( spl0_991
  <=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f767,plain,
    ( spl0_101
  <=> ! [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_101])]) ).

fof(f2018,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_101
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f768]) ).

fof(f768,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_101 ),
    inference(avatar_component_clause,[],[f767]) ).

fof(f31566,plain,
    ( spl0_989
    | ~ spl0_204
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2144,f2118,f1841,f31564]) ).

fof(f31564,plain,
    ( spl0_989
  <=> ! [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_989])]) ).

fof(f1841,plain,
    ( spl0_204
  <=> ! [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_204])]) ).

fof(f2144,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_204
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1842]) ).

fof(f1842,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_204 ),
    inference(avatar_component_clause,[],[f1841]) ).

fof(f31541,plain,
    ( spl0_988
    | ~ spl0_215
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2030,f1999,f1943,f31539]) ).

fof(f31539,plain,
    ( spl0_988
  <=> ! [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_988])]) ).

fof(f2030,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_215
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1944]) ).

fof(f31537,plain,
    ( spl0_987
    | ~ spl0_214
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2029,f1999,f1939,f31535]) ).

fof(f31535,plain,
    ( spl0_987
  <=> ! [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_987])]) ).

fof(f2029,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_214
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1940]) ).

fof(f31533,plain,
    ( spl0_986
    | ~ spl0_94
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2028,f1999,f725,f31531]) ).

fof(f31531,plain,
    ( spl0_986
  <=> ! [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_986])]) ).

fof(f725,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(f2028,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_216 ),
    inference(resolution,[],[f2000,f726]) ).

fof(f726,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,[],[f725]) ).

fof(f31469,plain,
    ( spl0_985
    | ~ spl0_216
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2149,f2122,f1999,f31467]) ).

fof(f31467,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(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_985])]) ).

fof(f2122,plain,
    ( spl0_222
  <=> ! [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_222])]) ).

fof(f2149,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_216
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f2000]) ).

fof(f2123,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_222 ),
    inference(avatar_component_clause,[],[f2122]) ).

fof(f31432,plain,
    ( spl0_984
    | ~ spl0_192
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2125,f2118,f1646,f31430]) ).

fof(f31430,plain,
    ( spl0_984
  <=> ! [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_984])]) ).

fof(f2125,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_192
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1647]) ).

fof(f31368,plain,
    ( spl0_983
    | ~ spl0_93
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2168,f2122,f719,f31366]) ).

fof(f31366,plain,
    ( spl0_983
  <=> ! [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_983])]) ).

fof(f2168,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_222 ),
    inference(resolution,[],[f2123,f720]) ).

fof(f31331,plain,
    ( spl0_982
    | ~ spl0_72
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2146,f2118,f605,f31329]) ).

fof(f31329,plain,
    ( spl0_982
  <=> ! [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_982])]) ).

fof(f605,plain,
    ( spl0_72
  <=> ! [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_72])]) ).

fof(f2146,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_72
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f606]) ).

fof(f606,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_72 ),
    inference(avatar_component_clause,[],[f605]) ).

fof(f31307,plain,
    ( spl0_981
    | ~ spl0_212
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2183,f2175,f1889,f31305]) ).

fof(f31305,plain,
    ( spl0_981
  <=> ! [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_981])]) ).

fof(f2175,plain,
    ( spl0_223
  <=> ! [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_223])]) ).

fof(f2183,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_212
    | ~ spl0_223 ),
    inference(resolution,[],[f2176,f1890]) ).

fof(f2176,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_223 ),
    inference(avatar_component_clause,[],[f2175]) ).

fof(f31249,plain,
    ( spl0_980
    | ~ spl0_211
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2172,f2122,f1883,f31247]) ).

fof(f31247,plain,
    ( spl0_980
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_980])]) ).

fof(f2172,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_211
    | ~ spl0_222 ),
    inference(duplicate_literal_removal,[],[f2163]) ).

fof(f2163,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_211
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1884]) ).

fof(f31224,plain,
    ( spl0_979
    | ~ spl0_212
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1992,f1943,f1889,f31222]) ).

fof(f31222,plain,
    ( spl0_979
  <=> ! [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_979])]) ).

fof(f1992,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_212
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1890]) ).

fof(f31220,plain,
    ( spl0_978
    | ~ spl0_212
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1966,f1939,f1889,f31218]) ).

fof(f31218,plain,
    ( spl0_978
  <=> ! [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_978])]) ).

fof(f1966,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_212
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1890]) ).

fof(f31216,plain,
    ( spl0_977
    | ~ spl0_94
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1910,f1889,f725,f31214]) ).

fof(f31214,plain,
    ( spl0_977
  <=> ! [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_977])]) ).

fof(f1910,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_212 ),
    inference(resolution,[],[f1890,f726]) ).

fof(f30949,plain,
    ( spl0_976
    | ~ spl0_161
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1981,f1943,f1351,f30947]) ).

fof(f30947,plain,
    ( spl0_976
  <=> ! [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_976])]) ).

fof(f1981,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_161
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1352]) ).

fof(f30945,plain,
    ( spl0_975
    | ~ spl0_160
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1975,f1943,f1347,f30943]) ).

fof(f30943,plain,
    ( spl0_975
  <=> ! [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_975])]) ).

fof(f1975,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_160
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1348]) ).

fof(f30941,plain,
    ( spl0_974
    | ~ spl0_161
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1955,f1939,f1351,f30939]) ).

fof(f30939,plain,
    ( spl0_974
  <=> ! [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_974])]) ).

fof(f1955,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_161
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1352]) ).

fof(f30937,plain,
    ( spl0_973
    | ~ spl0_160
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1949,f1939,f1347,f30935]) ).

fof(f30935,plain,
    ( spl0_973
  <=> ! [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_973])]) ).

fof(f1949,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_160
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1348]) ).

fof(f30933,plain,
    ( spl0_972
    | ~ spl0_94
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1395,f1351,f725,f30931]) ).

fof(f30931,plain,
    ( spl0_972
  <=> ! [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_972])]) ).

fof(f1395,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_161 ),
    inference(resolution,[],[f1352,f726]) ).

fof(f30929,plain,
    ( spl0_971
    | ~ spl0_94
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1374,f1347,f725,f30927]) ).

fof(f30927,plain,
    ( spl0_971
  <=> ! [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_971])]) ).

fof(f1374,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_160 ),
    inference(resolution,[],[f1348,f726]) ).

fof(f30866,plain,
    ( spl0_970
    | ~ spl0_34
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1974,f1943,f361,f30864]) ).

fof(f30864,plain,
    ( spl0_970
  <=> ! [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_970])]) ).

fof(f1974,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_34
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f362]) ).

fof(f30862,plain,
    ( spl0_969
    | ~ spl0_34
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1948,f1939,f361,f30860]) ).

fof(f30860,plain,
    ( spl0_969
  <=> ! [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_969])]) ).

fof(f1948,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_34
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f362]) ).

fof(f30814,plain,
    ( spl0_968
    | ~ spl0_139
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2190,f2186,f1089,f30812]) ).

fof(f30812,plain,
    ( spl0_968
  <=> ! [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_968])]) ).

fof(f2186,plain,
    ( spl0_224
  <=> ! [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_224])]) ).

fof(f2190,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_139
    | ~ spl0_224 ),
    inference(resolution,[],[f2187,f1090]) ).

fof(f2187,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_224 ),
    inference(avatar_component_clause,[],[f2186]) ).

fof(f30651,plain,
    ( spl0_967
    | ~ spl0_99
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2017,f1999,f759,f30649]) ).

fof(f30649,plain,
    ( spl0_967
  <=> ! [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_967])]) ).

fof(f759,plain,
    ( spl0_99
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f2017,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_99
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f760]) ).

fof(f760,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_99 ),
    inference(avatar_component_clause,[],[f759]) ).

fof(f30647,plain,
    ( spl0_965
    | ~ spl0_966
    | ~ spl0_101
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1714,f1646,f767,f30644,f30641]) ).

fof(f30641,plain,
    ( spl0_965
  <=> ! [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_965])]) ).

fof(f30644,plain,
    ( spl0_966
  <=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f1714,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_101
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f768]) ).

fof(f30275,plain,
    ( spl0_964
    | ~ spl0_56
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2157,f2122,f496,f30273]) ).

fof(f30273,plain,
    ( spl0_964
  <=> ! [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_964])]) ).

fof(f2157,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_56
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f497]) ).

fof(f30271,plain,
    ( ~ spl0_963
    | ~ spl0_168
    | spl0_787 ),
    inference(avatar_split_clause,[],[f27702,f18712,f1428,f30268]) ).

fof(f30268,plain,
    ( spl0_963
  <=> member(singleton_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f18712,plain,
    ( spl0_787
  <=> member(y,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f27702,plain,
    ( ~ member(singleton_relation,successor_relation)
    | ~ spl0_168
    | spl0_787 ),
    inference(superposition,[],[f18714,f1430]) ).

fof(f18714,plain,
    ( ~ member(y,successor_relation)
    | spl0_787 ),
    inference(avatar_component_clause,[],[f18712]) ).

fof(f30266,plain,
    ( spl0_962
    | ~ spl0_56
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2134,f2118,f496,f30264]) ).

fof(f30264,plain,
    ( spl0_962
  <=> ! [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_962])]) ).

fof(f2134,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_56
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f497]) ).

fof(f30199,plain,
    ( spl0_961
    | ~ spl0_51
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2159,f2122,f472,f30197]) ).

fof(f30197,plain,
    ( spl0_961
  <=> ! [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_961])]) ).

fof(f2159,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_51
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f473]) ).

fof(f30195,plain,
    ( spl0_960
    | ~ spl0_51
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2136,f2118,f472,f30193]) ).

fof(f30193,plain,
    ( spl0_960
  <=> ! [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_960])]) ).

fof(f2136,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_51
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f473]) ).

fof(f29947,plain,
    ( spl0_959
    | ~ spl0_38
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2153,f2122,f377,f29945]) ).

fof(f29945,plain,
    ( spl0_959
  <=> ! [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_959])]) ).

fof(f2153,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_38
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f378]) ).

fof(f29943,plain,
    ( ~ spl0_958
    | ~ spl0_168
    | spl0_305 ),
    inference(avatar_split_clause,[],[f13933,f3484,f1428,f29940]) ).

fof(f29940,plain,
    ( spl0_958
  <=> member(singleton_relation,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f3484,plain,
    ( spl0_305
  <=> member(y,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f13933,plain,
    ( ~ member(singleton_relation,domain_relation)
    | ~ spl0_168
    | spl0_305 ),
    inference(superposition,[],[f3486,f1430]) ).

fof(f3486,plain,
    ( ~ member(y,domain_relation)
    | spl0_305 ),
    inference(avatar_component_clause,[],[f3484]) ).

fof(f29938,plain,
    ( spl0_957
    | ~ spl0_36
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2152,f2122,f369,f29936]) ).

fof(f29936,plain,
    ( spl0_957
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_957])]) ).

fof(f2152,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_36
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f370]) ).

fof(f29934,plain,
    ( spl0_956
    | ~ spl0_38
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2130,f2118,f377,f29932]) ).

fof(f29932,plain,
    ( spl0_956
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_956])]) ).

fof(f2130,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_38
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f378]) ).

fof(f29930,plain,
    ( spl0_955
    | ~ spl0_36
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2129,f2118,f369,f29928]) ).

fof(f29928,plain,
    ( spl0_955
  <=> ! [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_955])]) ).

fof(f2129,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_36
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f370]) ).

fof(f29908,plain,
    ( spl0_954
    | ~ spl0_32
    | ~ spl0_102
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2005,f1999,f773,f347,f29906]) ).

fof(f29906,plain,
    ( spl0_954
  <=> ! [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_954])]) ).

fof(f773,plain,
    ( spl0_102
  <=> ! [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_102])]) ).

fof(f2005,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_102
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f774]) ).

fof(f774,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_102 ),
    inference(avatar_component_clause,[],[f773]) ).

fof(f29887,plain,
    ( spl0_953
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(avatar_split_clause,[],[f29883,f29875,f1428,f29885]) ).

fof(f29885,plain,
    ( spl0_953
  <=> ! [X0,X3,X2,X1] :
        ( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f29883,plain,
    ( ! [X2,X3,X0,X1] :
        ( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3) )
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f29882,f1430]) ).

fof(f29882,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | ~ operation(X3)
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f29881,f1430]) ).

fof(f29881,plain,
    ( ! [X2,X3,X0,X1] :
        ( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f29880,f1430]) ).

fof(f29880,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f29879,f1430]) ).

fof(f29879,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(domain_of(domain_of(flip(cross_product(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,universal_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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f29878,f1430]) ).

fof(f29878,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(singleton_relation,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_952 ),
    inference(forward_demodulation,[],[f29876,f1430]) ).

fof(f29877,plain,
    ( spl0_952
    | ~ spl0_7
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2210,f2203,f238,f29875]) ).

fof(f238,plain,
    ( spl0_7
  <=> ! [X0] :
        ( y = X0
        | intersection(X0,regular(X0)) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f2210,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_226 ),
    inference(superposition,[],[f2204,f239]) ).

fof(f239,plain,
    ( ! [X0] :
        ( intersection(X0,regular(X0)) = y
        | y = X0 )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f29840,plain,
    ( spl0_951
    | ~ spl0_139
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2179,f2175,f1089,f29838]) ).

fof(f29838,plain,
    ( spl0_951
  <=> ! [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_951])]) ).

fof(f2179,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_139
    | ~ spl0_223 ),
    inference(resolution,[],[f2176,f1090]) ).

fof(f29836,plain,
    ( ~ spl0_950
    | ~ spl0_168
    | spl0_268 ),
    inference(avatar_split_clause,[],[f13927,f2805,f1428,f29833]) ).

fof(f29833,plain,
    ( spl0_950
  <=> member(singleton_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f2805,plain,
    ( spl0_268
  <=> member(y,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f13927,plain,
    ( ~ member(singleton_relation,identity_relation)
    | ~ spl0_168
    | spl0_268 ),
    inference(superposition,[],[f2806,f1430]) ).

fof(f2806,plain,
    ( ~ member(y,identity_relation)
    | spl0_268 ),
    inference(avatar_component_clause,[],[f2805]) ).

fof(f29788,plain,
    ( spl0_949
    | ~ spl0_80
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2189,f2186,f647,f29786]) ).

fof(f29786,plain,
    ( spl0_949
  <=> ! [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_949])]) ).

fof(f2189,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_80
    | ~ spl0_224 ),
    inference(resolution,[],[f2187,f648]) ).

fof(f29526,plain,
    ( spl0_375
    | ~ spl0_21
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f13916,f1428,f301,f4993]) ).

fof(f13916,plain,
    ( member(singleton_relation,universal_class)
    | ~ spl0_21
    | ~ spl0_168 ),
    inference(superposition,[],[f302,f1430]) ).

fof(f29306,plain,
    ( ~ spl0_948
    | ~ spl0_168
    | spl0_238 ),
    inference(avatar_split_clause,[],[f2476,f2279,f1428,f29303]) ).

fof(f29303,plain,
    ( spl0_948
  <=> subset_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f2476,plain,
    ( subset_relation != singleton_relation
    | ~ spl0_168
    | spl0_238 ),
    inference(superposition,[],[f2280,f1430]) ).

fof(f2280,plain,
    ( subset_relation != y
    | spl0_238 ),
    inference(avatar_component_clause,[],[f2279]) ).

fof(f29107,plain,
    ( ~ spl0_947
    | spl0_97
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2468,f1428,f750,f29104]) ).

fof(f29104,plain,
    ( spl0_947
  <=> member(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f750,plain,
    ( spl0_97
  <=> member(y,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f2468,plain,
    ( ~ member(singleton_relation,subset_relation)
    | spl0_97
    | ~ spl0_168 ),
    inference(superposition,[],[f751,f1430]) ).

fof(f751,plain,
    ( ~ member(y,subset_relation)
    | spl0_97 ),
    inference(avatar_component_clause,[],[f750]) ).

fof(f28911,plain,
    ( ~ spl0_946
    | spl0_69
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2467,f1428,f587,f28908]) ).

fof(f28908,plain,
    ( spl0_946
  <=> member(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f587,plain,
    ( spl0_69
  <=> member(y,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f2467,plain,
    ( ~ member(singleton_relation,element_relation)
    | spl0_69
    | ~ spl0_168 ),
    inference(superposition,[],[f588,f1430]) ).

fof(f588,plain,
    ( ~ member(y,element_relation)
    | spl0_69 ),
    inference(avatar_component_clause,[],[f587]) ).

fof(f28311,plain,
    ( spl0_945
    | ~ spl0_171
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2460,f2118,f1497,f28309]) ).

fof(f28309,plain,
    ( spl0_945
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(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)))),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(X0,X0))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(compose(X1,regular(cross_product(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)))),universal_class)))))
        | ~ member(X3,universal_class)
        | ~ 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_945])]) ).

fof(f1497,plain,
    ( spl0_171
  <=> ! [X2,X0,X1] :
        ( singleton_relation = 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(singleton_relation,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)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f2460,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(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)))),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(X0,X0))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(compose(X1,regular(cross_product(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)))),universal_class)))))
        | ~ member(X3,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_171
    | ~ spl0_221 ),
    inference(resolution,[],[f1498,f2119]) ).

fof(f1498,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(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1497]) ).

fof(f28307,plain,
    ( spl0_944
    | ~ spl0_171
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2459,f2122,f1497,f28305]) ).

fof(f28305,plain,
    ( spl0_944
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(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)))),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(X0,X0))),cross_product(universal_class,universal_class))
        | 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(X0,X0))),flip(compose(X1,regular(cross_product(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)))),universal_class)))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f2459,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(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)))),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(X0,X0))),cross_product(universal_class,universal_class))
        | 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(X0,X0))),flip(compose(X1,regular(cross_product(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)))),universal_class)))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_171
    | ~ spl0_222 ),
    inference(resolution,[],[f1498,f2123]) ).

fof(f28145,plain,
    ( spl0_943
    | ~ spl0_141
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1489,f1428,f1424,f1143,f28143]) ).

fof(f28143,plain,
    ( spl0_943
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_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,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)
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f1143,plain,
    ( spl0_141
  <=> ! [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)
        | ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1489,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_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,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)
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) )
    | ~ spl0_141
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1476,f1430]) ).

fof(f1476,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))))))),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)
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_141
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1144]) ).

fof(f1144,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)
        | ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1143]) ).

fof(f28141,plain,
    ( spl0_942
    | ~ spl0_140
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1483,f1428,f1424,f1139,f28139]) ).

fof(f28139,plain,
    ( spl0_942
  <=> ! [X0] :
        ( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,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(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)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f1483,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,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(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)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class) )
    | ~ spl0_140
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1469,f1430]) ).

fof(f1469,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))))))),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)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_140
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1140]) ).

fof(f28137,plain,
    ( spl0_941
    | ~ spl0_141
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1462,f1428,f1420,f1143,f28135]) ).

fof(f28135,plain,
    ( spl0_941
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_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)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f1420,plain,
    ( spl0_166
  <=> ! [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_166])]) ).

fof(f1462,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_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)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class) )
    | ~ spl0_141
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1451,f1430]) ).

fof(f1451,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(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)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_141
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1144]) ).

fof(f1421,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1420]) ).

fof(f28133,plain,
    ( spl0_940
    | ~ spl0_140
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1456,f1428,f1420,f1139,f28131]) ).

fof(f28131,plain,
    ( spl0_940
  <=> ! [X0] :
        ( singleton_relation = intersection(complement(compose(element_relation,complement(identity_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)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f1456,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(complement(compose(element_relation,complement(identity_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)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class) )
    | ~ spl0_140
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1444,f1430]) ).

fof(f1444,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_140
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1140]) ).

fof(f28128,plain,
    ( spl0_939
    | ~ spl0_144
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2463,f1497,f1199,f28126]) ).

fof(f1199,plain,
    ( spl0_144
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f2463,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(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = y )
    | ~ spl0_144
    | ~ spl0_171 ),
    inference(superposition,[],[f1498,f1200]) ).

fof(f1200,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) = y )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1199]) ).

fof(f28018,plain,
    ( ~ spl0_938
    | ~ spl0_168
    | spl0_442 ),
    inference(avatar_split_clause,[],[f13940,f5884,f1428,f28015]) ).

fof(f28015,plain,
    ( spl0_938
  <=> function(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f5884,plain,
    ( spl0_442
  <=> function(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f13940,plain,
    ( ~ function(singleton_relation)
    | ~ spl0_168
    | spl0_442 ),
    inference(superposition,[],[f5885,f1430]) ).

fof(f5885,plain,
    ( ~ function(y)
    | spl0_442 ),
    inference(avatar_component_clause,[],[f5884]) ).

fof(f27954,plain,
    ( spl0_937
    | ~ spl0_134
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1488,f1428,f1424,f1043,f27952]) ).

fof(f27952,plain,
    ( spl0_937
  <=> ! [X0] :
        ( 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(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)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f1043,plain,
    ( spl0_134
  <=> ! [X0,X1] :
        ( ~ 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)
        | ~ member(X0,universal_class)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1488,plain,
    ( ! [X0] :
        ( 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(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)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_134
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1475,f1430]) ).

fof(f1475,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | 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)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | y = X0 )
    | ~ spl0_134
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1044]) ).

fof(f1044,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | y = X0 )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1043]) ).

fof(f27950,plain,
    ( spl0_936
    | ~ spl0_134
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1461,f1428,f1420,f1043,f27948]) ).

fof(f27948,plain,
    ( spl0_936
  <=> ! [X0] :
        ( 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(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)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f1461,plain,
    ( ! [X0] :
        ( 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(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)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class) )
    | ~ spl0_134
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1450,f1430]) ).

fof(f1450,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | 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)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | y = X0 )
    | ~ spl0_134
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1044]) ).

fof(f27881,plain,
    ( spl0_935
    | ~ spl0_112
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1487,f1428,f1424,f856,f27879]) ).

fof(f27879,plain,
    ( spl0_935
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f1487,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ 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) )
    | ~ spl0_112
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1474,f1430]) ).

fof(f1474,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)
        | y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_112
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f857]) ).

fof(f27877,plain,
    ( spl0_934
    | ~ spl0_111
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1485,f1428,f1424,f852,f27875]) ).

fof(f27875,plain,
    ( spl0_934
  <=> ! [X0] :
        ( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f1485,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),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) )
    | ~ spl0_111
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1471,f1430]) ).

fof(f1471,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)
        | y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_111
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f853]) ).

fof(f27873,plain,
    ( ~ spl0_933
    | ~ spl0_168
    | spl0_441 ),
    inference(avatar_split_clause,[],[f13939,f5880,f1428,f27870]) ).

fof(f27870,plain,
    ( spl0_933
  <=> single_valued_class(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f5880,plain,
    ( spl0_441
  <=> single_valued_class(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f13939,plain,
    ( ~ single_valued_class(singleton_relation)
    | ~ spl0_168
    | spl0_441 ),
    inference(superposition,[],[f5882,f1430]) ).

fof(f5882,plain,
    ( ~ single_valued_class(y)
    | spl0_441 ),
    inference(avatar_component_clause,[],[f5880]) ).

fof(f27868,plain,
    ( spl0_932
    | ~ spl0_112
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1460,f1428,f1420,f856,f27866]) ).

fof(f27866,plain,
    ( spl0_932
  <=> ! [X0] :
        ( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f1460,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ 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) )
    | ~ spl0_112
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1449,f1430]) ).

fof(f1449,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)
        | y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_112
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f857]) ).

fof(f27864,plain,
    ( spl0_931
    | ~ spl0_111
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1458,f1428,f1420,f852,f27862]) ).

fof(f27862,plain,
    ( spl0_931
  <=> ! [X0] :
        ( singleton_relation = intersection(complement(compose(element_relation,complement(identity_relation))),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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f1458,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(complement(compose(element_relation,complement(identity_relation))),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) )
    | ~ spl0_111
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1446,f1430]) ).

fof(f1446,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)
        | y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_111
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f853]) ).

fof(f27758,plain,
    ( spl0_930
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1481,f1428,f1424,f500,f261,f27756]) ).

fof(f27756,plain,
    ( spl0_930
  <=> ! [X0] :
        ( singleton_relation = 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_930])]) ).

fof(f261,plain,
    ( spl0_12
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,domain_of(X0))
        | y = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1481,plain,
    ( ! [X0] :
        ( singleton_relation = 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_12
    | ~ spl0_57
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1480,f1430]) ).

fof(f1480,plain,
    ( ! [X0] :
        ( y = 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_12
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(forward_demodulation,[],[f1464,f501]) ).

fof(f1464,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
    | ~ spl0_12
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f262]) ).

fof(f262,plain,
    ( ! [X0,X4] :
        ( member(X4,domain_of(X0))
        | ~ member(X4,universal_class)
        | y = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f27719,plain,
    ( spl0_929
    | ~ spl0_109
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1486,f1428,f1424,f831,f27717]) ).

fof(f27717,plain,
    ( spl0_929
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f1486,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_109
    | ~ spl0_167
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1473,f1430]) ).

fof(f1473,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f832]) ).

fof(f27612,plain,
    ( spl0_928
    | ~ spl0_169
    | ~ spl0_166
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f2512,f2454,f1420,f1432,f27609]) ).

fof(f2512,plain,
    ( ~ member(regular(singleton_relation),element_relation)
    | member(regular(singleton_relation),singleton_relation)
    | ~ spl0_166
    | ~ spl0_249 ),
    inference(resolution,[],[f2456,f1421]) ).

fof(f26653,plain,
    ( spl0_926
    | ~ spl0_927
    | ~ spl0_106
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2444,f2426,f810,f26650,f26646]) ).

fof(f26646,plain,
    ( spl0_926
  <=> y = complement(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f26650,plain,
    ( spl0_927
  <=> subclass(complement(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f810,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f2444,plain,
    ( ~ subclass(complement(subset_relation),identity_relation)
    | y = complement(subset_relation)
    | ~ spl0_106
    | ~ spl0_246 ),
    inference(duplicate_literal_removal,[],[f2437]) ).

fof(f2437,plain,
    ( ~ subclass(complement(subset_relation),identity_relation)
    | y = complement(subset_relation)
    | y = complement(subset_relation)
    | ~ spl0_106
    | ~ spl0_246 ),
    inference(resolution,[],[f2427,f811]) ).

fof(f811,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = y )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f810]) ).

fof(f25843,plain,
    ( spl0_924
    | ~ spl0_925
    | ~ spl0_106
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2436,f2422,f810,f25840,f25836]) ).

fof(f25836,plain,
    ( spl0_924
  <=> complement(element_relation) = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f25840,plain,
    ( spl0_925
  <=> subclass(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f2436,plain,
    ( ~ subclass(complement(element_relation),singleton_relation)
    | complement(element_relation) = y
    | ~ spl0_106
    | ~ spl0_245 ),
    inference(duplicate_literal_removal,[],[f2429]) ).

fof(f2429,plain,
    ( ~ subclass(complement(element_relation),singleton_relation)
    | complement(element_relation) = y
    | complement(element_relation) = y
    | ~ spl0_106
    | ~ spl0_245 ),
    inference(resolution,[],[f2423,f811]) ).

fof(f25485,plain,
    ( spl0_923
    | ~ spl0_2
    | ~ spl0_520
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8956,f8731,f7933,f213,f25483]) ).

fof(f25483,plain,
    ( spl0_923
  <=> ! [X0] :
        ( subclass(X0,complement(y))
        | ~ subclass(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f7933,plain,
    ( spl0_520
  <=> ! [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_520])]) ).

fof(f8956,plain,
    ( ! [X0] :
        ( subclass(X0,complement(y))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_2
    | ~ spl0_520
    | ~ spl0_550 ),
    inference(forward_demodulation,[],[f8921,f8914]) ).

fof(f8914,plain,
    ( y = domain_of(y)
    | ~ spl0_2
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f214]) ).

fof(f8921,plain,
    ( ! [X0] :
        ( subclass(X0,complement(domain_of(y)))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_520
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f7934]) ).

fof(f7934,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_520 ),
    inference(avatar_component_clause,[],[f7933]) ).

fof(f25005,plain,
    ( spl0_168
    | ~ spl0_922
    | ~ spl0_109
    | spl0_911 ),
    inference(avatar_split_clause,[],[f23752,f22465,f831,f25002,f1428]) ).

fof(f22465,plain,
    ( spl0_911
  <=> member(regular(singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f23752,plain,
    ( ~ subclass(singleton_relation,subset_relation)
    | singleton_relation = y
    | ~ spl0_109
    | spl0_911 ),
    inference(resolution,[],[f22466,f832]) ).

fof(f22466,plain,
    ( ~ member(regular(singleton_relation),subset_relation)
    | spl0_911 ),
    inference(avatar_component_clause,[],[f22465]) ).

fof(f24326,plain,
    ( spl0_168
    | ~ spl0_921
    | ~ spl0_246
    | spl0_911 ),
    inference(avatar_split_clause,[],[f23750,f22465,f2426,f24323,f1428]) ).

fof(f23750,plain,
    ( ~ subclass(singleton_relation,identity_relation)
    | singleton_relation = y
    | ~ spl0_246
    | spl0_911 ),
    inference(resolution,[],[f22466,f2427]) ).

fof(f24016,plain,
    ( ~ spl0_920
    | ~ spl0_691
    | spl0_911 ),
    inference(avatar_split_clause,[],[f23751,f22465,f13889,f24013]) ).

fof(f24013,plain,
    ( spl0_920
  <=> subclass(element_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f23751,plain,
    ( ~ subclass(element_relation,subset_relation)
    | ~ spl0_691
    | spl0_911 ),
    inference(resolution,[],[f22466,f13890]) ).

fof(f22541,plain,
    ( ~ spl0_16
    | ~ spl0_918 ),
    inference(avatar_contradiction_clause,[],[f22500]) ).

fof(f22500,plain,
    ( $false
    | ~ spl0_16
    | ~ spl0_918 ),
    inference(resolution,[],[f22495,f279]) ).

fof(f22495,plain,
    ( ! [X2] : ~ member(X2,universal_class)
    | ~ spl0_918 ),
    inference(avatar_component_clause,[],[f22494]) ).

fof(f22494,plain,
    ( spl0_918
  <=> ! [X2] : ~ member(X2,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f22540,plain,
    ( ~ spl0_9
    | ~ spl0_918 ),
    inference(avatar_contradiction_clause,[],[f22501]) ).

fof(f22501,plain,
    ( $false
    | ~ spl0_9
    | ~ spl0_918 ),
    inference(resolution,[],[f22495,f248]) ).

fof(f248,plain,
    ( member(omega,universal_class)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f246,plain,
    ( spl0_9
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f22539,plain,
    ( ~ spl0_21
    | ~ spl0_918 ),
    inference(avatar_contradiction_clause,[],[f22503]) ).

fof(f22503,plain,
    ( $false
    | ~ spl0_21
    | ~ spl0_918 ),
    inference(resolution,[],[f22495,f302]) ).

fof(f22499,plain,
    ( spl0_918
    | spl0_919
    | ~ spl0_80
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2178,f2175,f647,f22497,f22494]) ).

fof(f22497,plain,
    ( spl0_919
  <=> ! [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_919])]) ).

fof(f2178,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_80
    | ~ spl0_223 ),
    inference(resolution,[],[f2176,f648]) ).

fof(f22492,plain,
    ( spl0_917
    | ~ spl0_96
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1712,f1646,f746,f22490]) ).

fof(f22490,plain,
    ( spl0_917
  <=> ! [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_917])]) ).

fof(f1712,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_192 ),
    inference(resolution,[],[f1647,f747]) ).

fof(f22488,plain,
    ( ~ spl0_915
    | spl0_916
    | ~ spl0_91
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1465,f1424,f710,f22486,f22482]) ).

fof(f22482,plain,
    ( spl0_915
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f22486,plain,
    ( spl0_916
  <=> ! [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_916])]) ).

fof(f1465,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_167 ),
    inference(resolution,[],[f1425,f711]) ).

fof(f22480,plain,
    ( spl0_913
    | ~ spl0_914
    | ~ spl0_203
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2025,f1999,f1816,f22477,f22474]) ).

fof(f22474,plain,
    ( spl0_913
  <=> ! [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_913])]) ).

fof(f22477,plain,
    ( spl0_914
  <=> 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_914])]) ).

fof(f2025,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_203
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1817]) ).

fof(f22472,plain,
    ( spl0_911
    | ~ spl0_912
    | ~ spl0_131
    | ~ spl0_691 ),
    inference(avatar_split_clause,[],[f15644,f13889,f1009,f22469,f22465]) ).

fof(f22469,plain,
    ( spl0_912
  <=> subclass(element_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f15644,plain,
    ( ~ subclass(element_relation,identity_relation)
    | member(regular(singleton_relation),subset_relation)
    | ~ spl0_131
    | ~ spl0_691 ),
    inference(resolution,[],[f13890,f1010]) ).

fof(f22414,plain,
    ( spl0_910
    | ~ spl0_189
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2158,f2122,f1625,f22412]) ).

fof(f22412,plain,
    ( spl0_910
  <=> ! [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_910])]) ).

fof(f1625,plain,
    ( spl0_189
  <=> ! [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_189])]) ).

fof(f2158,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_189
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1626]) ).

fof(f1626,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_189 ),
    inference(avatar_component_clause,[],[f1625]) ).

fof(f22410,plain,
    ( spl0_909
    | ~ spl0_189
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2135,f2118,f1625,f22408]) ).

fof(f22408,plain,
    ( spl0_909
  <=> ! [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_909])]) ).

fof(f2135,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_189
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1626]) ).

fof(f22385,plain,
    ( spl0_908
    | ~ spl0_197
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1983,f1943,f1750,f22383]) ).

fof(f22383,plain,
    ( spl0_908
  <=> ! [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_908])]) ).

fof(f1750,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

fof(f1983,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_197
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1751]) ).

fof(f1751,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_197 ),
    inference(avatar_component_clause,[],[f1750]) ).

fof(f22381,plain,
    ( spl0_907
    | ~ spl0_197
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1957,f1939,f1750,f22379]) ).

fof(f22379,plain,
    ( spl0_907
  <=> ! [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_907])]) ).

fof(f1957,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_197
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1751]) ).

fof(f22377,plain,
    ( spl0_906
    | ~ spl0_94
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1787,f1750,f725,f22375]) ).

fof(f22375,plain,
    ( spl0_906
  <=> ! [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_906])]) ).

fof(f1787,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_197 ),
    inference(resolution,[],[f1751,f726]) ).

fof(f22333,plain,
    ( spl0_905
    | ~ spl0_204
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2171,f2122,f1841,f22331]) ).

fof(f22331,plain,
    ( spl0_905
  <=> ! [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_905])]) ).

fof(f2171,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_204
    | ~ spl0_222 ),
    inference(duplicate_literal_removal,[],[f2167]) ).

fof(f2167,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_204
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1842]) ).

fof(f22287,plain,
    ( spl0_904
    | ~ spl0_192
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2148,f2122,f1646,f22285]) ).

fof(f22285,plain,
    ( spl0_904
  <=> ! [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_904])]) ).

fof(f2148,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_192
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1647]) ).

fof(f22259,plain,
    ( spl0_903
    | ~ spl0_192
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1982,f1943,f1646,f22257]) ).

fof(f22257,plain,
    ( spl0_903
  <=> ! [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_903])]) ).

fof(f1982,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_192
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1647]) ).

fof(f22255,plain,
    ( spl0_902
    | ~ spl0_192
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1956,f1939,f1646,f22253]) ).

fof(f22253,plain,
    ( spl0_902
  <=> ! [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_902])]) ).

fof(f1956,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_192
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1647]) ).

fof(f22251,plain,
    ( spl0_901
    | ~ spl0_94
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1723,f1646,f725,f22249]) ).

fof(f22249,plain,
    ( spl0_901
  <=> ! [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_901])]) ).

fof(f1723,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_192 ),
    inference(resolution,[],[f1647,f726]) ).

fof(f22247,plain,
    ( spl0_186
    | spl0_900
    | ~ spl0_261
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f14305,f4465,f2706,f22244,f1601]) ).

fof(f22244,plain,
    ( spl0_900
  <=> member(regular(y),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f2706,plain,
    ( spl0_261
  <=> ! [X0] :
        ( identity_relation = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f4465,plain,
    ( spl0_362
  <=> y = intersection(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f14305,plain,
    ( member(regular(y),element_relation)
    | identity_relation = y
    | ~ spl0_261
    | ~ spl0_362 ),
    inference(superposition,[],[f2707,f4467]) ).

fof(f4467,plain,
    ( y = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f4465]) ).

fof(f2707,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | identity_relation = intersection(singleton_relation,X0) )
    | ~ spl0_261 ),
    inference(avatar_component_clause,[],[f2706]) ).

fof(f22236,plain,
    ( spl0_899
    | ~ spl0_144
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2116,f2108,f1199,f22234]) ).

fof(f22234,plain,
    ( spl0_899
  <=> ! [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)
        | y = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f2108,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)
        | y = 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(f2116,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)
        | y = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = y )
    | ~ spl0_144
    | ~ spl0_220 ),
    inference(superposition,[],[f2109,f1200]) ).

fof(f2109,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)
        | y = 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,[],[f2108]) ).

fof(f22134,plain,
    ( spl0_898
    | ~ spl0_153
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2162,f2122,f1264,f22132]) ).

fof(f22132,plain,
    ( spl0_898
  <=> ! [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_898])]) ).

fof(f2162,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_153
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1265]) ).

fof(f22130,plain,
    ( spl0_897
    | ~ spl0_152
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2160,f2122,f1260,f22128]) ).

fof(f22128,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(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_897])]) ).

fof(f2160,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_152
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1261]) ).

fof(f22126,plain,
    ( spl0_896
    | ~ spl0_153
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2139,f2118,f1264,f22124]) ).

fof(f22124,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(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_896])]) ).

fof(f2139,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_153
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1265]) ).

fof(f22122,plain,
    ( spl0_895
    | ~ spl0_152
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2137,f2118,f1260,f22120]) ).

fof(f22120,plain,
    ( spl0_895
  <=> ! [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_895])]) ).

fof(f2137,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_152
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1261]) ).

fof(f22040,plain,
    ( spl0_894
    | ~ spl0_72
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2169,f2122,f605,f22038]) ).

fof(f22038,plain,
    ( spl0_894
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_894])]) ).

fof(f2169,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_72
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f606]) ).

fof(f22035,plain,
    ( spl0_892
    | ~ spl0_893
    | ~ spl0_167
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2032,f1999,f1424,f22032,f22029]) ).

fof(f22029,plain,
    ( spl0_892
  <=> ! [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_892])]) ).

fof(f22032,plain,
    ( spl0_893
  <=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f2032,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_167
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1425]) ).

fof(f22027,plain,
    ( spl0_890
    | ~ spl0_891
    | ~ spl0_166
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2027,f1999,f1420,f22024,f22021]) ).

fof(f22021,plain,
    ( spl0_890
  <=> ! [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_890])]) ).

fof(f22024,plain,
    ( spl0_891
  <=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f2027,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_166
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1421]) ).

fof(f22019,plain,
    ( spl0_889
    | ~ spl0_196
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1991,f1943,f1746,f22017]) ).

fof(f22017,plain,
    ( spl0_889
  <=> ! [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_889])]) ).

fof(f1991,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_196
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1747]) ).

fof(f22015,plain,
    ( spl0_888
    | ~ spl0_196
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1965,f1939,f1746,f22013]) ).

fof(f22013,plain,
    ( spl0_888
  <=> ! [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_888])]) ).

fof(f1965,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_196
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1747]) ).

fof(f22011,plain,
    ( spl0_887
    | ~ spl0_94
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1769,f1746,f725,f22009]) ).

fof(f22009,plain,
    ( spl0_887
  <=> ! [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_887])]) ).

fof(f1769,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_196 ),
    inference(resolution,[],[f1747,f726]) ).

fof(f21958,plain,
    ( spl0_886
    | ~ spl0_139
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2155,f2122,f1089,f21956]) ).

fof(f21956,plain,
    ( spl0_886
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_886])]) ).

fof(f2155,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_139
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1090]) ).

fof(f21954,plain,
    ( spl0_885
    | ~ spl0_139
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2132,f2118,f1089,f21952]) ).

fof(f21952,plain,
    ( spl0_885
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_885])]) ).

fof(f2132,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_139
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1090]) ).

fof(f21924,plain,
    ( spl0_884
    | ~ spl0_55
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2021,f1999,f492,f21922]) ).

fof(f21922,plain,
    ( spl0_884
  <=> ! [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_884])]) ).

fof(f492,plain,
    ( spl0_55
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f2021,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_55
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f493]) ).

fof(f493,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f492]) ).

fof(f21908,plain,
    ( spl0_883
    | ~ spl0_103
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1219,f1199,f778,f21906]) ).

fof(f21906,plain,
    ( spl0_883
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).

fof(f1219,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) = y )
    | ~ spl0_103
    | ~ spl0_144 ),
    inference(superposition,[],[f779,f1200]) ).

fof(f21904,plain,
    ( ~ spl0_881
    | spl0_882
    | ~ spl0_19
    | ~ spl0_720 ),
    inference(avatar_split_clause,[],[f21752,f15431,f292,f21901,f21897]) ).

fof(f21897,plain,
    ( spl0_881
  <=> inductive(complement(omega)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).

fof(f15431,plain,
    ( spl0_720
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f21752,plain,
    ( omega = y
    | ~ inductive(complement(omega))
    | ~ spl0_19
    | ~ spl0_720 ),
    inference(resolution,[],[f15432,f293]) ).

fof(f15432,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(X0))
        | y = X0 )
    | ~ spl0_720 ),
    inference(avatar_component_clause,[],[f15431]) ).

fof(f21889,plain,
    ( spl0_880
    | ~ spl0_203
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1907,f1889,f1816,f21887]) ).

fof(f21887,plain,
    ( spl0_880
  <=> ! [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_880])]) ).

fof(f1907,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_203
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f1817]) ).

fof(f21764,plain,
    ( spl0_879
    | ~ spl0_141
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1985,f1943,f1143,f21762]) ).

fof(f21762,plain,
    ( spl0_879
  <=> ! [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))
        | ~ 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)
        | y = 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_879])]) ).

fof(f1985,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))
        | ~ 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)
        | y = 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_141
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1144]) ).

fof(f21760,plain,
    ( spl0_878
    | ~ spl0_140
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1977,f1943,f1139,f21758]) ).

fof(f21758,plain,
    ( spl0_878
  <=> ! [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))
        | ~ 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)
        | y = 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_878])]) ).

fof(f1977,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))
        | ~ 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)
        | y = 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_140
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1140]) ).

fof(f21745,plain,
    ( spl0_877
    | ~ spl0_141
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1959,f1939,f1143,f21743]) ).

fof(f21743,plain,
    ( spl0_877
  <=> ! [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))
        | ~ 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)
        | y = 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_877])]) ).

fof(f1959,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))
        | ~ 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)
        | y = 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_141
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1144]) ).

fof(f21741,plain,
    ( spl0_876
    | ~ spl0_140
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1951,f1939,f1139,f21739]) ).

fof(f21739,plain,
    ( spl0_876
  <=> ! [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))
        | ~ 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)
        | y = 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_876])]) ).

fof(f1951,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))
        | ~ 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)
        | y = 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_140
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1140]) ).

fof(f21737,plain,
    ( spl0_875
    | ~ spl0_94
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1169,f1143,f725,f21735]) ).

fof(f21735,plain,
    ( spl0_875
  <=> ! [X0,X3,X2,X1] :
        ( ~ 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)
        | y = 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(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_875])]) ).

fof(f1169,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ 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)
        | y = 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(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_141 ),
    inference(resolution,[],[f1144,f726]) ).

fof(f21733,plain,
    ( spl0_874
    | ~ spl0_94
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1152,f1139,f725,f21731]) ).

fof(f21731,plain,
    ( spl0_874
  <=> ! [X0,X3,X2,X1] :
        ( ~ 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)
        | y = 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(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_874])]) ).

fof(f1152,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ 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)
        | y = 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(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_140 ),
    inference(resolution,[],[f1140,f726]) ).

fof(f21700,plain,
    ( spl0_873
    | ~ spl0_198
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2133,f2118,f1754,f21698]) ).

fof(f21698,plain,
    ( spl0_873
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_873])]) ).

fof(f1754,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

fof(f2133,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_198
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1755]) ).

fof(f1755,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_198 ),
    inference(avatar_component_clause,[],[f1754]) ).

fof(f21696,plain,
    ( spl0_872
    | ~ spl0_16
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2111,f2108,f278,f21694]) ).

fof(f21694,plain,
    ( spl0_872
  <=> ! [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)
        | y = 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_872])]) ).

fof(f2111,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)
        | y = 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_16
    | ~ spl0_220 ),
    inference(resolution,[],[f2109,f279]) ).

fof(f21663,plain,
    ( spl0_871
    | ~ spl0_198
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2173,f2122,f1754,f21661]) ).

fof(f21661,plain,
    ( spl0_871
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_871])]) ).

fof(f2173,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_198
    | ~ spl0_222 ),
    inference(duplicate_literal_removal,[],[f2156]) ).

fof(f2156,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_198
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1755]) ).

fof(f21627,plain,
    ( spl0_870
    | ~ spl0_28
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1976,f1943,f330,f21625]) ).

fof(f21625,plain,
    ( spl0_870
  <=> ! [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)
        | y = domain_of(domain_of(flip(cross_product(intersection(X1,cross_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_870])]) ).

fof(f330,plain,
    ( spl0_28
  <=> ! [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)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1976,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)
        | y = domain_of(domain_of(flip(cross_product(intersection(X1,cross_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_28
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f331]) ).

fof(f331,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)
        | y = X1 )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f21623,plain,
    ( spl0_869
    | ~ spl0_28
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1950,f1939,f330,f21621]) ).

fof(f21621,plain,
    ( spl0_869
  <=> ! [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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_869])]) ).

fof(f1950,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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_28
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f331]) ).

fof(f21591,plain,
    ( spl0_868
    | ~ spl0_139
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2094,f2090,f1089,f21589]) ).

fof(f21589,plain,
    ( spl0_868
  <=> ! [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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_868])]) ).

fof(f2090,plain,
    ( spl0_218
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f2094,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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_139
    | ~ spl0_218 ),
    inference(resolution,[],[f2091,f1090]) ).

fof(f2091,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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f2090]) ).

fof(f21548,plain,
    ( spl0_867
    | ~ spl0_179
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1986,f1943,f1537,f21546]) ).

fof(f21546,plain,
    ( spl0_867
  <=> ! [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_867])]) ).

fof(f1537,plain,
    ( spl0_179
  <=> ! [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_179])]) ).

fof(f1986,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_179
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1538]) ).

fof(f1538,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f1537]) ).

fof(f21544,plain,
    ( spl0_866
    | ~ spl0_179
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1960,f1939,f1537,f21542]) ).

fof(f21542,plain,
    ( spl0_866
  <=> ! [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_866])]) ).

fof(f1960,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_179
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1538]) ).

fof(f21540,plain,
    ( spl0_865
    | ~ spl0_167
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1912,f1889,f1424,f21538]) ).

fof(f21538,plain,
    ( spl0_865
  <=> ! [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_865])]) ).

fof(f1912,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_167
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f1425]) ).

fof(f21536,plain,
    ( spl0_864
    | ~ spl0_166
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1909,f1889,f1420,f21534]) ).

fof(f21534,plain,
    ( spl0_864
  <=> ! [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_864])]) ).

fof(f1909,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_166
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f1421]) ).

fof(f21532,plain,
    ( spl0_863
    | ~ spl0_94
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1557,f1537,f725,f21530]) ).

fof(f21530,plain,
    ( spl0_863
  <=> ! [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_863])]) ).

fof(f1557,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_179 ),
    inference(resolution,[],[f1538,f726]) ).

fof(f21510,plain,
    ( spl0_862
    | ~ spl0_55
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1903,f1889,f492,f21508]) ).

fof(f21508,plain,
    ( spl0_862
  <=> ! [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_862])]) ).

fof(f1903,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_55
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f493]) ).

fof(f21448,plain,
    ( spl0_238
    | ~ spl0_861
    | ~ spl0_109
    | spl0_781 ),
    inference(avatar_split_clause,[],[f18044,f17228,f831,f21445,f2279]) ).

fof(f21445,plain,
    ( spl0_861
  <=> subclass(subset_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f17228,plain,
    ( spl0_781
  <=> member(regular(subset_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f18044,plain,
    ( ~ subclass(subset_relation,element_relation)
    | subset_relation = y
    | ~ spl0_109
    | spl0_781 ),
    inference(resolution,[],[f17229,f832]) ).

fof(f17229,plain,
    ( ~ member(regular(subset_relation),element_relation)
    | spl0_781 ),
    inference(avatar_component_clause,[],[f17228]) ).

fof(f21335,plain,
    ( spl0_860
    | ~ spl0_80
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2154,f2122,f647,f21333]) ).

fof(f21333,plain,
    ( spl0_860
  <=> ! [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_860])]) ).

fof(f2154,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_80
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f648]) ).

fof(f21331,plain,
    ( spl0_859
    | ~ spl0_80
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2131,f2118,f647,f21329]) ).

fof(f21329,plain,
    ( spl0_859
  <=> ! [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_859])]) ).

fof(f2131,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_80
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f648]) ).

fof(f21327,plain,
    ( spl0_858
    | ~ spl0_99
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1713,f1646,f759,f21325]) ).

fof(f21325,plain,
    ( spl0_858
  <=> ! [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_858])]) ).

fof(f1713,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_99
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f760]) ).

fof(f21123,plain,
    ( spl0_857
    | ~ spl0_183
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1930,f1918,f1589,f21121]) ).

fof(f21121,plain,
    ( spl0_857
  <=> ! [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_857])]) ).

fof(f1589,plain,
    ( spl0_183
  <=> ! [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_183])]) ).

fof(f1918,plain,
    ( spl0_213
  <=> ! [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_213])]) ).

fof(f1930,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_183
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1590]) ).

fof(f1590,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_183 ),
    inference(avatar_component_clause,[],[f1589]) ).

fof(f1919,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_213 ),
    inference(avatar_component_clause,[],[f1918]) ).

fof(f21119,plain,
    ( spl0_856
    | ~ spl0_182
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1929,f1918,f1585,f21117]) ).

fof(f21117,plain,
    ( spl0_856
  <=> ! [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_856])]) ).

fof(f1585,plain,
    ( spl0_182
  <=> ! [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_182])]) ).

fof(f1929,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_182
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1586]) ).

fof(f1586,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_182 ),
    inference(avatar_component_clause,[],[f1585]) ).

fof(f21115,plain,
    ( ~ spl0_854
    | spl0_855
    | ~ spl0_7
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2213,f2203,f238,f21113,f21109]) ).

fof(f21113,plain,
    ( spl0_855
  <=> ! [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(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | y = 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(y,universal_class))),X3)
        | ~ compatible(X2,domain_of(flip(cross_product(y,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(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,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_855])]) ).

fof(f2213,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(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,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(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,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(y,universal_class))),X3)
        | homomorphism(X2,domain_of(flip(cross_product(y,universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(y,universal_class))))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_7
    | ~ spl0_226 ),
    inference(superposition,[],[f2204,f239]) ).

fof(f21091,plain,
    ( spl0_853
    | ~ spl0_7
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2097,f2090,f238,f21089]) ).

fof(f21089,plain,
    ( spl0_853
  <=> ! [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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f2097,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_218 ),
    inference(superposition,[],[f2091,f239]) ).

fof(f21001,plain,
    ( spl0_852
    | ~ spl0_154
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1990,f1943,f1287,f20999]) ).

fof(f20999,plain,
    ( spl0_852
  <=> ! [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_852])]) ).

fof(f1990,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_154
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1288]) ).

fof(f20997,plain,
    ( spl0_851
    | ~ spl0_154
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1964,f1939,f1287,f20995]) ).

fof(f20995,plain,
    ( spl0_851
  <=> ! [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_851])]) ).

fof(f1964,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_154
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1288]) ).

fof(f20993,plain,
    ( spl0_850
    | ~ spl0_142
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1934,f1918,f1181,f20991]) ).

fof(f20991,plain,
    ( spl0_850
  <=> ! [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_850])]) ).

fof(f1181,plain,
    ( spl0_142
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1934,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_142
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1182]) ).

fof(f1182,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1181]) ).

fof(f20989,plain,
    ( spl0_849
    | ~ spl0_94
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1316,f1287,f725,f20987]) ).

fof(f20987,plain,
    ( spl0_849
  <=> ! [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_849])]) ).

fof(f1316,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_154 ),
    inference(resolution,[],[f1288,f726]) ).

fof(f20985,plain,
    ( spl0_238
    | ~ spl0_848
    | ~ spl0_245
    | spl0_781 ),
    inference(avatar_split_clause,[],[f18043,f17228,f2422,f20982,f2279]) ).

fof(f20982,plain,
    ( spl0_848
  <=> subclass(subset_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f18043,plain,
    ( ~ subclass(subset_relation,singleton_relation)
    | subset_relation = y
    | ~ spl0_245
    | spl0_781 ),
    inference(resolution,[],[f17229,f2423]) ).

fof(f20795,plain,
    ( spl0_847
    | ~ spl0_173
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1924,f1918,f1511,f20793]) ).

fof(f20793,plain,
    ( spl0_847
  <=> ! [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_847])]) ).

fof(f1511,plain,
    ( spl0_173
  <=> ! [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_173])]) ).

fof(f1924,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_173
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1512]) ).

fof(f1512,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f1511]) ).

fof(f20791,plain,
    ( spl0_846
    | ~ spl0_82
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1391,f1351,f665,f20789]) ).

fof(f20789,plain,
    ( spl0_846
  <=> ! [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_846])]) ).

fof(f665,plain,
    ( spl0_82
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f1391,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,cross_product(X1,X2)),X3)
        | not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) )
    | ~ spl0_82
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f666]) ).

fof(f666,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f665]) ).

fof(f20787,plain,
    ( spl0_845
    | ~ spl0_82
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1370,f1347,f665,f20785]) ).

fof(f20785,plain,
    ( spl0_845
  <=> ! [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_845])]) ).

fof(f1370,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(cross_product(X0,X1),X2),X3)
        | not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) )
    | ~ spl0_82
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f666]) ).

fof(f20754,plain,
    ( spl0_844
    | ~ spl0_80
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2093,f2090,f647,f20752]) ).

fof(f20752,plain,
    ( spl0_844
  <=> ! [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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_844])]) ).

fof(f2093,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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_80
    | ~ spl0_218 ),
    inference(resolution,[],[f2091,f648]) ).

fof(f20724,plain,
    ( ~ spl0_843
    | ~ spl0_691
    | spl0_696 ),
    inference(avatar_split_clause,[],[f16788,f14688,f13889,f20721]) ).

fof(f20721,plain,
    ( spl0_843
  <=> subclass(element_relation,compose(element_relation,complement(identity_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f14688,plain,
    ( spl0_696
  <=> member(regular(singleton_relation),compose(element_relation,complement(identity_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f16788,plain,
    ( ~ subclass(element_relation,compose(element_relation,complement(identity_relation)))
    | ~ spl0_691
    | spl0_696 ),
    inference(resolution,[],[f14690,f13890]) ).

fof(f14690,plain,
    ( ~ member(regular(singleton_relation),compose(element_relation,complement(identity_relation)))
    | spl0_696 ),
    inference(avatar_component_clause,[],[f14688]) ).

fof(f20547,plain,
    ( spl0_842
    | ~ spl0_137
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1989,f1943,f1078,f20545]) ).

fof(f20545,plain,
    ( spl0_842
  <=> ! [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_842])]) ).

fof(f1989,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_137
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1079]) ).

fof(f20543,plain,
    ( spl0_841
    | ~ spl0_137
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1963,f1939,f1078,f20541]) ).

fof(f20541,plain,
    ( spl0_841
  <=> ! [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_841])]) ).

fof(f1963,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_137
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1079]) ).

fof(f20539,plain,
    ( spl0_840
    | ~ spl0_202
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1931,f1918,f1809,f20537]) ).

fof(f20537,plain,
    ( spl0_840
  <=> ! [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_840])]) ).

fof(f1809,plain,
    ( spl0_202
  <=> ! [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_202])]) ).

fof(f1931,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_202
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1810]) ).

fof(f1810,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_202 ),
    inference(avatar_component_clause,[],[f1809]) ).

fof(f20535,plain,
    ( spl0_839
    | ~ spl0_94
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1117,f1078,f725,f20533]) ).

fof(f20533,plain,
    ( spl0_839
  <=> ! [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_839])]) ).

fof(f1117,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_137 ),
    inference(resolution,[],[f1079,f726]) ).

fof(f20520,plain,
    ( spl0_838
    | ~ spl0_190
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1863,f1860,f1638,f20518]) ).

fof(f20518,plain,
    ( spl0_838
  <=> ! [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_838])]) ).

fof(f1638,plain,
    ( spl0_190
  <=> ! [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_190])]) ).

fof(f1860,plain,
    ( spl0_208
  <=> ! [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_208])]) ).

fof(f1863,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_190
    | ~ spl0_208 ),
    inference(resolution,[],[f1861,f1639]) ).

fof(f1639,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_190 ),
    inference(avatar_component_clause,[],[f1638]) ).

fof(f1861,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_208 ),
    inference(avatar_component_clause,[],[f1860]) ).

fof(f20466,plain,
    ( spl0_244
    | ~ spl0_591
    | ~ spl0_612
    | ~ spl0_640 ),
    inference(avatar_split_clause,[],[f20338,f12137,f11087,f10596,f2322]) ).

fof(f2322,plain,
    ( spl0_244
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f10596,plain,
    ( spl0_591
  <=> subclass(universal_class,complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f12137,plain,
    ( spl0_640
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f20338,plain,
    ( member(subset_relation,universal_class)
    | ~ spl0_591
    | ~ spl0_612
    | ~ spl0_640 ),
    inference(forward_demodulation,[],[f20333,f11089]) ).

fof(f20333,plain,
    ( member(subset_relation,complement(y))
    | ~ spl0_591
    | ~ spl0_640 ),
    inference(resolution,[],[f12138,f10598]) ).

fof(f10598,plain,
    ( subclass(universal_class,complement(y))
    | ~ spl0_591 ),
    inference(avatar_component_clause,[],[f10596]) ).

fof(f12138,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(subset_relation,X0) )
    | ~ spl0_640 ),
    inference(avatar_component_clause,[],[f12137]) ).

fof(f20425,plain,
    ( spl0_837
    | ~ spl0_137
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2150,f2122,f1078,f20423]) ).

fof(f20423,plain,
    ( spl0_837
  <=> ! [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_837])]) ).

fof(f2150,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_137
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1079]) ).

fof(f20421,plain,
    ( spl0_836
    | ~ spl0_137
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2127,f2118,f1078,f20419]) ).

fof(f20419,plain,
    ( spl0_836
  <=> ! [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_836])]) ).

fof(f2127,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_137
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1079]) ).

fof(f20417,plain,
    ( spl0_835
    | ~ spl0_189
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1678,f1642,f1625,f20415]) ).

fof(f20415,plain,
    ( spl0_835
  <=> ! [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_835])]) ).

fof(f1642,plain,
    ( spl0_191
  <=> ! [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_191])]) ).

fof(f1678,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_189
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1626]) ).

fof(f1643,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_191 ),
    inference(avatar_component_clause,[],[f1642]) ).

fof(f20391,plain,
    ( spl0_834
    | ~ spl0_46
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2020,f1999,f424,f20389]) ).

fof(f20389,plain,
    ( spl0_834
  <=> ! [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_834])]) ).

fof(f2020,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_46
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f425]) ).

fof(f20386,plain,
    ( spl0_833
    | spl0_747
    | ~ spl0_82
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1552,f1537,f665,f16075,f20384]) ).

fof(f20384,plain,
    ( spl0_833
  <=> ! [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_833])]) ).

fof(f16075,plain,
    ( spl0_747
  <=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f1552,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) )
    | ~ spl0_82
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f666]) ).

fof(f20300,plain,
    ( spl0_832
    | ~ spl0_39
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2024,f1999,f381,f20298]) ).

fof(f20298,plain,
    ( spl0_832
  <=> ! [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_832])]) ).

fof(f2024,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_39
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f382]) ).

fof(f20296,plain,
    ( spl0_831
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2023,f1999,f385,f20294]) ).

fof(f20294,plain,
    ( spl0_831
  <=> ! [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_831])]) ).

fof(f2023,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_40
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f386]) ).

fof(f20292,plain,
    ( spl0_830
    | ~ spl0_90
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2013,f1999,f706,f20290]) ).

fof(f20290,plain,
    ( spl0_830
  <=> ! [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_830])]) ).

fof(f706,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(f2013,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_216 ),
    inference(resolution,[],[f2000,f707]) ).

fof(f707,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,[],[f706]) ).

fof(f20288,plain,
    ( spl0_829
    | ~ spl0_85
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1895,f1889,f683,f20286]) ).

fof(f20286,plain,
    ( spl0_829
  <=> ! [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_829])]) ).

fof(f683,plain,
    ( spl0_85
  <=> ! [X0,X1] :
        ( ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1895,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_85
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f684]) ).

fof(f684,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f683]) ).

fof(f19907,plain,
    ( spl0_828
    | ~ spl0_16
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2151,f2122,f278,f19905]) ).

fof(f19905,plain,
    ( spl0_828
  <=> ! [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_828])]) ).

fof(f2151,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_16
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f279]) ).

fof(f19903,plain,
    ( spl0_827
    | ~ spl0_16
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2128,f2118,f278,f19901]) ).

fof(f19901,plain,
    ( spl0_827
  <=> ! [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_827])]) ).

fof(f2128,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_16
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f279]) ).

fof(f19899,plain,
    ( spl0_826
    | ~ spl0_29
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2026,f1999,f334,f19897]) ).

fof(f19897,plain,
    ( spl0_826
  <=> ! [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_826])]) ).

fof(f2026,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_29
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f335]) ).

fof(f19895,plain,
    ( spl0_825
    | spl0_177
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1928,f1918,f1528,f19892]) ).

fof(f19892,plain,
    ( spl0_825
  <=> 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_825])]) ).

fof(f1528,plain,
    ( spl0_177
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f1928,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_177
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1530]) ).

fof(f1530,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | spl0_177 ),
    inference(avatar_component_clause,[],[f1528]) ).

fof(f19889,plain,
    ( spl0_824
    | ~ spl0_33
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f19801,f1515,f352,f19886]) ).

fof(f19886,plain,
    ( spl0_824
  <=> subclass(application_function,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f1515,plain,
    ( spl0_174
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f19801,plain,
    ( subclass(application_function,composition_function)
    | ~ spl0_33
    | ~ spl0_174 ),
    inference(superposition,[],[f354,f1517]) ).

fof(f1517,plain,
    ( composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f1515]) ).

fof(f19884,plain,
    ( ~ spl0_823
    | ~ spl0_174
    | spl0_235 ),
    inference(avatar_split_clause,[],[f19805,f2263,f1515,f19881]) ).

fof(f19805,plain,
    ( ~ member(y,composition_function)
    | ~ spl0_174
    | spl0_235 ),
    inference(superposition,[],[f2264,f1517]) ).

fof(f19799,plain,
    ( spl0_822
    | spl0_175
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1927,f1918,f1519,f19796]) ).

fof(f19796,plain,
    ( spl0_822
  <=> 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_822])]) ).

fof(f1519,plain,
    ( spl0_175
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1927,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_175
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1521]) ).

fof(f1521,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | spl0_175 ),
    inference(avatar_component_clause,[],[f1519]) ).

fof(f19794,plain,
    ( spl0_821
    | ~ spl0_163
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1925,f1918,f1359,f19792]) ).

fof(f19792,plain,
    ( spl0_821
  <=> ! [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_821])]) ).

fof(f1359,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

fof(f1925,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_163
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1360]) ).

fof(f1360,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1359]) ).

fof(f19790,plain,
    ( spl0_819
    | ~ spl0_820
    | ~ spl0_130
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2035,f1999,f1005,f19787,f19784]) ).

fof(f19784,plain,
    ( spl0_819
  <=> ! [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))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f19787,plain,
    ( spl0_820
  <=> subclass(composition_function,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f2035,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,singleton_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) )
    | ~ spl0_130
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1006]) ).

fof(f19782,plain,
    ( spl0_817
    | ~ spl0_818
    | ~ spl0_131
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2033,f1999,f1009,f19779,f19776]) ).

fof(f19776,plain,
    ( spl0_817
  <=> ! [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_817])]) ).

fof(f19779,plain,
    ( spl0_818
  <=> subclass(composition_function,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f2033,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_131
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1010]) ).

fof(f19748,plain,
    ( spl0_239
    | ~ spl0_39
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f4049,f3977,f381,f2283]) ).

fof(f4049,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_39
    | ~ spl0_332 ),
    inference(resolution,[],[f3979,f382]) ).

fof(f19721,plain,
    ( spl0_816
    | ~ spl0_48
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1933,f1918,f432,f19719]) ).

fof(f19719,plain,
    ( spl0_816
  <=> ! [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_816])]) ).

fof(f432,plain,
    ( spl0_48
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1933,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_48
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f433]) ).

fof(f433,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f19717,plain,
    ( spl0_815
    | ~ spl0_90
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1899,f1889,f706,f19715]) ).

fof(f19715,plain,
    ( spl0_815
  <=> ! [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_815])]) ).

fof(f1899,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_212 ),
    inference(resolution,[],[f1890,f707]) ).

fof(f19713,plain,
    ( spl0_814
    | ~ spl0_95
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1133,f1089,f741,f19711]) ).

fof(f19711,plain,
    ( spl0_814
  <=> ! [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_814])]) ).

fof(f741,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(f1133,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_139 ),
    inference(resolution,[],[f1090,f742]) ).

fof(f742,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,[],[f741]) ).

fof(f19632,plain,
    ( spl0_813
    | ~ spl0_57
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1969,f1939,f500,f19630]) ).

fof(f19630,plain,
    ( spl0_813
  <=> ! [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_813])]) ).

fof(f1969,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_57
    | ~ spl0_214 ),
    inference(superposition,[],[f1940,f501]) ).

fof(f19626,plain,
    ( spl0_812
    | ~ spl0_162
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1921,f1918,f1355,f19624]) ).

fof(f19624,plain,
    ( spl0_812
  <=> ! [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_812])]) ).

fof(f1355,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

fof(f1921,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_162
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1356]) ).

fof(f1356,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1355]) ).

fof(f19622,plain,
    ( ~ spl0_810
    | spl0_811
    | ~ spl0_192
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1829,f1816,f1646,f19620,f19616]) ).

fof(f19616,plain,
    ( spl0_810
  <=> 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_810])]) ).

fof(f19620,plain,
    ( spl0_811
  <=> ! [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_811])]) ).

fof(f1829,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_192
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f1647]) ).

fof(f19600,plain,
    ( spl0_809
    | ~ spl0_102
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1218,f1199,f773,f19598]) ).

fof(f19598,plain,
    ( spl0_809
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f1218,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) = y )
    | ~ spl0_102
    | ~ spl0_144 ),
    inference(superposition,[],[f774,f1200]) ).

fof(f19593,plain,
    ( spl0_808
    | ~ spl0_46
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1902,f1889,f424,f19591]) ).

fof(f19591,plain,
    ( spl0_808
  <=> ! [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_808])]) ).

fof(f1902,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_46
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f425]) ).

fof(f19549,plain,
    ( spl0_807
    | ~ spl0_39
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1906,f1889,f381,f19547]) ).

fof(f19547,plain,
    ( spl0_807
  <=> ! [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_807])]) ).

fof(f1906,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_39
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f382]) ).

fof(f19545,plain,
    ( spl0_806
    | ~ spl0_40
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1905,f1889,f385,f19543]) ).

fof(f19543,plain,
    ( spl0_806
  <=> ! [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_806])]) ).

fof(f1905,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_40
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f386]) ).

fof(f19529,plain,
    ( spl0_805
    | ~ spl0_82
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1165,f1143,f665,f19527]) ).

fof(f19527,plain,
    ( spl0_805
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | y = intersection(X0,cross_product(X1,X2))
        | 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_805])]) ).

fof(f1165,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | y = intersection(X0,cross_product(X1,X2))
        | 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_82
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f666]) ).

fof(f19525,plain,
    ( spl0_804
    | ~ spl0_82
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1148,f1139,f665,f19523]) ).

fof(f19523,plain,
    ( spl0_804
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | y = intersection(cross_product(X0,X1),X2)
        | 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_804])]) ).

fof(f1148,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | y = intersection(cross_product(X0,X1),X2)
        | 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_82
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f666]) ).

fof(f19483,plain,
    ( spl0_803
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1908,f1889,f334,f19481]) ).

fof(f19481,plain,
    ( spl0_803
  <=> ! [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_803])]) ).

fof(f1908,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_29
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f335]) ).

fof(f19465,plain,
    ( spl0_802
    | ~ spl0_144
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f2184,f2175,f1199,f19463]) ).

fof(f19463,plain,
    ( spl0_802
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f2184,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) = y )
    | ~ spl0_144
    | ~ spl0_223 ),
    inference(superposition,[],[f2176,f1200]) ).

fof(f19443,plain,
    ( spl0_801
    | ~ spl0_130
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1915,f1889,f1005,f19441]) ).

fof(f19441,plain,
    ( spl0_801
  <=> ! [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_801])]) ).

fof(f1915,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_130
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f1006]) ).

fof(f19439,plain,
    ( ~ spl0_800
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_776 ),
    inference(avatar_split_clause,[],[f16997,f16784,f9421,f8731,f19436]) ).

fof(f16784,plain,
    ( spl0_776
  <=> ! [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_776])]) ).

fof(f16997,plain,
    ( ~ subclass(universal_class,flip(y))
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_776 ),
    inference(forward_demodulation,[],[f16982,f9423]) ).

fof(f16982,plain,
    ( ~ subclass(universal_class,flip(domain_of(y)))
    | ~ spl0_550
    | ~ spl0_776 ),
    inference(resolution,[],[f16785,f8732]) ).

fof(f16785,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_776 ),
    inference(avatar_component_clause,[],[f16784]) ).

fof(f19434,plain,
    ( spl0_799
    | ~ spl0_131
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1913,f1889,f1009,f19432]) ).

fof(f19432,plain,
    ( spl0_799
  <=> ! [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_799])]) ).

fof(f1913,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_131
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f1010]) ).

fof(f19352,plain,
    ( spl0_798
    | ~ spl0_46
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1887,f1883,f424,f19350]) ).

fof(f19350,plain,
    ( spl0_798
  <=> ! [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_798])]) ).

fof(f1887,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_46
    | ~ spl0_211 ),
    inference(resolution,[],[f1884,f425]) ).

fof(f19246,plain,
    ( spl0_797
    | ~ spl0_181
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2165,f2122,f1575,f19244]) ).

fof(f19244,plain,
    ( spl0_797
  <=> ! [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(y,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))
        | y = 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_797])]) ).

fof(f1575,plain,
    ( spl0_181
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(y,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))
        | y = 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_181])]) ).

fof(f2165,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(y,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))
        | y = 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_181
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1576]) ).

fof(f1576,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(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f1575]) ).

fof(f19242,plain,
    ( spl0_796
    | ~ spl0_12
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2161,f2122,f261,f19240]) ).

fof(f19240,plain,
    ( spl0_796
  <=> ! [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)
        | y = 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_796])]) ).

fof(f2161,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)
        | y = 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_12
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f262]) ).

fof(f19238,plain,
    ( spl0_795
    | ~ spl0_181
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2142,f2118,f1575,f19236]) ).

fof(f19236,plain,
    ( spl0_795
  <=> ! [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(y,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))
        | y = 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_795])]) ).

fof(f2142,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(y,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))
        | y = 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_181
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1576]) ).

fof(f19234,plain,
    ( spl0_794
    | ~ spl0_12
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2138,f2118,f261,f19232]) ).

fof(f19232,plain,
    ( spl0_794
  <=> ! [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)
        | y = 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_794])]) ).

fof(f2138,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)
        | y = 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_12
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f262]) ).

fof(f18953,plain,
    ( spl0_793
    | ~ spl0_17
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f18744,f1251,f282,f18950]) ).

fof(f18950,plain,
    ( spl0_793
  <=> subclass(element_relation,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f1251,plain,
    ( spl0_150
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f18744,plain,
    ( subclass(element_relation,domain_relation)
    | ~ spl0_17
    | ~ spl0_150 ),
    inference(superposition,[],[f284,f1253]) ).

fof(f1253,plain,
    ( cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1251]) ).

fof(f18948,plain,
    ( ~ spl0_792
    | spl0_126
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f18762,f1251,f986,f18945]) ).

fof(f18945,plain,
    ( spl0_792
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(domain_relation,universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f986,plain,
    ( spl0_126
  <=> 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_126])]) ).

fof(f18762,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(domain_relation,universal_class)),universal_class)))))
    | spl0_126
    | ~ spl0_150 ),
    inference(superposition,[],[f988,f1253]) ).

fof(f988,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | spl0_126 ),
    inference(avatar_component_clause,[],[f986]) ).

fof(f18943,plain,
    ( ~ spl0_791
    | ~ spl0_150
    | spl0_276 ),
    inference(avatar_split_clause,[],[f18790,f2842,f1251,f18940]) ).

fof(f18940,plain,
    ( spl0_791
  <=> y = complement(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f18790,plain,
    ( y != complement(domain_relation)
    | ~ spl0_150
    | spl0_276 ),
    inference(superposition,[],[f2843,f1253]) ).

fof(f2843,plain,
    ( y != complement(cross_product(universal_class,universal_class))
    | spl0_276 ),
    inference(avatar_component_clause,[],[f2842]) ).

fof(f18743,plain,
    ( spl0_790
    | spl0_151
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1926,f1918,f1255,f18740]) ).

fof(f18740,plain,
    ( spl0_790
  <=> 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_790])]) ).

fof(f1255,plain,
    ( spl0_151
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1926,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_151
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1257]) ).

fof(f1257,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | spl0_151 ),
    inference(avatar_component_clause,[],[f1255]) ).

fof(f18726,plain,
    ( spl0_789
    | ~ spl0_17
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f18516,f1242,f282,f18723]) ).

fof(f18723,plain,
    ( spl0_789
  <=> subclass(element_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f1242,plain,
    ( spl0_148
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f18516,plain,
    ( subclass(element_relation,successor_relation)
    | ~ spl0_17
    | ~ spl0_148 ),
    inference(superposition,[],[f284,f1244]) ).

fof(f1244,plain,
    ( cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_148 ),
    inference(avatar_component_clause,[],[f1242]) ).

fof(f18721,plain,
    ( ~ spl0_788
    | spl0_126
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f18534,f1242,f986,f18718]) ).

fof(f18718,plain,
    ( spl0_788
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(successor_relation,universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f18534,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(successor_relation,universal_class)),universal_class)))))
    | spl0_126
    | ~ spl0_148 ),
    inference(superposition,[],[f988,f1244]) ).

fof(f18715,plain,
    ( ~ spl0_787
    | spl0_124
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f18533,f1242,f978,f18712]) ).

fof(f18533,plain,
    ( ~ member(y,successor_relation)
    | spl0_124
    | ~ spl0_148 ),
    inference(superposition,[],[f980,f1244]) ).

fof(f18515,plain,
    ( spl0_786
    | spl0_149
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1923,f1918,f1246,f18512]) ).

fof(f18512,plain,
    ( spl0_786
  <=> 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_786])]) ).

fof(f1246,plain,
    ( spl0_149
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1923,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_149
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1248]) ).

fof(f1248,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_149 ),
    inference(avatar_component_clause,[],[f1246]) ).

fof(f18377,plain,
    ( ~ spl0_785
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_775 ),
    inference(avatar_split_clause,[],[f16893,f16780,f9421,f8731,f18374]) ).

fof(f16780,plain,
    ( spl0_775
  <=> ! [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_775])]) ).

fof(f16893,plain,
    ( ~ subclass(universal_class,rotate(y))
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_775 ),
    inference(forward_demodulation,[],[f16878,f9423]) ).

fof(f16878,plain,
    ( ~ subclass(universal_class,rotate(domain_of(y)))
    | ~ spl0_550
    | ~ spl0_775 ),
    inference(resolution,[],[f16781,f8732]) ).

fof(f16781,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_775 ),
    inference(avatar_component_clause,[],[f16780]) ).

fof(f17743,plain,
    ( spl0_238
    | ~ spl0_244
    | spl0_784
    | ~ spl0_79
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1177,f1143,f642,f17740,f2322,f2279]) ).

fof(f17740,plain,
    ( spl0_784
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f1177,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(subset_relation,universal_class)
    | subset_relation = y
    | ~ spl0_79
    | ~ spl0_141 ),
    inference(superposition,[],[f1144,f644]) ).

fof(f17736,plain,
    ( spl0_440
    | ~ spl0_144
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f17347,f1754,f1199,f5876]) ).

fof(f5876,plain,
    ( spl0_440
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f17347,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) = y )
    | ~ spl0_144
    | ~ spl0_198 ),
    inference(superposition,[],[f1755,f1200]) ).

fof(f17359,plain,
    ( spl0_783
    | ~ spl0_238
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f4035,f4032,f2279,f17357]) ).

fof(f17357,plain,
    ( spl0_783
  <=> ! [X2,X0,X1] :
        ( unordered_pair(X0,X1) = subset_relation
        | member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f4035,plain,
    ( ! [X2,X0,X1] :
        ( unordered_pair(X0,X1) = subset_relation
        | member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_238
    | ~ spl0_335 ),
    inference(forward_demodulation,[],[f4033,f2281]) ).

fof(f2281,plain,
    ( subset_relation = y
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f2279]) ).

fof(f17329,plain,
    ( spl0_782
    | ~ spl0_18
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f17028,f1233,f287,f17326]) ).

fof(f17326,plain,
    ( spl0_782
  <=> subclass(successor_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f1233,plain,
    ( spl0_146
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f17028,plain,
    ( subclass(successor_relation,element_relation)
    | ~ spl0_18
    | ~ spl0_146 ),
    inference(superposition,[],[f289,f1235]) ).

fof(f1235,plain,
    ( element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1233]) ).

fof(f17231,plain,
    ( spl0_781
    | ~ spl0_146
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f17071,f2283,f1233,f17228]) ).

fof(f17071,plain,
    ( member(regular(subset_relation),element_relation)
    | ~ spl0_146
    | ~ spl0_239 ),
    inference(superposition,[],[f2285,f1235]) ).

fof(f17226,plain,
    ( ~ spl0_780
    | spl0_126
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f17045,f1233,f986,f17223]) ).

fof(f17223,plain,
    ( spl0_780
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f17045,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class)))))
    | spl0_126
    | ~ spl0_146 ),
    inference(superposition,[],[f988,f1235]) ).

fof(f17026,plain,
    ( spl0_779
    | spl0_147
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1922,f1918,f1237,f17023]) ).

fof(f17023,plain,
    ( spl0_779
  <=> 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_779])]) ).

fof(f1237,plain,
    ( spl0_147
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1922,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_147
    | ~ spl0_213 ),
    inference(resolution,[],[f1919,f1239]) ).

fof(f1239,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_147 ),
    inference(avatar_component_clause,[],[f1237]) ).

fof(f17005,plain,
    ( spl0_778
    | ~ spl0_144
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2170,f2122,f1199,f17003]) ).

fof(f17003,plain,
    ( spl0_778
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f2170,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) = y )
    | ~ spl0_144
    | ~ spl0_222 ),
    inference(superposition,[],[f2123,f1200]) ).

fof(f17001,plain,
    ( spl0_777
    | ~ spl0_116
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2031,f1999,f912,f16999]) ).

fof(f16999,plain,
    ( spl0_777
  <=> ! [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))
        | y = 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_777])]) ).

fof(f2031,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))
        | y = 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_116
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f913]) ).

fof(f16786,plain,
    ( spl0_776
    | ~ spl0_99
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1108,f1078,f759,f16784]) ).

fof(f1108,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_99
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f760]) ).

fof(f16782,plain,
    ( spl0_775
    | ~ spl0_96
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1107,f1078,f746,f16780]) ).

fof(f1107,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_137 ),
    inference(resolution,[],[f1079,f747]) ).

fof(f16775,plain,
    ( spl0_773
    | ~ spl0_774
    | ~ spl0_81
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2012,f1999,f661,f16772,f16769]) ).

fof(f16769,plain,
    ( spl0_773
  <=> ! [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_773])]) ).

fof(f16772,plain,
    ( spl0_774
  <=> subclass(composition_function,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f661,plain,
    ( spl0_81
  <=> ! [X0,X1] :
        ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f2012,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_81
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f662]) ).

fof(f662,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f661]) ).

fof(f16767,plain,
    ( spl0_772
    | ~ spl0_81
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1898,f1889,f661,f16765]) ).

fof(f16765,plain,
    ( spl0_772
  <=> ! [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_772])]) ).

fof(f1898,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),successor_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) )
    | ~ spl0_81
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f662]) ).

fof(f16717,plain,
    ( spl0_771
    | ~ spl0_170
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2164,f2122,f1491,f16715]) ).

fof(f16715,plain,
    ( spl0_771
  <=> ! [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(y,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))
        | y = 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_771])]) ).

fof(f1491,plain,
    ( spl0_170
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f2164,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(y,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))
        | y = 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_170
    | ~ spl0_222 ),
    inference(resolution,[],[f2123,f1492]) ).

fof(f1492,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(y,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))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_170 ),
    inference(avatar_component_clause,[],[f1491]) ).

fof(f16713,plain,
    ( spl0_770
    | ~ spl0_170
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2141,f2118,f1491,f16711]) ).

fof(f16711,plain,
    ( spl0_770
  <=> ! [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(y,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))
        | y = 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_770])]) ).

fof(f2141,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(y,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))
        | y = 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_170
    | ~ spl0_221 ),
    inference(resolution,[],[f2119,f1492]) ).

fof(f16660,plain,
    ( spl0_769
    | ~ spl0_101
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1217,f1199,f767,f16658]) ).

fof(f16658,plain,
    ( spl0_769
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f1217,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) = y )
    | ~ spl0_101
    | ~ spl0_144 ),
    inference(superposition,[],[f768,f1200]) ).

fof(f16630,plain,
    ( spl0_768
    | ~ spl0_55
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1781,f1750,f492,f16628]) ).

fof(f16628,plain,
    ( spl0_768
  <=> ! [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_768])]) ).

fof(f1781,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_55
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f493]) ).

fof(f16625,plain,
    ( spl0_766
    | ~ spl0_767
    | ~ spl0_167
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1725,f1646,f1424,f16622,f16619]) ).

fof(f16619,plain,
    ( spl0_766
  <=> ! [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_766])]) ).

fof(f16622,plain,
    ( spl0_767
  <=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f1725,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_167
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f1425]) ).

fof(f16617,plain,
    ( spl0_764
    | ~ spl0_765
    | ~ spl0_166
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1722,f1646,f1420,f16614,f16611]) ).

fof(f16611,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f16614,plain,
    ( spl0_765
  <=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f1722,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_166
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f1421]) ).

fof(f16609,plain,
    ( spl0_763
    | ~ spl0_82
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1312,f1287,f665,f16607]) ).

fof(f16607,plain,
    ( spl0_763
  <=> ! [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_763])]) ).

fof(f1312,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) )
    | ~ spl0_82
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f666]) ).

fof(f16605,plain,
    ( ~ spl0_762
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_693 ),
    inference(avatar_split_clause,[],[f16439,f14096,f9421,f8731,f16602]) ).

fof(f16602,plain,
    ( spl0_762
  <=> subclass(subset_relation,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f14096,plain,
    ( spl0_693
  <=> ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f16439,plain,
    ( ~ subclass(subset_relation,y)
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_693 ),
    inference(forward_demodulation,[],[f16429,f9423]) ).

fof(f16429,plain,
    ( ~ subclass(subset_relation,domain_of(y))
    | ~ spl0_550
    | ~ spl0_693 ),
    inference(resolution,[],[f14097,f8732]) ).

fof(f14097,plain,
    ( ! [X0] :
        ( member(regular(identity_relation),X0)
        | ~ subclass(subset_relation,X0) )
    | ~ spl0_693 ),
    inference(avatar_component_clause,[],[f14096]) ).

fof(f16455,plain,
    ( spl0_761
    | ~ spl0_112
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1988,f1943,f856,f16453]) ).

fof(f16453,plain,
    ( spl0_761
  <=> ! [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))
        | y = 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_761])]) ).

fof(f1988,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))
        | y = 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_112
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f857]) ).

fof(f16451,plain,
    ( spl0_760
    | ~ spl0_111
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1979,f1943,f852,f16449]) ).

fof(f16449,plain,
    ( spl0_760
  <=> ! [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))
        | y = 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_760])]) ).

fof(f1979,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))
        | y = 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_111
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f853]) ).

fof(f16447,plain,
    ( spl0_759
    | ~ spl0_112
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1962,f1939,f856,f16445]) ).

fof(f16445,plain,
    ( spl0_759
  <=> ! [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))
        | y = 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_759])]) ).

fof(f1962,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))
        | y = 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_112
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f857]) ).

fof(f16443,plain,
    ( spl0_758
    | ~ spl0_111
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1953,f1939,f852,f16441]) ).

fof(f16441,plain,
    ( spl0_758
  <=> ! [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))
        | y = 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_758])]) ).

fof(f1953,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))
        | y = 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_111
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f853]) ).

fof(f16395,plain,
    ( spl0_757
    | ~ spl0_94
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f879,f856,f725,f16393]) ).

fof(f16393,plain,
    ( spl0_757
  <=> ! [X0,X3,X2,X1] :
        ( y = 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_757])]) ).

fof(f879,plain,
    ( ! [X2,X3,X0,X1] :
        ( y = 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_112 ),
    inference(resolution,[],[f857,f726]) ).

fof(f16391,plain,
    ( spl0_756
    | ~ spl0_94
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f865,f852,f725,f16389]) ).

fof(f16389,plain,
    ( spl0_756
  <=> ! [X0,X3,X2,X1] :
        ( y = 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_756])]) ).

fof(f865,plain,
    ( ! [X2,X3,X0,X1] :
        ( y = 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_111 ),
    inference(resolution,[],[f853,f726]) ).

fof(f16242,plain,
    ( spl0_755
    | ~ spl0_76
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2014,f1999,f625,f16240]) ).

fof(f16240,plain,
    ( spl0_755
  <=> ! [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_755])]) ).

fof(f625,plain,
    ( spl0_76
  <=> ! [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_76])]) ).

fof(f2014,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_76
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f626]) ).

fof(f626,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_76 ),
    inference(avatar_component_clause,[],[f625]) ).

fof(f16238,plain,
    ( spl0_754
    | ~ spl0_55
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1763,f1746,f492,f16236]) ).

fof(f16236,plain,
    ( spl0_754
  <=> ! [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_754])]) ).

fof(f1763,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_55
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f493]) ).

fof(f16234,plain,
    ( spl0_753
    | ~ spl0_55
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1717,f1646,f492,f16232]) ).

fof(f16232,plain,
    ( spl0_753
  <=> ! [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_753])]) ).

fof(f1717,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_55
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f493]) ).

fof(f16230,plain,
    ( spl0_752
    | ~ spl0_56
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1677,f1642,f496,f16228]) ).

fof(f16228,plain,
    ( spl0_752
  <=> ! [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_752])]) ).

fof(f1677,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_56
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f497]) ).

fof(f16226,plain,
    ( spl0_751
    | ~ spl0_145
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1632,f1625,f1229,f16224]) ).

fof(f16224,plain,
    ( spl0_751
  <=> ! [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_751])]) ).

fof(f1229,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1632,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_145
    | ~ spl0_189 ),
    inference(resolution,[],[f1626,f1230]) ).

fof(f1230,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1229]) ).

fof(f16190,plain,
    ( spl0_750
    | ~ spl0_57
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1875,f1866,f500,f16188]) ).

fof(f16188,plain,
    ( spl0_750
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(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))))),regular(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)))))))),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(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))))),regular(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)))))))),compose(X2,X1))
        | y = 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)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1866,plain,
    ( spl0_209
  <=> ! [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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_209])]) ).

fof(f1875,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(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))))),regular(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)))))))),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(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))))),regular(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)))))))),compose(X2,X1))
        | y = 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)))) )
    | ~ spl0_57
    | ~ spl0_209 ),
    inference(superposition,[],[f1867,f501]) ).

fof(f1867,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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_209 ),
    inference(avatar_component_clause,[],[f1866]) ).

fof(f16186,plain,
    ( spl0_749
    | ~ spl0_57
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1872,f1866,f500,f16184]) ).

fof(f16184,plain,
    ( spl0_749
  <=> ! [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)))))))),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(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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_749])]) ).

fof(f1872,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)))))))),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(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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_57
    | ~ spl0_209 ),
    inference(superposition,[],[f1867,f501]) ).

fof(f16167,plain,
    ( spl0_748
    | ~ spl0_73
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2007,f1999,f609,f16165]) ).

fof(f16165,plain,
    ( spl0_748
  <=> ! [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_748])]) ).

fof(f609,plain,
    ( spl0_73
  <=> ! [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_73])]) ).

fof(f2007,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_73
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f610]) ).

fof(f610,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_73 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f16077,plain,
    ( spl0_746
    | spl0_747
    | ~ spl0_82
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1113,f1078,f665,f16075,f16072]) ).

fof(f16072,plain,
    ( spl0_746
  <=> ! [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_746])]) ).

fof(f1113,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) )
    | ~ spl0_82
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f666]) ).

fof(f16070,plain,
    ( ~ spl0_745
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_691 ),
    inference(avatar_split_clause,[],[f15652,f13889,f9421,f8731,f16067]) ).

fof(f15652,plain,
    ( ~ subclass(element_relation,y)
    | ~ spl0_550
    | ~ spl0_567
    | ~ spl0_691 ),
    inference(forward_demodulation,[],[f15642,f9423]) ).

fof(f15642,plain,
    ( ~ subclass(element_relation,domain_of(y))
    | ~ spl0_550
    | ~ spl0_691 ),
    inference(resolution,[],[f13890,f8732]) ).

fof(f16038,plain,
    ( spl0_744
    | ~ spl0_139
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1870,f1866,f1089,f16036]) ).

fof(f16036,plain,
    ( spl0_744
  <=> ! [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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_744])]) ).

fof(f1870,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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_139
    | ~ spl0_209 ),
    inference(resolution,[],[f1867,f1090]) ).

fof(f16003,plain,
    ( spl0_743
    | ~ spl0_100
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1216,f1199,f763,f16001]) ).

fof(f16001,plain,
    ( spl0_743
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f763,plain,
    ( spl0_100
  <=> ! [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_100])]) ).

fof(f1216,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) = y )
    | ~ spl0_100
    | ~ spl0_144 ),
    inference(superposition,[],[f764,f1200]) ).

fof(f764,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_100 ),
    inference(avatar_component_clause,[],[f763]) ).

fof(f15938,plain,
    ( spl0_741
    | ~ spl0_742
    | ~ spl0_68
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2015,f1999,f583,f15935,f15932]) ).

fof(f15932,plain,
    ( spl0_741
  <=> ! [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_741])]) ).

fof(f15935,plain,
    ( spl0_742
  <=> subclass(composition_function,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f583,plain,
    ( spl0_68
  <=> ! [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_68])]) ).

fof(f2015,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_68
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f584]) ).

fof(f584,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f583]) ).

fof(f15930,plain,
    ( spl0_740
    | ~ spl0_90
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1709,f1646,f706,f15928]) ).

fof(f15928,plain,
    ( spl0_740
  <=> ! [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_740])]) ).

fof(f1709,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_192 ),
    inference(resolution,[],[f1647,f707]) ).

fof(f15926,plain,
    ( spl0_739
    | ~ spl0_35
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1631,f1625,f365,f15924]) ).

fof(f15924,plain,
    ( spl0_739
  <=> ! [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_739])]) ).

fof(f1631,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_35
    | ~ spl0_189 ),
    inference(resolution,[],[f1626,f366]) ).

fof(f15727,plain,
    ( spl0_737
    | ~ spl0_738
    | ~ spl0_65
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2010,f1999,f569,f15724,f15721]) ).

fof(f15721,plain,
    ( spl0_737
  <=> ! [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_737])]) ).

fof(f15724,plain,
    ( spl0_738
  <=> subclass(composition_function,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f569,plain,
    ( spl0_65
  <=> ! [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_65])]) ).

fof(f2010,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_65
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f570]) ).

fof(f570,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f569]) ).

fof(f15719,plain,
    ( spl0_736
    | ~ spl0_153
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1682,f1642,f1264,f15717]) ).

fof(f15717,plain,
    ( spl0_736
  <=> ! [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_736])]) ).

fof(f1682,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_153
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1265]) ).

fof(f15715,plain,
    ( ~ spl0_735
    | ~ spl0_31
    | spl0_727 ),
    inference(avatar_split_clause,[],[f15661,f15657,f342,f15712]) ).

fof(f15712,plain,
    ( spl0_735
  <=> function(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f15657,plain,
    ( spl0_727
  <=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f15661,plain,
    ( ~ function(composition_function)
    | ~ spl0_31
    | spl0_727 ),
    inference(resolution,[],[f15659,f343]) ).

fof(f15659,plain,
    ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
    | spl0_727 ),
    inference(avatar_component_clause,[],[f15657]) ).

fof(f15710,plain,
    ( spl0_734
    | ~ spl0_152
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1680,f1642,f1260,f15708]) ).

fof(f15708,plain,
    ( spl0_734
  <=> ! [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_734])]) ).

fof(f1680,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_152
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1261]) ).

fof(f15706,plain,
    ( spl0_733
    | ~ spl0_161
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1477,f1424,f1351,f15704]) ).

fof(f15704,plain,
    ( spl0_733
  <=> ! [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_733])]) ).

fof(f1477,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_161
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1352]) ).

fof(f15702,plain,
    ( spl0_732
    | ~ spl0_160
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1467,f1424,f1347,f15700]) ).

fof(f15700,plain,
    ( spl0_732
  <=> ! [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_732])]) ).

fof(f1467,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_160
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1348]) ).

fof(f15698,plain,
    ( spl0_731
    | ~ spl0_161
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1452,f1420,f1351,f15696]) ).

fof(f15696,plain,
    ( spl0_731
  <=> ! [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_731])]) ).

fof(f1452,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_161
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1352]) ).

fof(f15694,plain,
    ( spl0_730
    | ~ spl0_160
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1442,f1420,f1347,f15692]) ).

fof(f15692,plain,
    ( spl0_730
  <=> ! [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_730])]) ).

fof(f1442,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_160
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1348]) ).

fof(f15690,plain,
    ( spl0_729
    | ~ spl0_89
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1134,f1089,f701,f15688]) ).

fof(f15688,plain,
    ( spl0_729
  <=> ! [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_729])]) ).

fof(f701,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(f1134,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_139 ),
    inference(resolution,[],[f1090,f702]) ).

fof(f702,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,[],[f701]) ).

fof(f15665,plain,
    ( spl0_728
    | ~ spl0_82
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1048,f1043,f665,f15663]) ).

fof(f15663,plain,
    ( spl0_728
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | y = X0
        | domain_of(intersection(element_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_728])]) ).

fof(f1048,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | y = X0
        | domain_of(intersection(element_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_82
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f666]) ).

fof(f15660,plain,
    ( spl0_726
    | ~ spl0_727
    | ~ spl0_180
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2008,f1999,f1566,f15657,f15654]) ).

fof(f15654,plain,
    ( spl0_726
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | y = intersection(cross_product(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),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(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(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))))))),compose(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f1566,plain,
    ( spl0_180
  <=> ! [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)
        | y = 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_180])]) ).

fof(f2008,plain,
    ( ! [X2,X3,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))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),universal_class)
        | y = intersection(cross_product(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),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_180
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f1567]) ).

fof(f1567,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)
        | y = 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_180 ),
    inference(avatar_component_clause,[],[f1566]) ).

fof(f15500,plain,
    ( spl0_725
    | ~ spl0_144
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2147,f2118,f1199,f15498]) ).

fof(f15498,plain,
    ( spl0_725
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f2147,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) = y )
    | ~ spl0_144
    | ~ spl0_221 ),
    inference(superposition,[],[f2119,f1200]) ).

fof(f15496,plain,
    ( spl0_724
    | ~ spl0_116
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1911,f1889,f912,f15494]) ).

fof(f15494,plain,
    ( spl0_724
  <=> ! [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)
        | y = 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_724])]) ).

fof(f1911,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)
        | y = 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_116
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f913]) ).

fof(f15492,plain,
    ( spl0_723
    | ~ spl0_99
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1215,f1199,f759,f15490]) ).

fof(f15490,plain,
    ( spl0_723
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f1215,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) = y )
    | ~ spl0_99
    | ~ spl0_144 ),
    inference(superposition,[],[f760,f1200]) ).

fof(f15441,plain,
    ( spl0_722
    | ~ spl0_154
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1837,f1816,f1287,f15439]) ).

fof(f15439,plain,
    ( spl0_722
  <=> ! [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_722])]) ).

fof(f1837,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_154
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f1288]) ).

fof(f15437,plain,
    ( spl0_721
    | ~ spl0_51
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1679,f1642,f472,f15435]) ).

fof(f15435,plain,
    ( spl0_721
  <=> ! [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_721])]) ).

fof(f1679,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_51
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f473]) ).

fof(f15433,plain,
    ( spl0_720
    | ~ spl0_2
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2680,f2450,f213,f15431]) ).

fof(f2680,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_2
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f2651]) ).

fof(f2651,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,complement(X0))
        | y = X0 )
    | ~ spl0_2
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f214]) ).

fof(f15387,plain,
    ( spl0_719
    | ~ spl0_7
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2193,f2186,f238,f15385]) ).

fof(f15385,plain,
    ( spl0_719
  <=> ! [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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X1),universal_class)))),X2)
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f2193,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(y,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X1),universal_class)))),X2)
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_224 ),
    inference(superposition,[],[f2187,f239]) ).

fof(f15383,plain,
    ( spl0_718
    | ~ spl0_134
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1984,f1943,f1043,f15381]) ).

fof(f15381,plain,
    ( spl0_718
  <=> ! [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))
        | ~ 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)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f1984,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))
        | ~ 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)
        | y = X1 )
    | ~ spl0_134
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f1044]) ).

fof(f15379,plain,
    ( spl0_717
    | ~ spl0_134
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1958,f1939,f1043,f15377]) ).

fof(f15377,plain,
    ( spl0_717
  <=> ! [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))
        | ~ 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)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f1958,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))
        | ~ 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)
        | y = X1 )
    | ~ spl0_134
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f1044]) ).

fof(f15375,plain,
    ( spl0_716
    | ~ spl0_94
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1052,f1043,f725,f15373]) ).

fof(f15373,plain,
    ( spl0_716
  <=> ! [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)))))
        | ~ member(X0,universal_class)
        | y = X0
        | 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_716])]) ).

fof(f1052,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)))))
        | ~ member(X0,universal_class)
        | y = X0
        | 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_134 ),
    inference(resolution,[],[f1044,f726]) ).

fof(f15326,plain,
    ( spl0_715
    | ~ spl0_46
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f15322,f973,f424,f15324]) ).

fof(f15324,plain,
    ( spl0_715
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(domain_of(flip(cross_product(y,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f15322,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(domain_of(domain_of(flip(cross_product(y,universal_class)))),X0) )
    | ~ spl0_46
    | ~ spl0_123 ),
    inference(resolution,[],[f975,f425]) ).

fof(f975,plain,
    ( member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f973]) ).

fof(f15309,plain,
    ( spl0_714
    | ~ spl0_662
    | ~ spl0_713 ),
    inference(avatar_split_clause,[],[f15305,f15300,f13193,f15307]) ).

fof(f15307,plain,
    ( spl0_714
  <=> ! [X0,X1] :
        ( y = domain_of(domain_of(flip(cross_product(intersection(cross_product(y,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f15300,plain,
    ( spl0_713
  <=> ! [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(y,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(y,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(y,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(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f15305,plain,
    ( ! [X0,X1] :
        ( y = domain_of(domain_of(flip(cross_product(intersection(cross_product(y,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_662
    | ~ spl0_713 ),
    inference(forward_demodulation,[],[f15304,f13195]) ).

fof(f13195,plain,
    ( y = domain_of(domain_of(flip(cross_product(y,universal_class))))
    | ~ spl0_662 ),
    inference(avatar_component_clause,[],[f13193]) ).

fof(f15304,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_662
    | ~ spl0_713 ),
    inference(forward_demodulation,[],[f15303,f13195]) ).

fof(f15303,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(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,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(y,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(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_662
    | ~ spl0_713 ),
    inference(forward_demodulation,[],[f15301,f13195]) ).

fof(f15301,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(y,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(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_713 ),
    inference(avatar_component_clause,[],[f15300]) ).

fof(f15302,plain,
    ( spl0_713
    | ~ spl0_7
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1873,f1866,f238,f15300]) ).

fof(f1873,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(y,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(y,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(y,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(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_209 ),
    inference(superposition,[],[f1867,f239]) ).

fof(f15220,plain,
    ( spl0_712
    | ~ spl0_76
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1900,f1889,f625,f15218]) ).

fof(f15218,plain,
    ( spl0_712
  <=> ! [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_712])]) ).

fof(f1900,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_76
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f626]) ).

fof(f15216,plain,
    ( ~ spl0_711
    | spl0_186
    | ~ spl0_187
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2669,f2450,f1605,f1601,f15213]) ).

fof(f15213,plain,
    ( spl0_711
  <=> subclass(identity_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f2669,plain,
    ( identity_relation = y
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_187
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f1607]) ).

fof(f15211,plain,
    ( spl0_710
    | ~ spl0_90
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1098,f1078,f706,f15209]) ).

fof(f15209,plain,
    ( spl0_710
  <=> ! [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_710])]) ).

fof(f1098,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_137 ),
    inference(resolution,[],[f1079,f707]) ).

fof(f15096,plain,
    ( spl0_709
    | ~ spl0_46
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1845,f1841,f424,f15094]) ).

fof(f15094,plain,
    ( spl0_709
  <=> ! [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_709])]) ).

fof(f1845,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_46
    | ~ spl0_204 ),
    inference(resolution,[],[f1842,f425]) ).

fof(f15092,plain,
    ( ~ spl0_707
    | spl0_708
    | ~ spl0_137
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1836,f1816,f1078,f15090,f15086]) ).

fof(f15086,plain,
    ( spl0_707
  <=> 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_707])]) ).

fof(f15090,plain,
    ( spl0_708
  <=> ! [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_708])]) ).

fof(f1836,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_137
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f1079]) ).

fof(f15084,plain,
    ( spl0_706
    | ~ spl0_79
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1687,f1642,f642,f15082]) ).

fof(f15082,plain,
    ( spl0_706
  <=> ! [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_706])]) ).

fof(f1687,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_79
    | ~ spl0_191 ),
    inference(superposition,[],[f1643,f644]) ).

fof(f14969,plain,
    ( spl0_705
    | ~ spl0_80
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1869,f1866,f647,f14967]) ).

fof(f14967,plain,
    ( spl0_705
  <=> ! [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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_705])]) ).

fof(f1869,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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_80
    | ~ spl0_209 ),
    inference(resolution,[],[f1867,f648]) ).

fof(f14965,plain,
    ( spl0_704
    | ~ spl0_96
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1214,f1199,f746,f14963]) ).

fof(f14963,plain,
    ( spl0_704
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f1214,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) = y )
    | ~ spl0_96
    | ~ spl0_144 ),
    inference(superposition,[],[f747,f1200]) ).

fof(f14896,plain,
    ( spl0_703
    | ~ spl0_68
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1901,f1889,f583,f14894]) ).

fof(f14894,plain,
    ( spl0_703
  <=> ! [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_703])]) ).

fof(f1901,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_68
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f584]) ).

fof(f14892,plain,
    ( spl0_702
    | ~ spl0_142
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1668,f1638,f1181,f14890]) ).

fof(f14890,plain,
    ( spl0_702
  <=> ! [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_702])]) ).

fof(f1668,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_142
    | ~ spl0_190 ),
    inference(resolution,[],[f1639,f1182]) ).

fof(f14888,plain,
    ( spl0_701
    | ~ spl0_79
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1546,f1533,f642,f14886]) ).

fof(f14886,plain,
    ( spl0_701
  <=> ! [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_701])]) ).

fof(f1533,plain,
    ( spl0_178
  <=> ! [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_178])]) ).

fof(f1546,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_79
    | ~ spl0_178 ),
    inference(superposition,[],[f1534,f644]) ).

fof(f1534,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f1533]) ).

fof(f14833,plain,
    ( ~ spl0_700
    | spl0_168
    | ~ spl0_169
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2659,f2450,f1432,f1428,f14830]) ).

fof(f2659,plain,
    ( singleton_relation = y
    | ~ subclass(singleton_relation,complement(element_relation))
    | ~ spl0_169
    | ~ spl0_248 ),
    inference(resolution,[],[f2451,f1434]) ).

fof(f14729,plain,
    ( spl0_699
    | ~ spl0_65
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1896,f1889,f569,f14727]) ).

fof(f14727,plain,
    ( spl0_699
  <=> ! [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_699])]) ).

fof(f1896,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_65
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f570]) ).

fof(f14707,plain,
    ( spl0_698
    | ~ spl0_20
    | ~ spl0_85
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1705,f1646,f683,f296,f14705]) ).

fof(f14705,plain,
    ( spl0_698
  <=> ! [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_698])]) ).

fof(f1705,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | ~ member(X0,domain_of(X0)) )
    | ~ spl0_85
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f684]) ).

fof(f14695,plain,
    ( spl0_697
    | ~ spl0_90
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2458,f1497,f706,f14693]) ).

fof(f14693,plain,
    ( spl0_697
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),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(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_697])]) ).

fof(f2458,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),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(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_171 ),
    inference(resolution,[],[f1498,f707]) ).

fof(f14691,plain,
    ( ~ spl0_696
    | ~ spl0_29
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f2513,f2454,f334,f14688]) ).

fof(f2513,plain,
    ( ~ member(regular(singleton_relation),compose(element_relation,complement(identity_relation)))
    | ~ spl0_29
    | ~ spl0_249 ),
    inference(resolution,[],[f2456,f335]) ).

fof(f14331,plain,
    ( spl0_186
    | ~ spl0_199
    | spl0_695
    | ~ spl0_50
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1162,f1139,f441,f14328,f1758,f1601]) ).

fof(f1758,plain,
    ( spl0_199
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f14328,plain,
    ( spl0_695
  <=> 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_695])]) ).

fof(f1162,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))))
    | ~ member(identity_relation,universal_class)
    | identity_relation = y
    | ~ spl0_50
    | ~ spl0_140 ),
    inference(superposition,[],[f1140,f443]) ).

fof(f14152,plain,
    ( spl0_694
    | ~ spl0_186
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f2530,f2527,f1601,f14150]) ).

fof(f14150,plain,
    ( spl0_694
  <=> ! [X0] :
        ( identity_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f2530,plain,
    ( ! [X0] :
        ( identity_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) )
    | ~ spl0_186
    | ~ spl0_253 ),
    inference(forward_demodulation,[],[f2528,f1603]) ).

fof(f1603,plain,
    ( identity_relation = y
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1601]) ).

fof(f14098,plain,
    ( spl0_693
    | ~ spl0_46
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1937,f1605,f424,f14096]) ).

fof(f1937,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) )
    | ~ spl0_46
    | ~ spl0_187 ),
    inference(resolution,[],[f1607,f425]) ).

fof(f13965,plain,
    ( spl0_692
    | ~ spl0_109
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1459,f1428,f1420,f831,f13963]) ).

fof(f13963,plain,
    ( spl0_692
  <=> ! [X0] :
        ( singleton_relation = X0
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f1459,plain,
    ( ! [X0] :
        ( singleton_relation = X0
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_109
    | ~ spl0_166
    | ~ spl0_168 ),
    inference(forward_demodulation,[],[f1448,f1430]) ).

fof(f1448,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f832]) ).

fof(f13891,plain,
    ( spl0_691
    | ~ spl0_46
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1564,f1432,f424,f13889]) ).

fof(f1564,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_46
    | ~ spl0_169 ),
    inference(resolution,[],[f1434,f425]) ).

fof(f13887,plain,
    ( spl0_690
    | ~ spl0_139
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1676,f1642,f1089,f13885]) ).

fof(f13885,plain,
    ( spl0_690
  <=> ! [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_690])]) ).

fof(f1676,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_139
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1090]) ).

fof(f13883,plain,
    ( spl0_689
    | ~ spl0_34
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1466,f1424,f361,f13881]) ).

fof(f13881,plain,
    ( spl0_689
  <=> ! [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_689])]) ).

fof(f1466,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_34
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f362]) ).

fof(f13879,plain,
    ( spl0_688
    | ~ spl0_34
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1441,f1420,f361,f13877]) ).

fof(f13877,plain,
    ( spl0_688
  <=> ! [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_688])]) ).

fof(f1441,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_34
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f362]) ).

fof(f13875,plain,
    ( spl0_687
    | ~ spl0_55
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1390,f1351,f492,f13873]) ).

fof(f13873,plain,
    ( spl0_687
  <=> ! [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_687])]) ).

fof(f1390,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_55
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f493]) ).

fof(f13871,plain,
    ( spl0_686
    | ~ spl0_55
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1369,f1347,f492,f13869]) ).

fof(f13869,plain,
    ( spl0_686
  <=> ! [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_686])]) ).

fof(f1369,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_55
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f493]) ).

fof(f13867,plain,
    ( spl0_685
    | ~ spl0_85
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1130,f1089,f683,f13865]) ).

fof(f13865,plain,
    ( spl0_685
  <=> ! [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_685])]) ).

fof(f1130,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_85
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f684]) ).

fof(f13863,plain,
    ( ~ spl0_5
    | ~ spl0_683
    | spl0_684
    | ~ spl0_67
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1124,f1082,f577,f13860,f13856,f228]) ).

fof(f228,plain,
    ( spl0_5
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f13856,plain,
    ( spl0_683
  <=> 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_683])]) ).

fof(f13860,plain,
    ( spl0_684
  <=> 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_684])]) ).

fof(f577,plain,
    ( spl0_67
  <=> ! [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_67])]) ).

fof(f1082,plain,
    ( spl0_138
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1124,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_67
    | ~ spl0_138 ),
    inference(resolution,[],[f1083,f578]) ).

fof(f578,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f577]) ).

fof(f1083,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1082]) ).

fof(f13814,plain,
    ( spl0_682
    | ~ spl0_73
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1893,f1889,f609,f13812]) ).

fof(f13812,plain,
    ( spl0_682
  <=> ! [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_682])]) ).

fof(f1893,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_73
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f610]) ).

fof(f13810,plain,
    ( spl0_681
    | ~ spl0_74
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1892,f1889,f613,f13808]) ).

fof(f13808,plain,
    ( spl0_681
  <=> ! [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_681])]) ).

fof(f613,plain,
    ( spl0_74
  <=> ! [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_74])]) ).

fof(f1892,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_74
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f614]) ).

fof(f614,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f13806,plain,
    ( spl0_680
    | ~ spl0_48
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1666,f1638,f432,f13804]) ).

fof(f13804,plain,
    ( spl0_680
  <=> ! [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_680])]) ).

fof(f1666,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_48
    | ~ spl0_190 ),
    inference(resolution,[],[f1639,f433]) ).

fof(f13802,plain,
    ( spl0_679
    | ~ spl0_55
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1551,f1537,f492,f13800]) ).

fof(f13800,plain,
    ( spl0_679
  <=> ! [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_679])]) ).

fof(f1551,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_55
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f493]) ).

fof(f13574,plain,
    ( spl0_678
    | ~ spl0_31
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1814,f1809,f342,f13572]) ).

fof(f13572,plain,
    ( spl0_678
  <=> ! [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_678])]) ).

fof(f1814,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_31
    | ~ spl0_202 ),
    inference(resolution,[],[f1810,f343]) ).

fof(f13570,plain,
    ( spl0_677
    | ~ spl0_46
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1795,f1754,f424,f13568]) ).

fof(f13568,plain,
    ( spl0_677
  <=> ! [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_677])]) ).

fof(f1795,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_46
    | ~ spl0_198 ),
    inference(resolution,[],[f1755,f425]) ).

fof(f13566,plain,
    ( spl0_676
    | ~ spl0_46
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1780,f1750,f424,f13564]) ).

fof(f13564,plain,
    ( spl0_676
  <=> ! [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_676])]) ).

fof(f1780,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_46
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f425]) ).

fof(f13562,plain,
    ( spl0_675
    | ~ spl0_46
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1762,f1746,f424,f13560]) ).

fof(f1762,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_46
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f425]) ).

fof(f13558,plain,
    ( spl0_674
    | ~ spl0_138
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1667,f1638,f1082,f13556]) ).

fof(f13556,plain,
    ( spl0_674
  <=> ! [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_674])]) ).

fof(f1667,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_138
    | ~ spl0_190 ),
    inference(resolution,[],[f1639,f1083]) ).

fof(f13538,plain,
    ( spl0_673
    | ~ spl0_7
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2196,f2186,f238,f13536]) ).

fof(f13536,plain,
    ( spl0_673
  <=> ! [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(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),X2)
        | y = 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_673])]) ).

fof(f2196,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(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,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(y,universal_class)))),X2)
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_7
    | ~ spl0_224 ),
    inference(superposition,[],[f2187,f239]) ).

fof(f13534,plain,
    ( spl0_672
    | ~ spl0_180
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1894,f1889,f1566,f13532]) ).

fof(f13532,plain,
    ( spl0_672
  <=> ! [X4,X0,X3,X2,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)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | y = 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)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f1894,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ 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)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | y = 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)))) )
    | ~ spl0_180
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f1567]) ).

fof(f13530,plain,
    ( ~ spl0_671
    | spl0_572
    | ~ spl0_662 ),
    inference(avatar_split_clause,[],[f13203,f13193,f9489,f13527]) ).

fof(f13203,plain,
    ( y != cross_product(y,universal_class)
    | spl0_572
    | ~ spl0_662 ),
    inference(superposition,[],[f9490,f13195]) ).

fof(f13487,plain,
    ( spl0_670
    | ~ spl0_113
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2034,f1999,f888,f13485]) ).

fof(f13485,plain,
    ( spl0_670
  <=> ! [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))))))),y)
        | ~ 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)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f2034,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))))))),y)
        | ~ 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)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f889]) ).

fof(f13300,plain,
    ( spl0_669
    | ~ spl0_39
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1784,f1750,f381,f13298]) ).

fof(f13298,plain,
    ( spl0_669
  <=> ! [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_669])]) ).

fof(f1784,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_39
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f382]) ).

fof(f13296,plain,
    ( spl0_668
    | ~ spl0_40
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1783,f1750,f385,f13294]) ).

fof(f13294,plain,
    ( spl0_668
  <=> ! [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_668])]) ).

fof(f1783,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_40
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f386]) ).

fof(f13290,plain,
    ( ~ spl0_21
    | spl0_123
    | ~ spl0_662 ),
    inference(avatar_split_clause,[],[f13200,f13193,f973,f301]) ).

fof(f13200,plain,
    ( ~ member(y,universal_class)
    | spl0_123
    | ~ spl0_662 ),
    inference(superposition,[],[f974,f13195]) ).

fof(f13289,plain,
    ( spl0_667
    | ~ spl0_39
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1766,f1746,f381,f13287]) ).

fof(f13287,plain,
    ( spl0_667
  <=> ! [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_667])]) ).

fof(f1766,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_39
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f382]) ).

fof(f13285,plain,
    ( spl0_666
    | ~ spl0_40
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1765,f1746,f385,f13283]) ).

fof(f13283,plain,
    ( spl0_666
  <=> ! [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_666])]) ).

fof(f1765,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_40
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f386]) ).

fof(f13281,plain,
    ( spl0_665
    | ~ spl0_46
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1716,f1646,f424,f13279]) ).

fof(f13279,plain,
    ( spl0_665
  <=> ! [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_665])]) ).

fof(f1716,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_46
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f425]) ).

fof(f13277,plain,
    ( spl0_664
    | ~ spl0_56
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1268,f1229,f496,f13275]) ).

fof(f13275,plain,
    ( spl0_664
  <=> ! [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_664])]) ).

fof(f1268,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_56
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f497]) ).

fof(f13199,plain,
    ( spl0_662
    | spl0_663
    | ~ spl0_7
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1876,f1866,f238,f13197,f13193]) ).

fof(f13197,plain,
    ( spl0_663
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,universal_class)))))))),cross_product(universal_class,universal_class))
        | y = 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(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,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_663])]) ).

fof(f1876,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,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(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,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))
        | y = domain_of(domain_of(flip(cross_product(y,universal_class))))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_7
    | ~ spl0_209 ),
    inference(superposition,[],[f1867,f239]) ).

fof(f13178,plain,
    ( spl0_661
    | ~ spl0_116
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1053,f1043,f912,f13176]) ).

fof(f13176,plain,
    ( spl0_661
  <=> ! [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)
        | y = X0
        | y = 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_661])]) ).

fof(f1053,plain,
    ( ! [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)
        | y = X0
        | y = 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_116
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f913]) ).

fof(f13143,plain,
    ( spl0_660
    | ~ spl0_2
    | ~ spl0_154
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8974,f8731,f1287,f213,f13141]) ).

fof(f13141,plain,
    ( spl0_660
  <=> ! [X0,X1] :
        ( ~ subclass(X0,y)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f8974,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,y)
        | subclass(X0,X1) )
    | ~ spl0_2
    | ~ spl0_154
    | ~ spl0_550 ),
    inference(forward_demodulation,[],[f8933,f8914]) ).

fof(f8933,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,domain_of(y))
        | subclass(X0,X1) )
    | ~ spl0_154
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f1288]) ).

fof(f13073,plain,
    ( spl0_659
    | ~ spl0_74
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2006,f1999,f613,f13071]) ).

fof(f13071,plain,
    ( spl0_659
  <=> ! [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_659])]) ).

fof(f2006,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_74
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f614]) ).

fof(f13069,plain,
    ( spl0_658
    | ~ spl0_29
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1785,f1750,f334,f13067]) ).

fof(f13067,plain,
    ( spl0_658
  <=> ! [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_658])]) ).

fof(f1785,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_29
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f335]) ).

fof(f13065,plain,
    ( spl0_657
    | ~ spl0_29
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1767,f1746,f334,f13063]) ).

fof(f13063,plain,
    ( spl0_657
  <=> ! [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_657])]) ).

fof(f1767,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_29
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f335]) ).

fof(f13061,plain,
    ( spl0_656
    | ~ spl0_39
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1720,f1646,f381,f13059]) ).

fof(f13059,plain,
    ( spl0_656
  <=> ! [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_656])]) ).

fof(f1720,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_39
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f382]) ).

fof(f13057,plain,
    ( spl0_655
    | ~ spl0_40
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1719,f1646,f385,f13055]) ).

fof(f13055,plain,
    ( spl0_655
  <=> ! [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_655])]) ).

fof(f1719,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_40
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f386]) ).

fof(f13053,plain,
    ( spl0_654
    | ~ spl0_46
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1630,f1625,f424,f13051]) ).

fof(f13051,plain,
    ( spl0_654
  <=> ! [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_654])]) ).

fof(f1630,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_46
    | ~ spl0_189 ),
    inference(resolution,[],[f1626,f425]) ).

fof(f13048,plain,
    ( spl0_653
    | ~ spl0_2
    | ~ spl0_548
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8955,f8731,f8590,f213,f13046]) ).

fof(f13046,plain,
    ( spl0_653
  <=> ! [X0] : subclass(intersection(universal_class,X0),complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f8590,plain,
    ( spl0_548
  <=> ! [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_548])]) ).

fof(f8955,plain,
    ( ! [X0] : subclass(intersection(universal_class,X0),complement(y))
    | ~ spl0_2
    | ~ spl0_548
    | ~ spl0_550 ),
    inference(forward_demodulation,[],[f8920,f8914]) ).

fof(f8920,plain,
    ( ! [X0] : subclass(intersection(universal_class,X0),complement(domain_of(y)))
    | ~ spl0_548
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f8591]) ).

fof(f8591,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_548 ),
    inference(avatar_component_clause,[],[f8590]) ).

fof(f12915,plain,
    ( spl0_652
    | ~ spl0_2
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2045,f2038,f213,f12913]) ).

fof(f12913,plain,
    ( spl0_652
  <=> ! [X2,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))))))
        | ~ member(X0,X2)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f2038,plain,
    ( spl0_217
  <=> ! [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_217])]) ).

fof(f2045,plain,
    ( ! [X2,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))))))
        | ~ member(X0,X2)
        | y = X1 )
    | ~ spl0_2
    | ~ spl0_217 ),
    inference(resolution,[],[f2039,f214]) ).

fof(f2039,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X1,X2)
        | 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(X0,X3) )
    | ~ spl0_217 ),
    inference(avatar_component_clause,[],[f2038]) ).

fof(f12911,plain,
    ( spl0_651
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1076,f1066,f500,f261,f12909]) ).

fof(f12909,plain,
    ( spl0_651
  <=> ! [X0] :
        ( y = 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))
        | ~ member(complement(domain_of(X0)),universal_class)
        | y = complement(domain_of(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(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f1066,plain,
    ( spl0_136
  <=> ! [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)
        | ~ member(complement(X0),universal_class)
        | complement(X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1076,plain,
    ( ! [X0] :
        ( y = 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))
        | ~ member(complement(domain_of(X0)),universal_class)
        | y = complement(domain_of(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(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_136 ),
    inference(forward_demodulation,[],[f1073,f501]) ).

fof(f1073,plain,
    ( ! [X0] :
        ( ~ member(complement(domain_of(X0)),universal_class)
        | y = complement(domain_of(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(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
        | y = 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_12
    | ~ spl0_136 ),
    inference(resolution,[],[f1067,f262]) ).

fof(f1067,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)
        | ~ member(complement(X0),universal_class)
        | complement(X0) = y )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1066]) ).

fof(f12672,plain,
    ( spl0_650
    | ~ spl0_2
    | ~ spl0_547
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8954,f8731,f8586,f213,f12670]) ).

fof(f12670,plain,
    ( spl0_650
  <=> ! [X0] : subclass(intersection(X0,universal_class),complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f8586,plain,
    ( spl0_547
  <=> ! [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_547])]) ).

fof(f8954,plain,
    ( ! [X0] : subclass(intersection(X0,universal_class),complement(y))
    | ~ spl0_2
    | ~ spl0_547
    | ~ spl0_550 ),
    inference(forward_demodulation,[],[f8919,f8914]) ).

fof(f8919,plain,
    ( ! [X0] : subclass(intersection(X0,universal_class),complement(domain_of(y)))
    | ~ spl0_547
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f8587]) ).

fof(f8587,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_547 ),
    inference(avatar_component_clause,[],[f8586]) ).

fof(f12649,plain,
    ( spl0_648
    | ~ spl0_649
    | ~ spl0_87
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2003,f1999,f693,f12646,f12643]) ).

fof(f12643,plain,
    ( spl0_648
  <=> ! [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_648])]) ).

fof(f12646,plain,
    ( spl0_649
  <=> subclass(composition_function,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f693,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(f2003,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_216 ),
    inference(resolution,[],[f2000,f694]) ).

fof(f694,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,[],[f693]) ).

fof(f12641,plain,
    ( spl0_647
    | ~ spl0_29
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1721,f1646,f334,f12639]) ).

fof(f12639,plain,
    ( spl0_647
  <=> ! [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_647])]) ).

fof(f1721,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_29
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f335]) ).

fof(f12637,plain,
    ( spl0_646
    | ~ spl0_155
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1664,f1638,f1291,f12635]) ).

fof(f12635,plain,
    ( spl0_646
  <=> ! [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_646])]) ).

fof(f1291,plain,
    ( spl0_155
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1664,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_155
    | ~ spl0_190 ),
    inference(resolution,[],[f1639,f1292]) ).

fof(f1292,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f12633,plain,
    ( spl0_645
    | ~ spl0_156
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1663,f1638,f1295,f12631]) ).

fof(f12631,plain,
    ( spl0_645
  <=> ! [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_645])]) ).

fof(f1295,plain,
    ( spl0_156
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f1663,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_156
    | ~ spl0_190 ),
    inference(resolution,[],[f1639,f1296]) ).

fof(f1296,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_156 ),
    inference(avatar_component_clause,[],[f1295]) ).

fof(f12629,plain,
    ( spl0_644
    | ~ spl0_46
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1621,f1618,f424,f12627]) ).

fof(f12627,plain,
    ( spl0_644
  <=> ! [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_644])]) ).

fof(f1618,plain,
    ( spl0_188
  <=> ! [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_188])]) ).

fof(f1621,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_46
    | ~ spl0_188 ),
    inference(resolution,[],[f1619,f425]) ).

fof(f1619,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_188 ),
    inference(avatar_component_clause,[],[f1618]) ).

fof(f12625,plain,
    ( spl0_643
    | ~ spl0_154
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1479,f1424,f1287,f12623]) ).

fof(f12623,plain,
    ( spl0_643
  <=> ! [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_643])]) ).

fof(f1479,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_154
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1288]) ).

fof(f12621,plain,
    ( spl0_642
    | ~ spl0_154
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1454,f1420,f1287,f12619]) ).

fof(f12619,plain,
    ( spl0_642
  <=> ! [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_642])]) ).

fof(f1454,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_154
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1288]) ).

fof(f12593,plain,
    ( spl0_641
    | ~ spl0_160
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8909,f8731,f1347,f12591]) ).

fof(f12591,plain,
    ( spl0_641
  <=> ! [X0,X1] : subclass(intersection(domain_of(y),X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f8909,plain,
    ( ! [X0,X1] : subclass(intersection(domain_of(y),X0),X1)
    | ~ spl0_160
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f1348]) ).

fof(f12139,plain,
    ( spl0_640
    | ~ spl0_46
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f4108,f2322,f424,f12137]) ).

fof(f4108,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(subset_relation,X0) )
    | ~ spl0_46
    | ~ spl0_244 ),
    inference(resolution,[],[f2324,f425]) ).

fof(f2324,plain,
    ( member(subset_relation,universal_class)
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2322]) ).

fof(f11829,plain,
    ( spl0_639
    | ~ spl0_238
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f4030,f4027,f2279,f11827]) ).

fof(f4030,plain,
    ( ! [X2,X0,X1] :
        ( unordered_pair(X0,X1) = subset_relation
        | member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_238
    | ~ spl0_334 ),
    inference(forward_demodulation,[],[f4028,f2281]) ).

fof(f11752,plain,
    ( spl0_638
    | ~ spl0_332
    | ~ spl0_504 ),
    inference(avatar_split_clause,[],[f11668,f7572,f3977,f11749]) ).

fof(f11749,plain,
    ( spl0_638
  <=> member(regular(subset_relation),y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f7572,plain,
    ( spl0_504
  <=> y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f11668,plain,
    ( member(regular(subset_relation),y)
    | ~ spl0_332
    | ~ spl0_504 ),
    inference(superposition,[],[f3979,f7574]) ).

fof(f7574,plain,
    ( y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_504 ),
    inference(avatar_component_clause,[],[f7572]) ).

fof(f11661,plain,
    ( spl0_637
    | ~ spl0_111
    | spl0_505
    | ~ spl0_636 ),
    inference(avatar_split_clause,[],[f11657,f11654,f7576,f852,f11659]) ).

fof(f11659,plain,
    ( spl0_637
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),y)
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f7576,plain,
    ( spl0_505
  <=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f11654,plain,
    ( spl0_636
  <=> ! [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_636])]) ).

fof(f11657,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),y)
        | subclass(subset_relation,X0) )
    | ~ spl0_111
    | spl0_505
    | ~ spl0_636 ),
    inference(forward_demodulation,[],[f11655,f7589]) ).

fof(f7589,plain,
    ( y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_111
    | spl0_505 ),
    inference(resolution,[],[f7578,f853]) ).

fof(f7578,plain,
    ( ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
    | spl0_505 ),
    inference(avatar_component_clause,[],[f7576]) ).

fof(f11655,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_636 ),
    inference(avatar_component_clause,[],[f11654]) ).

fof(f11656,plain,
    ( spl0_636
    | ~ spl0_79
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1403,f1351,f642,f11654]) ).

fof(f1403,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_79
    | ~ spl0_161 ),
    inference(superposition,[],[f1352,f644]) ).

fof(f11558,plain,
    ( spl0_635
    | ~ spl0_141
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1476,f1424,f1143,f11556]) ).

fof(f11556,plain,
    ( spl0_635
  <=> ! [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))))))),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)
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f11554,plain,
    ( spl0_634
    | ~ spl0_140
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1469,f1424,f1139,f11552]) ).

fof(f11552,plain,
    ( spl0_634
  <=> ! [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))))))),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)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f11550,plain,
    ( spl0_633
    | ~ spl0_141
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1451,f1420,f1143,f11548]) ).

fof(f11548,plain,
    ( spl0_633
  <=> ! [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(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)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f11545,plain,
    ( spl0_632
    | ~ spl0_458
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8910,f8731,f6488,f11542]) ).

fof(f11542,plain,
    ( spl0_632
  <=> subclass(universal_class,complement(domain_of(y))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f6488,plain,
    ( spl0_458
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f8910,plain,
    ( subclass(universal_class,complement(domain_of(y)))
    | ~ spl0_458
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f6489]) ).

fof(f6489,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_458 ),
    inference(avatar_component_clause,[],[f6488]) ).

fof(f11540,plain,
    ( spl0_631
    | ~ spl0_140
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1444,f1420,f1139,f11538]) ).

fof(f11538,plain,
    ( spl0_631
  <=> ! [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)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f11523,plain,
    ( spl0_630
    | ~ spl0_144
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1580,f1575,f1199,f11521]) ).

fof(f11521,plain,
    ( spl0_630
  <=> ! [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(y,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | y = 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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f1580,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(y,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | y = 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) = y )
    | ~ spl0_144
    | ~ spl0_181 ),
    inference(superposition,[],[f1576,f1200]) ).

fof(f11516,plain,
    ( ~ spl0_629
    | ~ spl0_111
    | spl0_505
    | ~ spl0_612
    | spl0_628 ),
    inference(avatar_split_clause,[],[f11509,f11504,f11087,f7576,f852,f11513]) ).

fof(f11513,plain,
    ( spl0_629
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f11504,plain,
    ( spl0_628
  <=> 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_628])]) ).

fof(f11509,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_111
    | spl0_505
    | ~ spl0_612
    | spl0_628 ),
    inference(forward_demodulation,[],[f11508,f11089]) ).

fof(f11508,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(y),complement(y)),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_111
    | spl0_505
    | spl0_628 ),
    inference(forward_demodulation,[],[f11506,f7589]) ).

fof(f11506,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | spl0_628 ),
    inference(avatar_component_clause,[],[f11504]) ).

fof(f11507,plain,
    ( spl0_429
    | ~ spl0_627
    | ~ spl0_628
    | ~ spl0_136
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1633,f1625,f1066,f11504,f11500,f5772]) ).

fof(f5772,plain,
    ( spl0_429
  <=> y = 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_429])]) ).

fof(f11500,plain,
    ( spl0_627
  <=> 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_627])]) ).

fof(f1633,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ 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)
    | y = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_136
    | ~ spl0_189 ),
    inference(resolution,[],[f1626,f1067]) ).

fof(f11377,plain,
    ( spl0_626
    | ~ spl0_56
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1839,f1816,f496,f11375]) ).

fof(f11375,plain,
    ( spl0_626
  <=> ! [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_626])]) ).

fof(f1839,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_56
    | ~ spl0_203 ),
    inference(duplicate_literal_removal,[],[f1820]) ).

fof(f1820,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_56
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f497]) ).

fof(f11252,plain,
    ( spl0_624
    | ~ spl0_625
    | ~ spl0_130
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1728,f1646,f1005,f11249,f11246]) ).

fof(f11246,plain,
    ( spl0_624
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | 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_624])]) ).

fof(f11249,plain,
    ( spl0_625
  <=> subclass(domain_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f1728,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,singleton_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) )
    | ~ spl0_130
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f1006]) ).

fof(f11244,plain,
    ( spl0_622
    | ~ spl0_623
    | ~ spl0_131
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1726,f1646,f1009,f11241,f11238]) ).

fof(f11238,plain,
    ( spl0_622
  <=> ! [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_622])]) ).

fof(f11241,plain,
    ( spl0_623
  <=> subclass(domain_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f1726,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_131
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f1010]) ).

fof(f11236,plain,
    ( spl0_621
    | ~ spl0_51
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1269,f1229,f472,f11234]) ).

fof(f11234,plain,
    ( spl0_621
  <=> ! [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_621])]) ).

fof(f1269,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_51
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f473]) ).

fof(f11232,plain,
    ( spl0_620
    | ~ spl0_82
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1127,f1089,f665,f11230]) ).

fof(f11230,plain,
    ( spl0_620
  <=> ! [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_620])]) ).

fof(f1127,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
    | ~ spl0_82
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f666]) ).

fof(f11218,plain,
    ( spl0_619
    | ~ spl0_90
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1578,f1575,f706,f11216]) ).

fof(f11216,plain,
    ( spl0_619
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_619])]) ).

fof(f1578,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_181 ),
    inference(resolution,[],[f1576,f707]) ).

fof(f11160,plain,
    ( spl0_618
    | ~ spl0_55
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1311,f1287,f492,f11158]) ).

fof(f11158,plain,
    ( spl0_618
  <=> ! [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_618])]) ).

fof(f1311,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_55
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f493]) ).

fof(f11156,plain,
    ( spl0_617
    | ~ spl0_145
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1281,f1264,f1229,f11154]) ).

fof(f11154,plain,
    ( spl0_617
  <=> ! [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_617])]) ).

fof(f1281,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_145
    | ~ spl0_153 ),
    inference(resolution,[],[f1265,f1230]) ).

fof(f11152,plain,
    ( spl0_616
    | ~ spl0_145
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1276,f1260,f1229,f11150]) ).

fof(f11150,plain,
    ( spl0_616
  <=> ! [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_616])]) ).

fof(f1276,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_145
    | ~ spl0_152 ),
    inference(resolution,[],[f1261,f1230]) ).

fof(f11108,plain,
    ( spl0_615
    | ~ spl0_113
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1914,f1889,f888,f11106]) ).

fof(f11106,plain,
    ( spl0_615
  <=> ! [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)))),y)
        | ~ 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)
        | y = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f1914,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)))),y)
        | ~ 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)
        | y = X3 )
    | ~ spl0_113
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f889]) ).

fof(f11104,plain,
    ( spl0_614
    | ~ spl0_144
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1572,f1566,f1199,f11102]) ).

fof(f11102,plain,
    ( spl0_614
  <=> ! [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)
        | y = 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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1572,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)
        | y = 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) = y )
    | ~ spl0_144
    | ~ spl0_180 ),
    inference(superposition,[],[f1567,f1200]) ).

fof(f11094,plain,
    ( spl0_613
    | ~ spl0_144
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1502,f1491,f1199,f11092]) ).

fof(f11092,plain,
    ( spl0_613
  <=> ! [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(y,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | y = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1502,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(y,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | y = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = y )
    | ~ spl0_144
    | ~ spl0_170 ),
    inference(superposition,[],[f1492,f1200]) ).

fof(f11090,plain,
    ( spl0_612
    | ~ spl0_129
    | ~ spl0_591 ),
    inference(avatar_split_clause,[],[f10868,f10596,f1001,f11087]) ).

fof(f1001,plain,
    ( spl0_129
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f10868,plain,
    ( universal_class = complement(y)
    | ~ spl0_129
    | ~ spl0_591 ),
    inference(resolution,[],[f10598,f1002]) ).

fof(f1002,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1001]) ).

fof(f10961,plain,
    ( spl0_610
    | ~ spl0_611
    | ~ spl0_81
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1708,f1646,f661,f10958,f10955]) ).

fof(f10955,plain,
    ( spl0_610
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f10958,plain,
    ( spl0_611
  <=> subclass(domain_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f1708,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,successor_relation)
        | ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
    | ~ spl0_81
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f662]) ).

fof(f10953,plain,
    ( spl0_609
    | ~ spl0_50
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1689,f1642,f441,f10951]) ).

fof(f10951,plain,
    ( spl0_609
  <=> ! [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_609])]) ).

fof(f1689,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_50
    | ~ spl0_191 ),
    inference(superposition,[],[f1643,f443]) ).

fof(f10949,plain,
    ( spl0_608
    | ~ spl0_49
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1688,f1642,f436,f10947]) ).

fof(f10947,plain,
    ( spl0_608
  <=> ! [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_608])]) ).

fof(f1688,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_49
    | ~ spl0_191 ),
    inference(superposition,[],[f1643,f438]) ).

fof(f10945,plain,
    ( spl0_607
    | ~ spl0_46
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1550,f1537,f424,f10943]) ).

fof(f1550,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_46
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f425]) ).

fof(f10939,plain,
    ( ~ spl0_605
    | spl0_606
    | ~ spl0_137
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1478,f1424,f1078,f10937,f10933]) ).

fof(f10933,plain,
    ( spl0_605
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f10937,plain,
    ( spl0_606
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f1478,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_137
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f1079]) ).

fof(f10930,plain,
    ( spl0_604
    | ~ spl0_132
    | ~ spl0_591 ),
    inference(avatar_split_clause,[],[f10867,f10596,f1033,f10927]) ).

fof(f10927,plain,
    ( spl0_604
  <=> member(y,complement(y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f1033,plain,
    ( spl0_132
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f10867,plain,
    ( member(y,complement(y))
    | ~ spl0_132
    | ~ spl0_591 ),
    inference(resolution,[],[f10598,f1034]) ).

fof(f1034,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(y,X0) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1033]) ).

fof(f10925,plain,
    ( ~ spl0_602
    | spl0_603
    | ~ spl0_137
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1453,f1420,f1078,f10923,f10919]) ).

fof(f10919,plain,
    ( spl0_602
  <=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f10923,plain,
    ( spl0_603
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f1453,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_137
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f1079]) ).

fof(f10894,plain,
    ( spl0_366
    | ~ spl0_599
    | spl0_600
    | ~ spl0_601
    | ~ spl0_28
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1468,f1424,f330,f10891,f10887,f10883,f4488]) ).

fof(f10883,plain,
    ( spl0_599
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f10887,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(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_600])]) ).

fof(f10891,plain,
    ( spl0_601
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_601])]) ).

fof(f1468,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)
    | y = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_28
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f331]) ).

fof(f10865,plain,
    ( spl0_363
    | ~ spl0_596
    | spl0_597
    | ~ spl0_598
    | ~ spl0_28
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1443,f1420,f330,f10862,f10858,f10854,f4470]) ).

fof(f10854,plain,
    ( spl0_596
  <=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f10858,plain,
    ( spl0_597
  <=> 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_597])]) ).

fof(f10862,plain,
    ( spl0_598
  <=> 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_598])]) ).

fof(f1443,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)
    | complement(compose(element_relation,complement(identity_relation))) = y
    | ~ spl0_28
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f331]) ).

fof(f10852,plain,
    ( spl0_595
    | ~ spl0_55
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1164,f1143,f492,f10850]) ).

fof(f10850,plain,
    ( spl0_595
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | y = intersection(X0,unordered_pair(X1,X2))
        | 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_595])]) ).

fof(f1164,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | y = intersection(X0,unordered_pair(X1,X2))
        | 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_55
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f493]) ).

fof(f10848,plain,
    ( spl0_594
    | ~ spl0_55
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1147,f1139,f492,f10846]) ).

fof(f10846,plain,
    ( spl0_594
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | y = intersection(unordered_pair(X0,X1),X2)
        | 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_594])]) ).

fof(f1147,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | y = intersection(unordered_pair(X0,X1),X2)
        | 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_55
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f493]) ).

fof(f10719,plain,
    ( spl0_593
    | ~ spl0_21
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2709,f2038,f301,f10717]) ).

fof(f10717,plain,
    ( spl0_593
  <=> ! [X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))))))
        | ~ member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f2709,plain,
    ( ! [X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))))))
        | ~ member(X0,X1) )
    | ~ spl0_21
    | ~ spl0_217 ),
    inference(resolution,[],[f302,f2039]) ).

fof(f10715,plain,
    ( spl0_592
    | ~ spl0_46
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1579,f1575,f424,f10713]) ).

fof(f10713,plain,
    ( spl0_592
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_592])]) ).

fof(f1579,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_46
    | ~ spl0_181 ),
    inference(resolution,[],[f1576,f425]) ).

fof(f10599,plain,
    ( spl0_591
    | ~ spl0_458
    | ~ spl0_585 ),
    inference(avatar_split_clause,[],[f10259,f9669,f6488,f10596]) ).

fof(f10259,plain,
    ( subclass(universal_class,complement(y))
    | ~ spl0_458
    | ~ spl0_585 ),
    inference(resolution,[],[f9670,f6489]) ).

fof(f10531,plain,
    ( spl0_590
    | ~ spl0_531
    | ~ spl0_572
    | ~ spl0_589 ),
    inference(avatar_split_clause,[],[f10527,f10523,f9489,f8328,f10529]) ).

fof(f10529,plain,
    ( spl0_590
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_590])]) ).

fof(f10523,plain,
    ( spl0_589
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = 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_589])]) ).

fof(f10527,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_531
    | ~ spl0_572
    | ~ spl0_589 ),
    inference(forward_demodulation,[],[f10526,f8329]) ).

fof(f10526,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(y,X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | y = 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_572
    | ~ spl0_589 ),
    inference(forward_demodulation,[],[f10524,f9491]) ).

fof(f9491,plain,
    ( y = cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
    | ~ spl0_572 ),
    inference(avatar_component_clause,[],[f9489]) ).

fof(f10524,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = 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_589 ),
    inference(avatar_component_clause,[],[f10523]) ).

fof(f10525,plain,
    ( spl0_589
    | ~ spl0_90
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1500,f1491,f706,f10523]) ).

fof(f1500,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = 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_170 ),
    inference(resolution,[],[f1492,f707]) ).

fof(f10521,plain,
    ( spl0_588
    | ~ spl0_113
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1171,f1143,f888,f10519]) ).

fof(f10519,plain,
    ( spl0_588
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,regular(X1)),universal_class)
        | y = intersection(X0,regular(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,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),y)
        | ~ member(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)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f1171,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,regular(X1)),universal_class)
        | y = intersection(X0,regular(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,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),y)
        | ~ member(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)
        | y = X1 )
    | ~ spl0_113
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f889]) ).

fof(f10517,plain,
    ( spl0_587
    | ~ spl0_113
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1154,f1139,f888,f10515]) ).

fof(f10515,plain,
    ( spl0_587
  <=> ! [X0,X1] :
        ( ~ member(intersection(regular(X0),X1),universal_class)
        | y = intersection(regular(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(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),y)
        | ~ 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)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f1154,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(regular(X0),X1),universal_class)
        | y = intersection(regular(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(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),y)
        | ~ 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)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f889]) ).

fof(f9675,plain,
    ( spl0_586
    | ~ spl0_160
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1692,f1642,f1347,f9673]) ).

fof(f9673,plain,
    ( spl0_586
  <=> ! [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_586])]) ).

fof(f1692,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_160
    | ~ spl0_191 ),
    inference(duplicate_literal_removal,[],[f1673]) ).

fof(f1673,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_160
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1348]) ).

fof(f9671,plain,
    ( spl0_585
    | ~ spl0_550
    | ~ spl0_567 ),
    inference(avatar_split_clause,[],[f9592,f9421,f8731,f9669]) ).

fof(f9592,plain,
    ( ! [X0] : ~ member(X0,y)
    | ~ spl0_550
    | ~ spl0_567 ),
    inference(superposition,[],[f8732,f9423]) ).

fof(f9667,plain,
    ( spl0_584
    | ~ spl0_161
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1691,f1642,f1351,f9665]) ).

fof(f9665,plain,
    ( spl0_584
  <=> ! [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_584])]) ).

fof(f1691,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_161
    | ~ spl0_191 ),
    inference(duplicate_literal_removal,[],[f1674]) ).

fof(f1674,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_161
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1352]) ).

fof(f9663,plain,
    ( spl0_583
    | ~ spl0_39
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1554,f1537,f381,f9661]) ).

fof(f9661,plain,
    ( spl0_583
  <=> ! [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_583])]) ).

fof(f1554,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_39
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f382]) ).

fof(f9659,plain,
    ( spl0_582
    | ~ spl0_40
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1553,f1537,f385,f9657]) ).

fof(f9657,plain,
    ( spl0_582
  <=> ! [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_582])]) ).

fof(f1553,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_40
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f386]) ).

fof(f9655,plain,
    ( spl0_581
    | ~ spl0_50
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1548,f1533,f441,f9653]) ).

fof(f9653,plain,
    ( spl0_581
  <=> ! [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_581])]) ).

fof(f1548,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_50
    | ~ spl0_178 ),
    inference(superposition,[],[f1534,f443]) ).

fof(f9651,plain,
    ( spl0_580
    | ~ spl0_49
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1547,f1533,f436,f9649]) ).

fof(f9649,plain,
    ( spl0_580
  <=> ! [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_580])]) ).

fof(f1547,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_49
    | ~ spl0_178 ),
    inference(superposition,[],[f1534,f438]) ).

fof(f9647,plain,
    ( spl0_579
    | ~ spl0_39
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1393,f1351,f381,f9645]) ).

fof(f9645,plain,
    ( spl0_579
  <=> ! [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_579])]) ).

fof(f1393,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_39
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f382]) ).

fof(f9643,plain,
    ( spl0_578
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1392,f1351,f385,f9641]) ).

fof(f9641,plain,
    ( spl0_578
  <=> ! [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_578])]) ).

fof(f1392,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f386]) ).

fof(f9639,plain,
    ( spl0_577
    | ~ spl0_39
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1372,f1347,f381,f9637]) ).

fof(f9637,plain,
    ( spl0_577
  <=> ! [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_577])]) ).

fof(f1372,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_39
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f382]) ).

fof(f9635,plain,
    ( spl0_576
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1371,f1347,f385,f9633]) ).

fof(f9633,plain,
    ( spl0_576
  <=> ! [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_576])]) ).

fof(f1371,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_40
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f386]) ).

fof(f9631,plain,
    ( spl0_575
    | ~ spl0_35
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1280,f1264,f365,f9629]) ).

fof(f9629,plain,
    ( spl0_575
  <=> ! [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_575])]) ).

fof(f1280,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_35
    | ~ spl0_153 ),
    inference(resolution,[],[f1265,f366]) ).

fof(f9591,plain,
    ( spl0_574
    | ~ spl0_35
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1275,f1260,f365,f9589]) ).

fof(f9589,plain,
    ( spl0_574
  <=> ! [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_574])]) ).

fof(f1275,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_35
    | ~ spl0_152 ),
    inference(resolution,[],[f1261,f366]) ).

fof(f9495,plain,
    ( spl0_572
    | spl0_573
    | ~ spl0_7
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1582,f1575,f238,f9493,f9489]) ).

fof(f9493,plain,
    ( spl0_573
  <=> ! [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(y,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = 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(y,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f1582,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(y,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | y = cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_181 ),
    inference(superposition,[],[f1576,f239]) ).

fof(f9487,plain,
    ( spl0_571
    | ~ spl0_57
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1581,f1575,f500,f9485]) ).

fof(f9485,plain,
    ( spl0_571
  <=> ! [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(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X1))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f1581,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(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X1))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_57
    | ~ spl0_181 ),
    inference(superposition,[],[f1576,f501]) ).

fof(f9480,plain,
    ( spl0_570
    | ~ spl0_116
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1788,f1750,f912,f9478]) ).

fof(f9478,plain,
    ( spl0_570
  <=> ! [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)
        | y = 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_570])]) ).

fof(f1788,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)
        | y = 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_116
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f913]) ).

fof(f9476,plain,
    ( spl0_568
    | ~ spl0_569
    | ~ spl0_7
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1344,f1337,f238,f9473,f9470]) ).

fof(f9470,plain,
    ( spl0_568
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
        | y = 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(y,y))),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_568])]) ).

fof(f1337,plain,
    ( spl0_159
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),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_159])]) ).

fof(f1344,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(y,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),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))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_7
    | ~ spl0_159 ),
    inference(superposition,[],[f1338,f239]) ).

fof(f1338,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(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,X2)) )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1337]) ).

fof(f9424,plain,
    ( spl0_567
    | ~ spl0_2
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8914,f8731,f213,f9421]) ).

fof(f9419,plain,
    ( spl0_566
    | ~ spl0_56
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1071,f1066,f496,f9417]) ).

fof(f9417,plain,
    ( spl0_566
  <=> ! [X0,X1] :
        ( ~ member(complement(intersection(X0,X1)),universal_class)
        | complement(intersection(X0,X1)) = y
        | ~ 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_566])]) ).

fof(f1071,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(intersection(X0,X1)),universal_class)
        | complement(intersection(X0,X1)) = y
        | ~ 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_56
    | ~ spl0_136 ),
    inference(resolution,[],[f1067,f497]) ).

fof(f9414,plain,
    ( spl0_565
    | ~ spl0_134
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1831,f1816,f1043,f9412]) ).

fof(f9412,plain,
    ( spl0_565
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f1831,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | y = X0 )
    | ~ spl0_134
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f1044]) ).

fof(f9083,plain,
    ( spl0_564
    | ~ spl0_154
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1690,f1642,f1287,f9081]) ).

fof(f9081,plain,
    ( spl0_564
  <=> ! [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_564])]) ).

fof(f1690,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_154
    | ~ spl0_191 ),
    inference(duplicate_literal_removal,[],[f1675]) ).

fof(f1675,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_154
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f1288]) ).

fof(f9078,plain,
    ( spl0_563
    | ~ spl0_34
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f8908,f8731,f361,f9076]) ).

fof(f9076,plain,
    ( spl0_563
  <=> ! [X0] : subclass(domain_of(y),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f8908,plain,
    ( ! [X0] : subclass(domain_of(y),X0)
    | ~ spl0_34
    | ~ spl0_550 ),
    inference(resolution,[],[f8732,f362]) ).

fof(f9074,plain,
    ( spl0_562
    | ~ spl0_29
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1555,f1537,f334,f9072]) ).

fof(f9072,plain,
    ( spl0_562
  <=> ! [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_562])]) ).

fof(f1555,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_29
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f335]) ).

fof(f9070,plain,
    ( spl0_561
    | ~ spl0_31
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1542,f1533,f342,f9068]) ).

fof(f9068,plain,
    ( spl0_561
  <=> ! [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_561])]) ).

fof(f1542,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) )
    | ~ spl0_31
    | ~ spl0_178 ),
    inference(resolution,[],[f1534,f343]) ).

fof(f9066,plain,
    ( spl0_560
    | ~ spl0_51
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1440,f1420,f472,f9064]) ).

fof(f9064,plain,
    ( spl0_560
  <=> ! [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_560])]) ).

fof(f1440,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_51
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f473]) ).

fof(f9062,plain,
    ( spl0_559
    | ~ spl0_46
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1389,f1351,f424,f9060]) ).

fof(f9060,plain,
    ( spl0_559
  <=> ! [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_559])]) ).

fof(f1389,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_46
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f425]) ).

fof(f9058,plain,
    ( spl0_558
    | ~ spl0_46
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1368,f1347,f424,f9056]) ).

fof(f9056,plain,
    ( spl0_558
  <=> ! [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_558])]) ).

fof(f1368,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_46
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f425]) ).

fof(f9054,plain,
    ( spl0_557
    | ~ spl0_55
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1112,f1078,f492,f9052]) ).

fof(f9052,plain,
    ( spl0_557
  <=> ! [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_557])]) ).

fof(f1112,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_55
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f493]) ).

fof(f9047,plain,
    ( spl0_556
    | ~ spl0_116
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1724,f1646,f912,f9045]) ).

fof(f9045,plain,
    ( spl0_556
  <=> ! [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)
        | y = 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_556])]) ).

fof(f1724,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)
        | y = 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_116
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f913]) ).

fof(f8991,plain,
    ( spl0_555
    | ~ spl0_46
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2462,f1497,f424,f8989]) ).

fof(f8989,plain,
    ( spl0_555
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,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_555])]) ).

fof(f2462,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
        | singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,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_46
    | ~ spl0_171 ),
    inference(resolution,[],[f1498,f425]) ).

fof(f8905,plain,
    ( spl0_554
    | ~ spl0_46
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1501,f1491,f424,f8903]) ).

fof(f8903,plain,
    ( spl0_554
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = 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_554])]) ).

fof(f1501,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = 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_46
    | ~ spl0_170 ),
    inference(resolution,[],[f1492,f425]) ).

fof(f8870,plain,
    ( spl0_553
    | ~ spl0_12
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1972,f1943,f261,f8868]) ).

fof(f8868,plain,
    ( spl0_553
  <=> ! [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)
        | y = 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_553])]) ).

fof(f1972,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)
        | y = 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_12
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f262]) ).

fof(f8866,plain,
    ( spl0_552
    | ~ spl0_12
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1946,f1939,f261,f8864]) ).

fof(f8864,plain,
    ( spl0_552
  <=> ! [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)
        | y = 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_552])]) ).

fof(f1946,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)
        | y = 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_12
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f262]) ).

fof(f8862,plain,
    ( spl0_551
    | ~ spl0_116
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1770,f1746,f912,f8860]) ).

fof(f1770,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)
        | y = 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_116
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f913]) ).

fof(f8733,plain,
    ( spl0_550
    | ~ spl0_115
    | ~ spl0_531 ),
    inference(avatar_split_clause,[],[f8578,f8328,f897,f8731]) ).

fof(f897,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( y != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f8578,plain,
    ( ! [X0] : ~ member(X0,domain_of(y))
    | ~ spl0_115
    | ~ spl0_531 ),
    inference(trivial_inequality_removal,[],[f8550]) ).

fof(f8550,plain,
    ( ! [X0] :
        ( y != y
        | ~ member(X0,domain_of(y)) )
    | ~ spl0_115
    | ~ spl0_531 ),
    inference(superposition,[],[f898,f8329]) ).

fof(f898,plain,
    ( ! [X0,X1] :
        ( y != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f897]) ).

fof(f8596,plain,
    ( spl0_549
    | ~ spl0_40
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1628,f1625,f385,f8594]) ).

fof(f8594,plain,
    ( spl0_549
  <=> ! [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_549])]) ).

fof(f1628,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_40
    | ~ spl0_189 ),
    inference(resolution,[],[f1626,f386]) ).

fof(f8592,plain,
    ( spl0_548
    | ~ spl0_160
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1615,f1593,f1347,f8590]) ).

fof(f1593,plain,
    ( spl0_184
  <=> ! [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_184])]) ).

fof(f1615,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_160
    | ~ spl0_184 ),
    inference(duplicate_literal_removal,[],[f1610]) ).

fof(f1610,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_160
    | ~ spl0_184 ),
    inference(resolution,[],[f1594,f1348]) ).

fof(f1594,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_184 ),
    inference(avatar_component_clause,[],[f1593]) ).

fof(f8588,plain,
    ( spl0_547
    | ~ spl0_161
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1614,f1593,f1351,f8586]) ).

fof(f1614,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_161
    | ~ spl0_184 ),
    inference(duplicate_literal_removal,[],[f1611]) ).

fof(f1611,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_161
    | ~ spl0_184 ),
    inference(resolution,[],[f1594,f1352]) ).

fof(f8503,plain,
    ( spl0_546
    | ~ spl0_31
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1438,f1416,f342,f8501]) ).

fof(f8501,plain,
    ( spl0_546
  <=> ! [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_546])]) ).

fof(f1416,plain,
    ( spl0_165
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f1438,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_31
    | ~ spl0_165 ),
    inference(resolution,[],[f1417,f343]) ).

fof(f1417,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1416]) ).

fof(f8499,plain,
    ( spl0_545
    | ~ spl0_29
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1394,f1351,f334,f8497]) ).

fof(f8497,plain,
    ( spl0_545
  <=> ! [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_545])]) ).

fof(f1394,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_29
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f335]) ).

fof(f8495,plain,
    ( spl0_544
    | ~ spl0_29
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1373,f1347,f334,f8493]) ).

fof(f8493,plain,
    ( spl0_544
  <=> ! [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_544])]) ).

fof(f1373,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_29
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f335]) ).

fof(f8491,plain,
    ( spl0_543
    | ~ spl0_46
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1310,f1287,f424,f8489]) ).

fof(f8489,plain,
    ( spl0_543
  <=> ! [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_543])]) ).

fof(f1310,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_46
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f425]) ).

fof(f8487,plain,
    ( spl0_542
    | ~ spl0_139
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1267,f1229,f1089,f8485]) ).

fof(f8485,plain,
    ( spl0_542
  <=> ! [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_542])]) ).

fof(f1267,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_139
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f1090]) ).

fof(f8483,plain,
    ( spl0_541
    | ~ spl0_73
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1132,f1089,f609,f8481]) ).

fof(f8481,plain,
    ( spl0_541
  <=> ! [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_541])]) ).

fof(f1132,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_73
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f610]) ).

fof(f8479,plain,
    ( spl0_540
    | ~ spl0_74
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1131,f1089,f613,f8477]) ).

fof(f8477,plain,
    ( spl0_540
  <=> ! [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_540])]) ).

fof(f1131,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_74
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f614]) ).

fof(f8424,plain,
    ( spl0_539
    | ~ spl0_344
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f8107,f7603,f4190,f8422]) ).

fof(f7603,plain,
    ( spl0_507
  <=> ! [X0] :
        ( y = X0
        | ~ subclass(X0,y) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f8107,plain,
    ( ! [X0] : y = intersection(X0,y)
    | ~ spl0_344
    | ~ spl0_507 ),
    inference(resolution,[],[f7604,f4191]) ).

fof(f7604,plain,
    ( ! [X0] :
        ( ~ subclass(X0,y)
        | y = X0 )
    | ~ spl0_507 ),
    inference(avatar_component_clause,[],[f7603]) ).

fof(f8398,plain,
    ( spl0_538
    | ~ spl0_109
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1987,f1943,f831,f8396]) ).

fof(f8396,plain,
    ( spl0_538
  <=> ! [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)))))
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1987,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)))))
        | y = X1 )
    | ~ spl0_109
    | ~ spl0_215 ),
    inference(resolution,[],[f1944,f832]) ).

fof(f8394,plain,
    ( spl0_537
    | ~ spl0_109
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f1961,f1939,f831,f8392]) ).

fof(f8392,plain,
    ( spl0_537
  <=> ! [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)))))
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f1961,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)))))
        | y = X1 )
    | ~ spl0_109
    | ~ spl0_214 ),
    inference(resolution,[],[f1940,f832]) ).

fof(f8390,plain,
    ( spl0_536
    | ~ spl0_51
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1072,f1066,f472,f8388]) ).

fof(f8388,plain,
    ( spl0_536
  <=> ! [X0] :
        ( ~ member(complement(complement(X0)),universal_class)
        | y = complement(complement(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))))))),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_536])]) ).

fof(f1072,plain,
    ( ! [X0] :
        ( ~ member(complement(complement(X0)),universal_class)
        | y = complement(complement(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))))))),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_51
    | ~ spl0_136 ),
    inference(resolution,[],[f1067,f473]) ).

fof(f8386,plain,
    ( spl0_535
    | ~ spl0_94
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f848,f831,f725,f8384]) ).

fof(f8384,plain,
    ( spl0_535
  <=> ! [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)))))
        | y = 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_535])]) ).

fof(f848,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)))))
        | y = 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_109 ),
    inference(resolution,[],[f832,f726]) ).

fof(f8352,plain,
    ( spl0_534
    | ~ spl0_7
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1994,f1943,f238,f8350]) ).

fof(f8350,plain,
    ( spl0_534
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f1994,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_215 ),
    inference(superposition,[],[f1944,f239]) ).

fof(f8343,plain,
    ( spl0_533
    | ~ spl0_112
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1835,f1816,f856,f8341]) ).

fof(f8341,plain,
    ( spl0_533
  <=> ! [X0] :
        ( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | y = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f1835,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
        | ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
        | y = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_112
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f857]) ).

fof(f8334,plain,
    ( spl0_532
    | ~ spl0_111
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1826,f1816,f852,f8332]) ).

fof(f8332,plain,
    ( spl0_532
  <=> ! [X0] :
        ( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | y = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f1826,plain,
    ( ! [X0] :
        ( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
        | ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
        | y = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
    | ~ spl0_111
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f853]) ).

fof(f8330,plain,
    ( spl0_531
    | ~ spl0_343
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f8106,f7603,f4186,f8328]) ).

fof(f8106,plain,
    ( ! [X0] : y = intersection(y,X0)
    | ~ spl0_343
    | ~ spl0_507 ),
    inference(resolution,[],[f7604,f4187]) ).

fof(f8326,plain,
    ( spl0_530
    | ~ spl0_139
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1570,f1566,f1089,f8324]) ).

fof(f8324,plain,
    ( spl0_530
  <=> ! [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)
        | y = 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_530])]) ).

fof(f1570,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)
        | y = 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_139
    | ~ spl0_180 ),
    inference(resolution,[],[f1567,f1090]) ).

fof(f8314,plain,
    ( spl0_528
    | ~ spl0_529
    | ~ spl0_107
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2036,f1999,f814,f8311,f8308]) ).

fof(f8308,plain,
    ( spl0_528
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | y = 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_528])]) ).

fof(f8311,plain,
    ( spl0_529
  <=> subclass(composition_function,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f814,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f2036,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,y)
        | ~ member(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))))))),X2)
        | y = X2 )
    | ~ spl0_107
    | ~ spl0_216 ),
    inference(resolution,[],[f2000,f815]) ).

fof(f815,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,X0)
        | y = X0 )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f814]) ).

fof(f8306,plain,
    ( spl0_527
    | ~ spl0_7
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1341,f1337,f238,f8304]) ).

fof(f8304,plain,
    ( spl0_527
  <=> ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f1341,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_159 ),
    inference(superposition,[],[f1338,f239]) ).

fof(f8102,plain,
    ( spl0_526
    | ~ spl0_144
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1669,f1638,f1199,f8100]) ).

fof(f8100,plain,
    ( spl0_526
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f1669,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) = y )
    | ~ spl0_144
    | ~ spl0_190 ),
    inference(superposition,[],[f1639,f1200]) ).

fof(f8098,plain,
    ( spl0_525
    | ~ spl0_92
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1213,f1199,f715,f8096]) ).

fof(f8096,plain,
    ( spl0_525
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f715,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(f1213,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) = y )
    | ~ spl0_92
    | ~ spl0_144 ),
    inference(superposition,[],[f716,f1200]) ).

fof(f716,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,[],[f715]) ).

fof(f8094,plain,
    ( spl0_524
    | ~ spl0_28
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f902,f888,f330,f8092]) ).

fof(f8092,plain,
    ( spl0_524
  <=> ! [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))))))),y)
        | ~ 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)
        | y = X0
        | ~ member(regular(X0),universal_class)
        | regular(X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f902,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))))))),y)
        | ~ 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)
        | y = X0
        | ~ member(regular(X0),universal_class)
        | regular(X0) = y )
    | ~ spl0_28
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f331]) ).

fof(f8090,plain,
    ( spl0_523
    | ~ spl0_82
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f875,f856,f665,f8088]) ).

fof(f875,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,cross_product(X1,X2))
        | regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) )
    | ~ spl0_82
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f666]) ).

fof(f8086,plain,
    ( spl0_522
    | ~ spl0_82
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f861,f852,f665,f8084]) ).

fof(f861,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(cross_product(X0,X1),X2)
        | regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) )
    | ~ spl0_82
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f666]) ).

fof(f7939,plain,
    ( spl0_521
    | ~ spl0_76
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1710,f1646,f625,f7937]) ).

fof(f7937,plain,
    ( spl0_521
  <=> ! [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_521])]) ).

fof(f1710,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) )
    | ~ spl0_76
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f626]) ).

fof(f7935,plain,
    ( spl0_520
    | ~ spl0_154
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1613,f1593,f1287,f7933]) ).

fof(f1613,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_154
    | ~ spl0_184 ),
    inference(duplicate_literal_removal,[],[f1612]) ).

fof(f1612,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_154
    | ~ spl0_184 ),
    inference(resolution,[],[f1594,f1288]) ).

fof(f7931,plain,
    ( spl0_519
    | ~ spl0_39
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1314,f1287,f381,f7929]) ).

fof(f7929,plain,
    ( spl0_519
  <=> ! [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_519])]) ).

fof(f1314,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_39
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f382]) ).

fof(f7927,plain,
    ( spl0_518
    | ~ spl0_40
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1313,f1287,f385,f7925]) ).

fof(f7925,plain,
    ( spl0_518
  <=> ! [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_518])]) ).

fof(f1313,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_40
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f386]) ).

fof(f7923,plain,
    ( spl0_517
    | ~ spl0_46
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1279,f1264,f424,f7921]) ).

fof(f7921,plain,
    ( spl0_517
  <=> ! [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_517])]) ).

fof(f1279,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_46
    | ~ spl0_153 ),
    inference(resolution,[],[f1265,f425]) ).

fof(f7919,plain,
    ( spl0_516
    | ~ spl0_46
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1274,f1260,f424,f7917]) ).

fof(f7917,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f1274,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_46
    | ~ spl0_152 ),
    inference(resolution,[],[f1261,f425]) ).

fof(f7915,plain,
    ( spl0_514
    | ~ spl0_515
    | ~ spl0_81
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1097,f1078,f661,f7912,f7909]) ).

fof(f7909,plain,
    ( spl0_514
  <=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f7912,plain,
    ( spl0_515
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f1097,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_81
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f662]) ).

fof(f7795,plain,
    ( spl0_513
    | ~ spl0_40
    | ~ spl0_346 ),
    inference(avatar_split_clause,[],[f6421,f4236,f385,f7793]) ).

fof(f7793,plain,
    ( spl0_513
  <=> ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f4236,plain,
    ( spl0_346
  <=> ! [X0] : y = intersection(complement(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f6421,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,X0) )
    | ~ spl0_40
    | ~ spl0_346 ),
    inference(superposition,[],[f386,f4237]) ).

fof(f4237,plain,
    ( ! [X0] : y = intersection(complement(X0),X0)
    | ~ spl0_346 ),
    inference(avatar_component_clause,[],[f4236]) ).

fof(f7627,plain,
    ( spl0_512
    | ~ spl0_16
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1507,f1504,f278,f7625]) ).

fof(f7625,plain,
    ( spl0_512
  <=> ! [X0,X1] :
        ( 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
        | 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
        | unordered_pair(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f1504,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( 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
        | ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1507,plain,
    ( ! [X0,X1] :
        ( 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
        | 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
        | unordered_pair(X0,X1) = y )
    | ~ spl0_16
    | ~ spl0_172 ),
    inference(resolution,[],[f1505,f279]) ).

fof(f1505,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_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))))))) = X1
        | 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
        | unordered_pair(X0,X1) = y )
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1504]) ).

fof(f7623,plain,
    ( spl0_511
    | ~ spl0_134
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1475,f1424,f1043,f7621]) ).

fof(f7621,plain,
    ( spl0_511
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | 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)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f7619,plain,
    ( spl0_510
    | ~ spl0_134
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1450,f1420,f1043,f7617]) ).

fof(f7617,plain,
    ( spl0_510
  <=> ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | 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)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f7615,plain,
    ( spl0_509
    | ~ spl0_118
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1225,f1199,f925,f7613]) ).

fof(f7613,plain,
    ( spl0_509
  <=> ! [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)))
        | y = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f925,plain,
    ( spl0_118
  <=> ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1225,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)))
        | y = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = y )
    | ~ spl0_118
    | ~ spl0_144 ),
    inference(superposition,[],[f926,f1200]) ).

fof(f926,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f925]) ).

fof(f7611,plain,
    ( spl0_508
    | ~ spl0_113
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1055,f1043,f888,f7609]) ).

fof(f7609,plain,
    ( spl0_508
  <=> ! [X0,X1] :
        ( ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | y = 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))))))),y)
        | ~ 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)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f1055,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | y = 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))))))),y)
        | ~ 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)
        | y = X1 )
    | ~ spl0_113
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f889]) ).

fof(f7605,plain,
    ( spl0_507
    | ~ spl0_48
    | ~ spl0_288 ),
    inference(avatar_split_clause,[],[f4987,f3142,f432,f7603]) ).

fof(f3142,plain,
    ( spl0_288
  <=> ! [X0] :
        ( y = X0
        | subclass(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f4987,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,y) )
    | ~ spl0_48
    | ~ spl0_288 ),
    inference(duplicate_literal_removal,[],[f4975]) ).

fof(f4975,plain,
    ( ! [X0] :
        ( y = X0
        | ~ subclass(X0,y)
        | y = X0 )
    | ~ spl0_48
    | ~ spl0_288 ),
    inference(resolution,[],[f3143,f433]) ).

fof(f3143,plain,
    ( ! [X0] :
        ( subclass(y,X0)
        | y = X0 )
    | ~ spl0_288 ),
    inference(avatar_component_clause,[],[f3142]) ).

fof(f7583,plain,
    ( spl0_504
    | ~ spl0_505
    | spl0_506
    | ~ spl0_2
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1825,f1816,f213,f7580,f7576,f7572]) ).

fof(f7580,plain,
    ( spl0_506
  <=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f1825,plain,
    ( member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
    | ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
    | y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_2
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f214]) ).

fof(f7569,plain,
    ( ~ spl0_502
    | spl0_503
    | ~ spl0_137
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1571,f1566,f1078,f7567,f7563]) ).

fof(f7563,plain,
    ( spl0_502
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f7567,plain,
    ( spl0_503
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | y = 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f1571,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)
        | y = 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))))
        | ~ subclass(universal_class,cross_product(universal_class,universal_class)) )
    | ~ spl0_137
    | ~ spl0_180 ),
    inference(resolution,[],[f1567,f1079]) ).

fof(f7561,plain,
    ( spl0_501
    | ~ spl0_144
    | ~ spl0_156 ),
    inference(avatar_split_clause,[],[f1332,f1295,f1199,f7559]) ).

fof(f7559,plain,
    ( spl0_501
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f1332,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) = y )
    | ~ spl0_144
    | ~ spl0_156 ),
    inference(superposition,[],[f1296,f1200]) ).

fof(f7557,plain,
    ( spl0_500
    | ~ spl0_55
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1047,f1043,f492,f7555]) ).

fof(f7555,plain,
    ( spl0_500
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | y = X0
        | domain_of(intersection(element_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_500])]) ).

fof(f1047,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | y = X0
        | domain_of(intersection(element_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_55
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f493]) ).

fof(f7550,plain,
    ( spl0_499
    | ~ spl0_29
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2999,f2269,f334,f7548]) ).

fof(f7548,plain,
    ( spl0_499
  <=> ! [X0] :
        ( ~ member(X0,y)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f2999,plain,
    ( ! [X0] :
        ( ~ member(X0,y)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_236 ),
    inference(superposition,[],[f335,f2271]) ).

fof(f7285,plain,
    ( spl0_498
    | ~ spl0_10
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1736,f1650,f251,f7283]) ).

fof(f7283,plain,
    ( spl0_498
  <=> ! [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_498])]) ).

fof(f1650,plain,
    ( spl0_193
  <=> ! [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_193])]) ).

fof(f1736,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_10
    | ~ spl0_193 ),
    inference(resolution,[],[f1651,f252]) ).

fof(f1651,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_193 ),
    inference(avatar_component_clause,[],[f1650]) ).

fof(f7281,plain,
    ( spl0_497
    | ~ spl0_63
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1735,f1650,f555,f7279]) ).

fof(f7279,plain,
    ( spl0_497
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f555,plain,
    ( spl0_63
  <=> ! [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_63])]) ).

fof(f1735,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_63
    | ~ spl0_193 ),
    inference(resolution,[],[f1651,f556]) ).

fof(f556,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f555]) ).

fof(f7277,plain,
    ( spl0_496
    | ~ spl0_73
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1703,f1646,f609,f7275]) ).

fof(f7275,plain,
    ( spl0_496
  <=> ! [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_496])]) ).

fof(f1703,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_73
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f610]) ).

fof(f7273,plain,
    ( spl0_495
    | ~ spl0_34
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1693,f1642,f361,f7271]) ).

fof(f1693,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_34
    | ~ spl0_191 ),
    inference(duplicate_literal_removal,[],[f1672]) ).

fof(f1672,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0))
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_34
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f362]) ).

fof(f7269,plain,
    ( spl0_494
    | ~ spl0_130
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1398,f1351,f1005,f7267]) ).

fof(f7267,plain,
    ( spl0_494
  <=> ! [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_494])]) ).

fof(f1398,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
    | ~ spl0_130
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f1006]) ).

fof(f7265,plain,
    ( spl0_493
    | ~ spl0_131
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1396,f1351,f1009,f7263]) ).

fof(f7263,plain,
    ( spl0_493
  <=> ! [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_493])]) ).

fof(f1396,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_131
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f1010]) ).

fof(f7261,plain,
    ( spl0_492
    | ~ spl0_50
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1384,f1347,f441,f7259]) ).

fof(f7259,plain,
    ( spl0_492
  <=> ! [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_492])]) ).

fof(f1384,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_50
    | ~ spl0_160 ),
    inference(superposition,[],[f1348,f443]) ).

fof(f7257,plain,
    ( spl0_491
    | ~ spl0_236
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f7117,f4788,f2269,f7254]) ).

fof(f7254,plain,
    ( spl0_491
  <=> y = intersection(universal_class,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f4788,plain,
    ( spl0_369
  <=> ! [X0] : y = intersection(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f7117,plain,
    ( y = intersection(universal_class,y)
    | ~ spl0_236
    | ~ spl0_369 ),
    inference(superposition,[],[f4789,f2271]) ).

fof(f4789,plain,
    ( ! [X0] : y = intersection(X0,complement(X0))
    | ~ spl0_369 ),
    inference(avatar_component_clause,[],[f4788]) ).

fof(f7252,plain,
    ( spl0_490
    | ~ spl0_49
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1383,f1347,f436,f7250]) ).

fof(f7250,plain,
    ( spl0_490
  <=> ! [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_490])]) ).

fof(f1383,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_49
    | ~ spl0_160 ),
    inference(superposition,[],[f1348,f438]) ).

fof(f7248,plain,
    ( spl0_489
    | ~ spl0_130
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1377,f1347,f1005,f7246]) ).

fof(f7246,plain,
    ( spl0_489
  <=> ! [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_489])]) ).

fof(f1377,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
    | ~ spl0_130
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f1006]) ).

fof(f7244,plain,
    ( spl0_488
    | ~ spl0_131
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1375,f1347,f1009,f7242]) ).

fof(f7242,plain,
    ( spl0_488
  <=> ! [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_488])]) ).

fof(f1375,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_131
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f1010]) ).

fof(f7240,plain,
    ( spl0_487
    | ~ spl0_31
    | ~ spl0_156 ),
    inference(avatar_split_clause,[],[f1331,f1295,f342,f7238]) ).

fof(f7238,plain,
    ( spl0_487
  <=> ! [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_487])]) ).

fof(f1331,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_31
    | ~ spl0_156 ),
    inference(resolution,[],[f1296,f343]) ).

fof(f7236,plain,
    ( spl0_486
    | ~ spl0_31
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f1327,f1291,f342,f7234]) ).

fof(f7234,plain,
    ( spl0_486
  <=> ! [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_486])]) ).

fof(f1327,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_31
    | ~ spl0_155 ),
    inference(resolution,[],[f1292,f343]) ).

fof(f7232,plain,
    ( spl0_485
    | ~ spl0_29
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1315,f1287,f334,f7230]) ).

fof(f1315,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_29
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f335]) ).

fof(f7228,plain,
    ( spl0_484
    | ~ spl0_35
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1129,f1089,f365,f7226]) ).

fof(f7226,plain,
    ( spl0_484
  <=> ! [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_484])]) ).

fof(f1129,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_35
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f366]) ).

fof(f7116,plain,
    ( spl0_483
    | ~ spl0_57
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1343,f1337,f500,f7114]) ).

fof(f7114,plain,
    ( spl0_483
  <=> ! [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(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f1343,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(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) )
    | ~ spl0_57
    | ~ spl0_159 ),
    inference(superposition,[],[f1338,f501]) ).

fof(f7112,plain,
    ( spl0_482
    | ~ spl0_57
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1340,f1337,f500,f7110]) ).

fof(f7110,plain,
    ( spl0_482
  <=> ! [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(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f1340,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(y,y))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) )
    | ~ spl0_57
    | ~ spl0_159 ),
    inference(superposition,[],[f1338,f501]) ).

fof(f7108,plain,
    ( spl0_481
    | ~ spl0_90
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1212,f1199,f706,f7106]) ).

fof(f7106,plain,
    ( spl0_481
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f1212,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) = y )
    | ~ spl0_90
    | ~ spl0_144 ),
    inference(superposition,[],[f707,f1200]) ).

fof(f7089,plain,
    ( spl0_480
    | ~ spl0_80
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1573,f1566,f647,f7087]) ).

fof(f7087,plain,
    ( spl0_480
  <=> ! [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)
        | y = 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_480])]) ).

fof(f1573,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)
        | y = 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_80
    | ~ spl0_180 ),
    inference(duplicate_literal_removal,[],[f1569]) ).

fof(f1569,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)
        | y = 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_80
    | ~ spl0_180 ),
    inference(resolution,[],[f1567,f648]) ).

fof(f7074,plain,
    ( spl0_479
    | ~ spl0_38
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1222,f1199,f377,f7072]) ).

fof(f7072,plain,
    ( spl0_479
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f1222,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) = y )
    | ~ spl0_38
    | ~ spl0_144 ),
    inference(superposition,[],[f378,f1200]) ).

fof(f7028,plain,
    ( spl0_478
    | ~ spl0_107
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f1916,f1889,f814,f7026]) ).

fof(f7026,plain,
    ( spl0_478
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),y)
        | ~ 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)
        | y = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f1916,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),y)
        | ~ 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)
        | y = X3 )
    | ~ spl0_107
    | ~ spl0_212 ),
    inference(resolution,[],[f1890,f815]) ).

fof(f6984,plain,
    ( spl0_321
    | ~ spl0_476
    | ~ spl0_477
    | ~ spl0_136
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1283,f1264,f1066,f6981,f6977,f3623]) ).

fof(f6977,plain,
    ( spl0_476
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f6981,plain,
    ( spl0_477
  <=> 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_477])]) ).

fof(f1283,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)
    | ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | y = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_136
    | ~ spl0_153 ),
    inference(resolution,[],[f1265,f1067]) ).

fof(f6973,plain,
    ( spl0_319
    | ~ spl0_474
    | ~ spl0_475
    | ~ spl0_136
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1277,f1260,f1066,f6970,f6966,f3612]) ).

fof(f6966,plain,
    ( spl0_474
  <=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f6970,plain,
    ( spl0_475
  <=> 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_475])]) ).

fof(f1277,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)
    | ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | y = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_136
    | ~ spl0_152 ),
    inference(resolution,[],[f1261,f1067]) ).

fof(f6879,plain,
    ( spl0_473
    | ~ spl0_74
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1702,f1646,f613,f6877]) ).

fof(f6877,plain,
    ( spl0_473
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f1702,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) )
    | ~ spl0_74
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f614]) ).

fof(f6875,plain,
    ( spl0_472
    | ~ spl0_130
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1320,f1287,f1005,f6873]) ).

fof(f6873,plain,
    ( spl0_472
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f1320,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_130
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f1006]) ).

fof(f6871,plain,
    ( spl0_471
    | ~ spl0_131
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1318,f1287,f1009,f6869]) ).

fof(f6869,plain,
    ( spl0_471
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f1318,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_131
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f1010]) ).

fof(f6867,plain,
    ( spl0_470
    | ~ spl0_46
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1128,f1089,f424,f6865]) ).

fof(f6865,plain,
    ( spl0_470
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f1128,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_46
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f425]) ).

fof(f6863,plain,
    ( spl0_469
    | ~ spl0_46
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1111,f1078,f424,f6861]) ).

fof(f6861,plain,
    ( spl0_469
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f1111,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_46
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f425]) ).

fof(f6820,plain,
    ( spl0_468
    | ~ spl0_55
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1223,f1199,f492,f6818]) ).

fof(f6818,plain,
    ( spl0_468
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f1223,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) = y )
    | ~ spl0_55
    | ~ spl0_144 ),
    inference(superposition,[],[f493,f1200]) ).

fof(f6816,plain,
    ( spl0_467
    | ~ spl0_110
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1224,f1199,f835,f6814]) ).

fof(f6814,plain,
    ( spl0_467
  <=> ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | y = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | y = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f835,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( y = X0
        | y = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1224,plain,
    ( ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | y = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | y = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = y )
    | ~ spl0_110
    | ~ spl0_144 ),
    inference(superposition,[],[f836,f1200]) ).

fof(f836,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | y = X1
        | y = X0 )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f835]) ).

fof(f6584,plain,
    ( spl0_466
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1694,f1642,f500,f261,f6582]) ).

fof(f6582,plain,
    ( spl0_466
  <=> ! [X2,X0,X1] :
        ( y = 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_466])]) ).

fof(f1694,plain,
    ( ! [X2,X0,X1] :
        ( y = 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_12
    | ~ spl0_57
    | ~ spl0_191 ),
    inference(forward_demodulation,[],[f1681,f501]) ).

fof(f1681,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)
        | y = 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_12
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f262]) ).

fof(f6580,plain,
    ( spl0_465
    | ~ spl0_39
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1167,f1143,f381,f6578]) ).

fof(f6578,plain,
    ( spl0_465
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | y = intersection(X0,intersection(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,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f1167,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | y = intersection(X0,intersection(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,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_39
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f382]) ).

fof(f6576,plain,
    ( spl0_464
    | ~ spl0_40
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1166,f1143,f385,f6574]) ).

fof(f6574,plain,
    ( spl0_464
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | y = intersection(X0,intersection(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,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f1166,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | y = intersection(X0,intersection(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,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
    | ~ spl0_40
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f386]) ).

fof(f6572,plain,
    ( spl0_463
    | ~ spl0_39
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1150,f1139,f381,f6570]) ).

fof(f6570,plain,
    ( spl0_463
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | y = intersection(intersection(X0,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(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f1150,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | y = intersection(intersection(X0,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(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_39
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f382]) ).

fof(f6568,plain,
    ( spl0_462
    | ~ spl0_40
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1149,f1139,f385,f6566]) ).

fof(f6566,plain,
    ( spl0_462
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | y = intersection(intersection(X0,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(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f1149,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | y = intersection(intersection(X0,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(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_40
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f386]) ).

fof(f6535,plain,
    ( spl0_461
    | ~ spl0_236
    | ~ spl0_346 ),
    inference(avatar_split_clause,[],[f6415,f4236,f2269,f6532]) ).

fof(f6532,plain,
    ( spl0_461
  <=> y = intersection(y,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f6415,plain,
    ( y = intersection(y,universal_class)
    | ~ spl0_236
    | ~ spl0_346 ),
    inference(superposition,[],[f4237,f2271]) ).

fof(f6498,plain,
    ( spl0_459
    | ~ spl0_460
    | ~ spl0_65
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1706,f1646,f569,f6495,f6492]) ).

fof(f6492,plain,
    ( spl0_459
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f6495,plain,
    ( spl0_460
  <=> subclass(domain_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f1706,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,element_relation)
        | ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) )
    | ~ spl0_65
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f570]) ).

fof(f6490,plain,
    ( spl0_458
    | ~ spl0_34
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f1616,f1593,f361,f6488]) ).

fof(f1616,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_34
    | ~ spl0_184 ),
    inference(duplicate_literal_removal,[],[f1609]) ).

fof(f1609,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_34
    | ~ spl0_184 ),
    inference(resolution,[],[f1594,f362]) ).

fof(f6486,plain,
    ( spl0_457
    | ~ spl0_79
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1382,f1347,f642,f6484]) ).

fof(f6484,plain,
    ( spl0_457
  <=> ! [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_457])]) ).

fof(f1382,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_79
    | ~ spl0_160 ),
    inference(superposition,[],[f1348,f644]) ).

fof(f6482,plain,
    ( spl0_456
    | ~ spl0_39
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1115,f1078,f381,f6480]) ).

fof(f6480,plain,
    ( spl0_456
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f1115,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_39
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f382]) ).

fof(f6478,plain,
    ( spl0_455
    | ~ spl0_40
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1114,f1078,f385,f6476]) ).

fof(f6476,plain,
    ( spl0_455
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f1114,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_40
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f386]) ).

fof(f6414,plain,
    ( spl0_454
    | ~ spl0_116
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1558,f1537,f912,f6412]) ).

fof(f6412,plain,
    ( spl0_454
  <=> ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class)
        | y = 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f1558,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class)
        | y = 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) )
    | ~ spl0_116
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f913]) ).

fof(f6390,plain,
    ( spl0_453
    | ~ spl0_113
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1791,f1750,f888,f6388]) ).

fof(f6388,plain,
    ( spl0_453
  <=> ! [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))))),y)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f1791,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))))),y)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_197 ),
    inference(resolution,[],[f1751,f889]) ).

fof(f6302,plain,
    ( spl0_452
    | ~ spl0_144
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f1328,f1291,f1199,f6300]) ).

fof(f6300,plain,
    ( spl0_452
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f1328,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) = y )
    | ~ spl0_144
    | ~ spl0_155 ),
    inference(superposition,[],[f1292,f1200]) ).

fof(f6298,plain,
    ( spl0_451
    | ~ spl0_81
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1208,f1199,f661,f6296]) ).

fof(f6296,plain,
    ( spl0_451
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f1208,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) = y )
    | ~ spl0_81
    | ~ spl0_144 ),
    inference(superposition,[],[f662,f1200]) ).

fof(f6294,plain,
    ( spl0_450
    | ~ spl0_29
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1168,f1143,f334,f6292]) ).

fof(f6292,plain,
    ( spl0_450
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,complement(X1)),universal_class)
        | y = intersection(X0,complement(X1))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f1168,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,complement(X1)),universal_class)
        | y = intersection(X0,complement(X1))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_29
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f335]) ).

fof(f6290,plain,
    ( spl0_449
    | ~ spl0_29
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1151,f1139,f334,f6288]) ).

fof(f6288,plain,
    ( spl0_449
  <=> ! [X0,X1] :
        ( ~ member(intersection(complement(X0),X1),universal_class)
        | y = intersection(complement(X0),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1151,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(complement(X0),X1),universal_class)
        | y = intersection(complement(X0),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_29
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f335]) ).

fof(f6283,plain,
    ( spl0_276
    | ~ spl0_447
    | ~ spl0_448
    | ~ spl0_136
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1135,f1089,f1066,f6280,f6276,f2842]) ).

fof(f6276,plain,
    ( spl0_447
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f6280,plain,
    ( spl0_448
  <=> 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_448])]) ).

fof(f1135,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(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
    | ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
    | y = complement(cross_product(universal_class,universal_class))
    | ~ spl0_136
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f1067]) ).

fof(f6117,plain,
    ( spl0_446
    | ~ spl0_8
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1540,f1533,f242,f6115]) ).

fof(f1540,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_8
    | ~ spl0_178 ),
    inference(resolution,[],[f1534,f243]) ).

fof(f6113,plain,
    ( spl0_445
    | ~ spl0_29
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1273,f1260,f334,f6111]) ).

fof(f1273,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_29
    | ~ spl0_152 ),
    inference(resolution,[],[f1261,f335]) ).

fof(f6109,plain,
    ( spl0_444
    | ~ spl0_29
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1116,f1078,f334,f6107]) ).

fof(f6107,plain,
    ( spl0_444
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f1116,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_29
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f335]) ).

fof(f6105,plain,
    ( spl0_443
    | ~ spl0_76
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1099,f1078,f625,f6103]) ).

fof(f6103,plain,
    ( spl0_443
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f1099,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_76
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f626]) ).

fof(f5887,plain,
    ( ~ spl0_441
    | spl0_442
    | ~ spl0_142
    | ~ spl0_427 ),
    inference(avatar_split_clause,[],[f5829,f5764,f1181,f5884,f5880]) ).

fof(f5829,plain,
    ( function(y)
    | ~ single_valued_class(y)
    | ~ spl0_142
    | ~ spl0_427 ),
    inference(resolution,[],[f5765,f1182]) ).

fof(f5878,plain,
    ( spl0_440
    | ~ spl0_144
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1796,f1754,f1199,f5876]) ).

fof(f1796,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) = y )
    | ~ spl0_144
    | ~ spl0_198 ),
    inference(superposition,[],[f1755,f1200]) ).

fof(f5874,plain,
    ( spl0_439
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1773,f1746,f888,f5872]) ).

fof(f1773,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)))),y)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | y = X1 )
    | ~ spl0_113
    | ~ spl0_196 ),
    inference(resolution,[],[f1747,f889]) ).

fof(f5870,plain,
    ( spl0_438
    | ~ spl0_113
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1727,f1646,f888,f5868]) ).

fof(f5868,plain,
    ( spl0_438
  <=> ! [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)))),y)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f1727,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)))),y)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f889]) ).

fof(f5866,plain,
    ( spl0_437
    | ~ spl0_107
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1173,f1143,f814,f5864]) ).

fof(f5864,plain,
    ( spl0_437
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,y),universal_class)
        | y = intersection(X0,y)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,y),intersection(X0,y)),universal_class)),universal_class))))))),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f1173,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,y),universal_class)
        | y = intersection(X0,y)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,y),intersection(X0,y)),universal_class)),universal_class))))))),X1)
        | y = X1 )
    | ~ spl0_107
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f815]) ).

fof(f5862,plain,
    ( spl0_436
    | ~ spl0_46
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1163,f1143,f424,f5860]) ).

fof(f5860,plain,
    ( spl0_436
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y
        | ~ 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_436])]) ).

fof(f1163,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y
        | ~ 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_46
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f425]) ).

fof(f5858,plain,
    ( spl0_435
    | ~ spl0_107
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1156,f1139,f814,f5856]) ).

fof(f5856,plain,
    ( spl0_435
  <=> ! [X0,X1] :
        ( ~ member(intersection(y,X0),universal_class)
        | y = intersection(y,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(y,X0),intersection(y,X0)),universal_class)),universal_class))))))),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1156,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(y,X0),universal_class)
        | y = intersection(y,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(y,X0),intersection(y,X0)),universal_class)),universal_class))))))),X1)
        | y = X1 )
    | ~ spl0_107
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f815]) ).

fof(f5854,plain,
    ( spl0_434
    | ~ spl0_46
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1146,f1139,f424,f5852]) ).

fof(f5852,plain,
    ( spl0_434
  <=> ! [X2,X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y
        | ~ 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_434])]) ).

fof(f1146,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y
        | ~ 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_46
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f425]) ).

fof(f5850,plain,
    ( spl0_433
    | ~ spl0_108
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1074,f1066,f826,f5848]) ).

fof(f5848,plain,
    ( spl0_433
  <=> ! [X0] :
        ( ~ member(complement(regular(X0)),universal_class)
        | y = complement(regular(X0))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),y)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f826,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,regular(X0))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1074,plain,
    ( ! [X0] :
        ( ~ member(complement(regular(X0)),universal_class)
        | y = complement(regular(X0))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),y)
        | y = X0 )
    | ~ spl0_108
    | ~ spl0_136 ),
    inference(resolution,[],[f1067,f827]) ).

fof(f827,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,y)
        | y = X0 )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f826]) ).

fof(f5845,plain,
    ( spl0_432
    | ~ spl0_88
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1211,f1199,f697,f5843]) ).

fof(f5843,plain,
    ( spl0_432
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f697,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(f1211,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) = y )
    | ~ spl0_88
    | ~ spl0_144 ),
    inference(superposition,[],[f698,f1200]) ).

fof(f698,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,[],[f697]) ).

fof(f5817,plain,
    ( spl0_431
    | ~ spl0_36
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1221,f1199,f369,f5815]) ).

fof(f5815,plain,
    ( spl0_431
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f1221,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) = y )
    | ~ spl0_36
    | ~ spl0_144 ),
    inference(superposition,[],[f370,f1200]) ).

fof(f5779,plain,
    ( spl0_429
    | ~ spl0_430
    | ~ spl0_106
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1634,f1625,f810,f5776,f5772]) ).

fof(f5776,plain,
    ( spl0_430
  <=> 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_430])]) ).

fof(f1634,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)
    | y = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_106
    | ~ spl0_189 ),
    inference(resolution,[],[f1626,f811]) ).

fof(f5770,plain,
    ( spl0_428
    | ~ spl0_130
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1172,f1143,f1005,f5768]) ).

fof(f5768,plain,
    ( spl0_428
  <=> ! [X0] :
        ( ~ member(intersection(X0,singleton_relation),universal_class)
        | y = 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,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f1172,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,singleton_relation),universal_class)
        | y = 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,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_130
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f1006]) ).

fof(f5766,plain,
    ( spl0_427
    | ~ spl0_8
    | ~ spl0_236
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f5750,f5696,f2269,f242,f5764]) ).

fof(f5696,plain,
    ( spl0_423
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f5750,plain,
    ( ! [X0] : subclass(y,X0)
    | ~ spl0_8
    | ~ spl0_236
    | ~ spl0_423 ),
    inference(forward_demodulation,[],[f5746,f2271]) ).

fof(f5746,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_8
    | ~ spl0_423 ),
    inference(resolution,[],[f5697,f243]) ).

fof(f5697,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_423 ),
    inference(avatar_component_clause,[],[f5696]) ).

fof(f5762,plain,
    ( spl0_426
    | ~ spl0_131
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1170,f1143,f1009,f5760]) ).

fof(f5760,plain,
    ( spl0_426
  <=> ! [X0] :
        ( ~ member(intersection(X0,identity_relation),universal_class)
        | y = intersection(X0,identity_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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f1170,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,identity_relation),universal_class)
        | y = intersection(X0,identity_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_131
    | ~ spl0_141 ),
    inference(resolution,[],[f1144,f1010]) ).

fof(f5758,plain,
    ( spl0_425
    | ~ spl0_130
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1155,f1139,f1005,f5756]) ).

fof(f5756,plain,
    ( spl0_425
  <=> ! [X0] :
        ( ~ member(intersection(singleton_relation,X0),universal_class)
        | y = 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(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f1155,plain,
    ( ! [X0] :
        ( ~ member(intersection(singleton_relation,X0),universal_class)
        | y = 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(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_130
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f1006]) ).

fof(f5754,plain,
    ( spl0_424
    | ~ spl0_131
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1153,f1139,f1009,f5752]) ).

fof(f5752,plain,
    ( spl0_424
  <=> ! [X0] :
        ( ~ member(intersection(identity_relation,X0),universal_class)
        | y = intersection(identity_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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f1153,plain,
    ( ! [X0] :
        ( ~ member(intersection(identity_relation,X0),universal_class)
        | y = intersection(identity_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_131
    | ~ spl0_140 ),
    inference(resolution,[],[f1140,f1010]) ).

fof(f5698,plain,
    ( spl0_423
    | ~ spl0_145
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1322,f1287,f1229,f5696]) ).

fof(f1322,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_145
    | ~ spl0_154 ),
    inference(duplicate_literal_removal,[],[f1309]) ).

fof(f1309,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_145
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f1230]) ).

fof(f5694,plain,
    ( spl0_422
    | ~ spl0_30
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1190,f1181,f338,f5692]) ).

fof(f5692,plain,
    ( spl0_422
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f1190,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_30
    | ~ spl0_142 ),
    inference(resolution,[],[f1182,f339]) ).

fof(f5690,plain,
    ( ~ spl0_420
    | spl0_421
    | ~ spl0_10
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1185,f1181,f251,f5687,f5683]) ).

fof(f5683,plain,
    ( spl0_420
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f5687,plain,
    ( spl0_421
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f1185,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_10
    | ~ spl0_142 ),
    inference(resolution,[],[f1182,f252]) ).

fof(f5681,plain,
    ( spl0_418
    | ~ spl0_419
    | ~ spl0_130
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1121,f1078,f1005,f5678,f5675]) ).

fof(f5675,plain,
    ( spl0_418
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f5678,plain,
    ( spl0_419
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f1121,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_130
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f1006]) ).

fof(f5673,plain,
    ( spl0_416
    | ~ spl0_417
    | ~ spl0_88
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1103,f1078,f697,f5670,f5667]) ).

fof(f5667,plain,
    ( spl0_416
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f5670,plain,
    ( spl0_417
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f1103,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_88
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f698]) ).

fof(f5665,plain,
    ( spl0_415
    | ~ spl0_73
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1093,f1078,f609,f5663]) ).

fof(f5663,plain,
    ( spl0_415
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f1093,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_73
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f610]) ).

fof(f5658,plain,
    ( spl0_414
    | ~ spl0_74
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1092,f1078,f613,f5656]) ).

fof(f5656,plain,
    ( spl0_414
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f1092,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_74
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f614]) ).

fof(f5654,plain,
    ( spl0_413
    | ~ spl0_34
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1025,f1009,f361,f5652]) ).

fof(f5652,plain,
    ( spl0_413
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f1025,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_34
    | ~ spl0_131 ),
    inference(resolution,[],[f1010,f362]) ).

fof(f5650,plain,
    ( spl0_412
    | ~ spl0_34
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1018,f1005,f361,f5648]) ).

fof(f1018,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_34
    | ~ spl0_130 ),
    inference(resolution,[],[f1006,f362]) ).

fof(f5646,plain,
    ( spl0_411
    | ~ spl0_45
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f923,f919,f405,f5644]) ).

fof(f5644,plain,
    ( spl0_411
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f919,plain,
    ( spl0_117
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f923,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_45
    | ~ spl0_117 ),
    inference(resolution,[],[f920,f406]) ).

fof(f920,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f919]) ).

fof(f5601,plain,
    ( spl0_410
    | ~ spl0_46
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1046,f1043,f424,f5599]) ).

fof(f5599,plain,
    ( spl0_410
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | y = X0
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f1046,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | y = X0
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_46
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f425]) ).

fof(f5560,plain,
    ( spl0_409
    | ~ spl0_295
    | ~ spl0_343 ),
    inference(avatar_split_clause,[],[f5224,f4186,f3222,f5557]) ).

fof(f5557,plain,
    ( spl0_409
  <=> subclass(y,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f3222,plain,
    ( spl0_295
  <=> y = intersection(complement(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f5224,plain,
    ( subclass(y,complement(subset_relation))
    | ~ spl0_295
    | ~ spl0_343 ),
    inference(superposition,[],[f4187,f3224]) ).

fof(f3224,plain,
    ( y = intersection(complement(subset_relation),identity_relation)
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f3222]) ).

fof(f5537,plain,
    ( spl0_408
    | ~ spl0_87
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1210,f1199,f693,f5535]) ).

fof(f5535,plain,
    ( spl0_408
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f1210,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) = y )
    | ~ spl0_87
    | ~ spl0_144 ),
    inference(superposition,[],[f694,f1200]) ).

fof(f5533,plain,
    ( spl0_407
    | ~ spl0_85
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1209,f1199,f683,f5531]) ).

fof(f5531,plain,
    ( spl0_407
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f1209,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) = y )
    | ~ spl0_85
    | ~ spl0_144 ),
    inference(superposition,[],[f684,f1200]) ).

fof(f5529,plain,
    ( spl0_406
    | ~ spl0_39
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1050,f1043,f381,f5527]) ).

fof(f5527,plain,
    ( spl0_406
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | y = 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))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f1050,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | y = 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))))))),X1) )
    | ~ spl0_39
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f382]) ).

fof(f5525,plain,
    ( spl0_405
    | ~ spl0_40
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1049,f1043,f385,f5523]) ).

fof(f5523,plain,
    ( spl0_405
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | y = 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))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f1049,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | y = 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))))))),X2) )
    | ~ spl0_40
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f386]) ).

fof(f5521,plain,
    ( spl0_404
    | ~ spl0_82
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f844,f831,f665,f5519]) ).

fof(f5519,plain,
    ( spl0_404
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | y = 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_404])]) ).

fof(f844,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | y = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) )
    | ~ spl0_82
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f666]) ).

fof(f5378,plain,
    ( spl0_403
    | ~ spl0_112
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1474,f1424,f856,f5376]) ).

fof(f5376,plain,
    ( spl0_403
  <=> ! [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)
        | y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f5374,plain,
    ( spl0_402
    | ~ spl0_111
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1471,f1424,f852,f5372]) ).

fof(f5372,plain,
    ( spl0_402
  <=> ! [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)
        | y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f5370,plain,
    ( spl0_401
    | ~ spl0_112
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1449,f1420,f856,f5368]) ).

fof(f5368,plain,
    ( spl0_401
  <=> ! [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)
        | y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f5366,plain,
    ( spl0_400
    | ~ spl0_111
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1446,f1420,f852,f5364]) ).

fof(f5364,plain,
    ( spl0_400
  <=> ! [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)
        | y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f5362,plain,
    ( spl0_399
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1272,f1229,f500,f261,f5360]) ).

fof(f5360,plain,
    ( spl0_399
  <=> ! [X0,X1] :
        ( y = 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_399])]) ).

fof(f1272,plain,
    ( ! [X0,X1] :
        ( y = 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_12
    | ~ spl0_57
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1270,f501]) ).

fof(f1270,plain,
    ( ! [X0,X1] :
        ( subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
        | y = 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_12
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f262]) ).

fof(f5358,plain,
    ( spl0_398
    | ~ spl0_29
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1051,f1043,f334,f5356]) ).

fof(f5356,plain,
    ( spl0_398
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | y = 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))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f1051,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | y = 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))))))),X1) )
    | ~ spl0_29
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f335]) ).

fof(f5354,plain,
    ( spl0_396
    | ~ spl0_397
    | ~ spl0_87
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1102,f1078,f693,f5351,f5348]) ).

fof(f5348,plain,
    ( spl0_396
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f5351,plain,
    ( spl0_397
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f1102,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_87
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f694]) ).

fof(f5346,plain,
    ( spl0_395
    | ~ spl0_295
    | ~ spl0_344 ),
    inference(avatar_split_clause,[],[f5225,f4190,f3222,f5343]) ).

fof(f5343,plain,
    ( spl0_395
  <=> subclass(y,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f5225,plain,
    ( subclass(y,identity_relation)
    | ~ spl0_295
    | ~ spl0_344 ),
    inference(superposition,[],[f4191,f3224]) ).

fof(f5341,plain,
    ( spl0_393
    | ~ spl0_394
    | ~ spl0_68
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1100,f1078,f583,f5338,f5335]) ).

fof(f5335,plain,
    ( spl0_393
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f5338,plain,
    ( spl0_394
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1100,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_68
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f584]) ).

fof(f5312,plain,
    ( spl0_392
    | ~ spl0_109
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1834,f1816,f831,f5310]) ).

fof(f5310,plain,
    ( spl0_392
  <=> ! [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)))))))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1834,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)))))))
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_203 ),
    inference(resolution,[],[f1817,f832]) ).

fof(f5308,plain,
    ( spl0_391
    | ~ spl0_130
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1056,f1043,f1005,f5306]) ).

fof(f5306,plain,
    ( spl0_391
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | ~ member(X0,universal_class)
        | y = X0
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f1056,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | ~ member(X0,universal_class)
        | y = X0
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_130
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f1006]) ).

fof(f5304,plain,
    ( spl0_390
    | ~ spl0_131
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1054,f1043,f1009,f5302]) ).

fof(f5302,plain,
    ( spl0_390
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | y = X0
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f1054,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | y = X0
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_131
    | ~ spl0_134 ),
    inference(resolution,[],[f1044,f1010]) ).

fof(f5279,plain,
    ( spl0_389
    | ~ spl0_136
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1549,f1537,f1066,f5277]) ).

fof(f5277,plain,
    ( spl0_389
  <=> ! [X0] :
        ( ~ 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)
        | ~ member(complement(X0),universal_class)
        | complement(X0) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f1549,plain,
    ( ! [X0] :
        ( ~ 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)
        | ~ member(complement(X0),universal_class)
        | complement(X0) = y )
    | ~ spl0_136
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f1067]) ).

fof(f5275,plain,
    ( spl0_388
    | ~ spl0_116
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1317,f1287,f912,f5273]) ).

fof(f5273,plain,
    ( spl0_388
  <=> ! [X0,X1] :
        ( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1)
        | y = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f1317,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1)
        | y = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class) )
    | ~ spl0_116
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f913]) ).

fof(f5271,plain,
    ( spl0_387
    | ~ spl0_80
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1207,f1199,f647,f5269]) ).

fof(f5269,plain,
    ( spl0_387
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f1207,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) = y )
    | ~ spl0_80
    | ~ spl0_144 ),
    inference(superposition,[],[f648,f1200]) ).

fof(f5264,plain,
    ( spl0_238
    | ~ spl0_244
    | spl0_386
    | ~ spl0_79
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1160,f1139,f642,f5261,f2322,f2279]) ).

fof(f5261,plain,
    ( spl0_386
  <=> 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_386])]) ).

fof(f1160,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))
    | ~ member(subset_relation,universal_class)
    | subset_relation = y
    | ~ spl0_79
    | ~ spl0_140 ),
    inference(superposition,[],[f1140,f644]) ).

fof(f5233,plain,
    ( spl0_385
    | ~ spl0_113
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f1561,f1537,f888,f5231]) ).

fof(f5231,plain,
    ( spl0_385
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),y)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f1561,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),y)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_179 ),
    inference(resolution,[],[f1538,f889]) ).

fof(f5229,plain,
    ( spl0_384
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f820,f810,f500,f261,f5227]) ).

fof(f5227,plain,
    ( spl0_384
  <=> ! [X0] :
        ( y = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | y = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f820,plain,
    ( ! [X0] :
        ( y = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | y = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) )
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_106 ),
    inference(forward_demodulation,[],[f819,f501]) ).

fof(f819,plain,
    ( ! [X0] :
        ( y = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class)
        | y = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
    | ~ spl0_12
    | ~ spl0_106 ),
    inference(resolution,[],[f811,f262]) ).

fof(f5033,plain,
    ( spl0_383
    | ~ spl0_108
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1683,f1642,f826,f5031]) ).

fof(f5031,plain,
    ( spl0_383
  <=> ! [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))),y)
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f1683,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))),y)
        | y = X2 )
    | ~ spl0_108
    | ~ spl0_191 ),
    inference(resolution,[],[f1643,f827]) ).

fof(f5029,plain,
    ( spl0_382
    | ~ spl0_133
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1406,f1351,f1037,f5027]) ).

fof(f5027,plain,
    ( spl0_382
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,universal_class),domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f1037,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( y = 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))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1406,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,universal_class),domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
    | ~ spl0_133
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1388]) ).

fof(f1388,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,universal_class),domain_of(X1))
        | subclass(intersection(X0,universal_class),domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
    | ~ spl0_133
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f1038]) ).

fof(f1038,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1037]) ).

fof(f5025,plain,
    ( spl0_381
    | ~ spl0_113
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1397,f1351,f888,f5023]) ).

fof(f1397,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,regular(X1)),X2)
        | member(not_subclass_element(intersection(X0,regular(X1)),X2),y)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | y = X1 )
    | ~ spl0_113
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f889]) ).

fof(f5021,plain,
    ( spl0_380
    | ~ spl0_133
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1385,f1347,f1037,f5019]) ).

fof(f5019,plain,
    ( spl0_380
  <=> ! [X0,X1] :
        ( subclass(intersection(universal_class,X0),domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f1385,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(universal_class,X0),domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
    | ~ spl0_133
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1367]) ).

fof(f1367,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(universal_class,X0),domain_of(X1))
        | subclass(intersection(universal_class,X0),domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
    | ~ spl0_133
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f1038]) ).

fof(f5017,plain,
    ( spl0_379
    | ~ spl0_113
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1376,f1347,f888,f5015]) ).

fof(f1376,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(regular(X0),X1),X2)
        | member(not_subclass_element(intersection(regular(X0),X1),X2),y)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f889]) ).

fof(f5013,plain,
    ( spl0_378
    | ~ spl0_76
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1206,f1199,f625,f5011]) ).

fof(f5011,plain,
    ( spl0_378
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f1206,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) = y )
    | ~ spl0_76
    | ~ spl0_144 ),
    inference(superposition,[],[f626,f1200]) ).

fof(f5007,plain,
    ( spl0_186
    | ~ spl0_199
    | spl0_377
    | ~ spl0_28
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1026,f1009,f330,f5004,f1758,f1601]) ).

fof(f5004,plain,
    ( spl0_377
  <=> 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_377])]) ).

fof(f1026,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)
    | identity_relation = y
    | ~ spl0_28
    | ~ spl0_131 ),
    inference(resolution,[],[f1010,f331]) ).

fof(f5000,plain,
    ( spl0_168
    | ~ spl0_375
    | spl0_376
    | ~ spl0_28
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1019,f1005,f330,f4997,f4993,f1428]) ).

fof(f4997,plain,
    ( spl0_376
  <=> 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_376])]) ).

fof(f1019,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)
    | singleton_relation = y
    | ~ spl0_28
    | ~ spl0_130 ),
    inference(resolution,[],[f1006,f331]) ).

fof(f4991,plain,
    ( spl0_374
    | ~ spl0_67
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f957,f953,f577,f4989]) ).

fof(f4989,plain,
    ( spl0_374
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f957,plain,
    ( ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ inductive(X1) )
    | ~ spl0_67
    | ~ spl0_119 ),
    inference(resolution,[],[f954,f578]) ).

fof(f4972,plain,
    ( spl0_373
    | ~ spl0_26
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1191,f1181,f322,f4970]) ).

fof(f4970,plain,
    ( spl0_373
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f1191,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_26
    | ~ spl0_142 ),
    inference(resolution,[],[f1182,f323]) ).

fof(f4968,plain,
    ( spl0_371
    | ~ spl0_372
    | ~ spl0_65
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1095,f1078,f569,f4965,f4962]) ).

fof(f4962,plain,
    ( spl0_371
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f4965,plain,
    ( spl0_372
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f1095,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_65
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f570]) ).

fof(f4957,plain,
    ( spl0_370
    | ~ spl0_116
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1118,f1078,f912,f4955]) ).

fof(f4955,plain,
    ( spl0_370
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class))))
        | y = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f1118,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class))))
        | y = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class) )
    | ~ spl0_116
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f913]) ).

fof(f4790,plain,
    ( spl0_369
    | ~ spl0_111
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2969,f2838,f852,f4788]) ).

fof(f2969,plain,
    ( ! [X0] : y = intersection(X0,complement(X0))
    | ~ spl0_111
    | ~ spl0_275 ),
    inference(duplicate_literal_removal,[],[f2947]) ).

fof(f2947,plain,
    ( ! [X0] :
        ( y = intersection(X0,complement(X0))
        | y = intersection(X0,complement(X0)) )
    | ~ spl0_111
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f853]) ).

fof(f4499,plain,
    ( spl0_366
    | spl0_367
    | ~ spl0_368
    | ~ spl0_2
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1470,f1424,f213,f4496,f4492,f4488]) ).

fof(f1470,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)
    | y = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_2
    | ~ spl0_167 ),
    inference(resolution,[],[f1425,f214]) ).

fof(f4481,plain,
    ( spl0_363
    | spl0_364
    | ~ spl0_365
    | ~ spl0_2
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1445,f1420,f213,f4478,f4474,f4470]) ).

fof(f1445,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | complement(compose(element_relation,complement(identity_relation))) = y
    | ~ spl0_2
    | ~ spl0_166 ),
    inference(resolution,[],[f1421,f214]) ).

fof(f4468,plain,
    ( spl0_362
    | ~ spl0_252
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2966,f2838,f2522,f4465]) ).

fof(f2966,plain,
    ( y = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_252
    | ~ spl0_275 ),
    inference(duplicate_literal_removal,[],[f2951]) ).

fof(f2951,plain,
    ( y = intersection(singleton_relation,complement(element_relation))
    | y = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_252
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f2523]) ).

fof(f4463,plain,
    ( spl0_361
    | ~ spl0_68
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1203,f1199,f583,f4461]) ).

fof(f4461,plain,
    ( spl0_361
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f1203,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) = y )
    | ~ spl0_68
    | ~ spl0_144 ),
    inference(superposition,[],[f584,f1200]) ).

fof(f4459,plain,
    ( spl0_360
    | ~ spl0_63
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f956,f953,f555,f4457]) ).

fof(f4457,plain,
    ( spl0_360
  <=> ! [X0,X1] :
        ( member(X0,domain_of(domain_of(X1)))
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f956,plain,
    ( ! [X0,X1] :
        ( member(X0,domain_of(domain_of(X1)))
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ operation(X1) )
    | ~ spl0_63
    | ~ spl0_119 ),
    inference(resolution,[],[f954,f556]) ).

fof(f4455,plain,
    ( spl0_359
    | ~ spl0_109
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f917,f912,f831,f4453]) ).

fof(f4453,plain,
    ( spl0_359
  <=> ! [X0] :
        ( y = 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))))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f917,plain,
    ( ! [X0] :
        ( y = 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))))
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_116 ),
    inference(resolution,[],[f913,f832]) ).

fof(f4451,plain,
    ( spl0_358
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f907,f888,f856,f4449]) ).

fof(f907,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),y)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | y = X1
        | y = intersection(X0,regular(X1)) )
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f857]) ).

fof(f4447,plain,
    ( spl0_357
    | ~ spl0_111
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f904,f888,f852,f4445]) ).

fof(f904,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),y)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | y = X0
        | y = intersection(regular(X0),X1) )
    | ~ spl0_111
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f853]) ).

fof(f4443,plain,
    ( spl0_356
    | ~ spl0_55
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f874,f856,f492,f4441]) ).

fof(f4441,plain,
    ( spl0_356
  <=> ! [X2,X0,X1] :
        ( y = 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_356])]) ).

fof(f874,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
    | ~ spl0_55
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f493]) ).

fof(f4439,plain,
    ( spl0_355
    | ~ spl0_55
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f860,f852,f492,f4437]) ).

fof(f4437,plain,
    ( spl0_355
  <=> ! [X2,X0,X1] :
        ( y = 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_355])]) ).

fof(f860,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
    | ~ spl0_55
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f493]) ).

fof(f4360,plain,
    ( spl0_354
    | ~ spl0_254
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2964,f2838,f2532,f4357]) ).

fof(f4357,plain,
    ( spl0_354
  <=> y = intersection(identity_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f2964,plain,
    ( y = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_254
    | ~ spl0_275 ),
    inference(duplicate_literal_removal,[],[f2960]) ).

fof(f2960,plain,
    ( y = intersection(identity_relation,complement(subset_relation))
    | y = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_254
    | ~ spl0_275 ),
    inference(resolution,[],[f2839,f2533]) ).

fof(f4305,plain,
    ( spl0_352
    | ~ spl0_353
    | ~ spl0_107
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1729,f1646,f814,f4302,f4299]) ).

fof(f4299,plain,
    ( spl0_352
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | y = 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_352])]) ).

fof(f4302,plain,
    ( spl0_353
  <=> subclass(domain_relation,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f1729,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,y)
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
        | y = X1 )
    | ~ spl0_107
    | ~ spl0_192 ),
    inference(resolution,[],[f1647,f815]) ).

fof(f4297,plain,
    ( spl0_351
    | ~ spl0_133
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1323,f1287,f1037,f4295]) ).

fof(f4295,plain,
    ( spl0_351
  <=> ! [X0,X1] :
        ( ~ subclass(X0,universal_class)
        | subclass(X0,domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f1323,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,universal_class)
        | subclass(X0,domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
    | ~ spl0_133
    | ~ spl0_154 ),
    inference(duplicate_literal_removal,[],[f1308]) ).

fof(f1308,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,universal_class)
        | subclass(X0,domain_of(X1))
        | subclass(X0,domain_of(X1))
        | y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
    | ~ spl0_133
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f1038]) ).

fof(f4293,plain,
    ( spl0_350
    | ~ spl0_65
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1202,f1199,f569,f4291]) ).

fof(f4291,plain,
    ( spl0_350
  <=> ! [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) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f1202,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) = y )
    | ~ spl0_65
    | ~ spl0_144 ),
    inference(superposition,[],[f570,f1200]) ).

fof(f4289,plain,
    ( spl0_349
    | ~ spl0_113
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f951,f925,f888,f4287]) ).

fof(f951,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,y)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_113
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f930]) ).

fof(f930,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,y)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_113
    | ~ spl0_118 ),
    inference(superposition,[],[f889,f926]) ).

fof(f4285,plain,
    ( spl0_348
    | ~ spl0_113
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f946,f925,f888,f4283]) ).

fof(f946,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,y)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_113
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f935]) ).

fof(f935,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,y)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_113
    | ~ spl0_118 ),
    inference(superposition,[],[f889,f926]) ).

fof(f4242,plain,
    ( spl0_347
    | ~ spl0_105
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f1665,f1638,f789,f4240]) ).

fof(f4240,plain,
    ( spl0_347
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(y,X2)
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f789,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(y,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f1665,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(y,X2)
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_105
    | ~ spl0_190 ),
    inference(resolution,[],[f1639,f790]) ).

fof(f790,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(y,X1)
        | ~ inductive(X0) )
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f789]) ).

fof(f4238,plain,
    ( spl0_346
    | ~ spl0_112
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2943,f2834,f856,f4236]) ).

fof(f2943,plain,
    ( ! [X0] : y = intersection(complement(X0),X0)
    | ~ spl0_112
    | ~ spl0_274 ),
    inference(duplicate_literal_removal,[],[f2919]) ).

fof(f2919,plain,
    ( ! [X0] :
        ( y = intersection(complement(X0),X0)
        | y = intersection(complement(X0),X0) )
    | ~ spl0_112
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f857]) ).

fof(f4234,plain,
    ( spl0_345
    | ~ spl0_12
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1480,f1424,f500,f261,f4232]) ).

fof(f4232,plain,
    ( spl0_345
  <=> ! [X0] :
        ( y = 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_345])]) ).

fof(f4192,plain,
    ( spl0_344
    | ~ spl0_35
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1407,f1351,f365,f4190]) ).

fof(f1407,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_35
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1387]) ).

fof(f1387,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_35
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f366]) ).

fof(f4188,plain,
    ( spl0_343
    | ~ spl0_35
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1386,f1347,f365,f4186]) ).

fof(f1386,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_35
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f1366]) ).

fof(f1366,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_35
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f366]) ).

fof(f4106,plain,
    ( spl0_342
    | ~ spl0_113
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1319,f1287,f888,f4104]) ).

fof(f1319,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,regular(X1))
        | subclass(X0,X2)
        | member(not_subclass_element(X0,X2),y)
        | ~ member(not_subclass_element(X0,X2),X1)
        | y = X1 )
    | ~ spl0_113
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f889]) ).

fof(f4102,plain,
    ( spl0_341
    | ~ spl0_74
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1205,f1199,f613,f4100]) ).

fof(f1205,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) = y )
    | ~ spl0_74
    | ~ spl0_144 ),
    inference(superposition,[],[f614,f1200]) ).

fof(f4098,plain,
    ( spl0_340
    | ~ spl0_73
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1204,f1199,f609,f4096]) ).

fof(f1204,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) = y )
    | ~ spl0_73
    | ~ spl0_144 ),
    inference(superposition,[],[f610,f1200]) ).

fof(f4094,plain,
    ( spl0_339
    | ~ spl0_31
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f960,f953,f342,f4092]) ).

fof(f960,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | y = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ function(domain_of(X1)) )
    | ~ spl0_31
    | ~ spl0_119 ),
    inference(resolution,[],[f954,f343]) ).

fof(f4090,plain,
    ( spl0_338
    | ~ spl0_56
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f817,f810,f496,f4088]) ).

fof(f4088,plain,
    ( spl0_338
  <=> ! [X0,X1] :
        ( complement(intersection(X0,X1)) = y
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f817,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = y
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_56
    | ~ spl0_106 ),
    inference(resolution,[],[f811,f497]) ).

fof(f4044,plain,
    ( spl0_337
    | ~ spl0_238
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f4025,f4021,f2279,f4042]) ).

fof(f4042,plain,
    ( spl0_337
  <=> ! [X0,X1] :
        ( subset_relation = X0
        | member(not_subclass_element(regular(X0),X1),subset_relation)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | subclass(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f4025,plain,
    ( ! [X0,X1] :
        ( subset_relation = X0
        | member(not_subclass_element(regular(X0),X1),subset_relation)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | subclass(regular(X0),X1) )
    | ~ spl0_238
    | ~ spl0_333 ),
    inference(forward_demodulation,[],[f4024,f2281]) ).

fof(f4024,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),subset_relation)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | y = X0
        | subclass(regular(X0),X1) )
    | ~ spl0_238
    | ~ spl0_333 ),
    inference(forward_demodulation,[],[f4022,f2281]) ).

fof(f4039,plain,
    ( spl0_336
    | ~ spl0_34
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1041,f1037,f361,f4037]) ).

fof(f4037,plain,
    ( spl0_336
  <=> ! [X0] :
        ( subclass(universal_class,domain_of(X0))
        | y = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f1041,plain,
    ( ! [X0] :
        ( subclass(universal_class,domain_of(X0))
        | y = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class)) )
    | ~ spl0_34
    | ~ spl0_133 ),
    inference(duplicate_literal_removal,[],[f1040]) ).

fof(f1040,plain,
    ( ! [X0] :
        ( subclass(universal_class,domain_of(X0))
        | y = 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_34
    | ~ spl0_133 ),
    inference(resolution,[],[f1038,f362]) ).

fof(f4034,plain,
    ( spl0_335
    | ~ spl0_109
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f950,f925,f831,f4032]) ).

fof(f950,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_109
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f931]) ).

fof(f931,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_109
    | ~ spl0_118 ),
    inference(superposition,[],[f832,f926]) ).

fof(f4029,plain,
    ( spl0_334
    | ~ spl0_109
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f945,f925,f831,f4027]) ).

fof(f945,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_109
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f936]) ).

fof(f936,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_109
    | ~ spl0_118 ),
    inference(superposition,[],[f832,f926]) ).

fof(f4023,plain,
    ( spl0_333
    | ~ spl0_34
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f901,f888,f361,f4021]) ).

fof(f901,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),y)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | y = X0
        | subclass(regular(X0),X1) )
    | ~ spl0_34
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f362]) ).

fof(f3980,plain,
    ( spl0_238
    | spl0_332
    | ~ spl0_79
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f884,f856,f642,f3977,f2279]) ).

fof(f884,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)))))))
    | subset_relation = y
    | ~ spl0_79
    | ~ spl0_112 ),
    inference(superposition,[],[f857,f644]) ).

fof(f3828,plain,
    ( spl0_331
    | ~ spl0_109
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1473,f1424,f831,f3826]) ).

fof(f3824,plain,
    ( spl0_330
    | ~ spl0_109
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1448,f1420,f831,f3822]) ).

fof(f3820,plain,
    ( spl0_329
    | ~ spl0_7
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f948,f925,f238,f3818]) ).

fof(f3818,plain,
    ( spl0_329
  <=> ! [X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f948,plain,
    ( ! [X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_7
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f933]) ).

fof(f933,plain,
    ( ! [X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_7
    | ~ spl0_118 ),
    inference(superposition,[],[f239,f926]) ).

fof(f3816,plain,
    ( spl0_328
    | ~ spl0_7
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f943,f925,f238,f3814]) ).

fof(f3814,plain,
    ( spl0_328
  <=> ! [X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f943,plain,
    ( ! [X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_7
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f938]) ).

fof(f938,plain,
    ( ! [X0,X1] :
        ( y = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_7
    | ~ spl0_118 ),
    inference(superposition,[],[f239,f926]) ).

fof(f3812,plain,
    ( spl0_327
    | ~ spl0_109
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f906,f888,f831,f3810]) ).

fof(f906,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),y)
        | ~ member(regular(X0),X1)
        | y = X1
        | ~ subclass(X0,regular(X1))
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f832]) ).

fof(f3807,plain,
    ( spl0_326
    | ~ spl0_241
    | ~ spl0_306 ),
    inference(avatar_split_clause,[],[f3712,f3490,f2306,f3804]) ).

fof(f3712,plain,
    ( member(second(y),universal_class)
    | ~ spl0_241
    | ~ spl0_306 ),
    inference(resolution,[],[f3491,f2308]) ).

fof(f2308,plain,
    ( member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f2306]) ).

fof(f3709,plain,
    ( spl0_325
    | ~ spl0_74
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f3445,f965,f613,f3707]) ).

fof(f3707,plain,
    ( spl0_325
  <=> ! [X0,X1] :
        ( ~ member(y,cross_product(X0,X1))
        | member(first(y),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f965,plain,
    ( spl0_121
  <=> y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f3445,plain,
    ( ! [X0,X1] :
        ( ~ member(y,cross_product(X0,X1))
        | member(first(y),X0) )
    | ~ spl0_74
    | ~ spl0_121 ),
    inference(superposition,[],[f614,f967]) ).

fof(f967,plain,
    ( y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y))))
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f965]) ).

fof(f3701,plain,
    ( spl0_324
    | spl0_124
    | ~ spl0_30
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f802,f789,f338,f978,f3699]) ).

fof(f3699,plain,
    ( spl0_324
  <=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f802,plain,
    ( ! [X0,X1] :
        ( member(y,cross_product(universal_class,universal_class))
        | ~ inductive(compose(X0,X1)) )
    | ~ spl0_30
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f339]) ).

fof(f3697,plain,
    ( spl0_124
    | ~ spl0_10
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2256,f2235,f251,f978]) ).

fof(f2235,plain,
    ( spl0_231
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2256,plain,
    ( member(y,cross_product(universal_class,universal_class))
    | ~ spl0_10
    | ~ spl0_231 ),
    inference(resolution,[],[f2236,f252]) ).

fof(f2236,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(y,X0) )
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f2235]) ).

fof(f3636,plain,
    ( spl0_323
    | ~ spl0_7
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1684,f1642,f238,f3634]) ).

fof(f1684,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,y),regular(X0))
        | ~ member(not_subclass_element(X1,y),X0)
        | subclass(X1,y)
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_191 ),
    inference(superposition,[],[f1643,f239]) ).

fof(f3630,plain,
    ( spl0_321
    | ~ spl0_322
    | ~ spl0_106
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1284,f1264,f810,f3627,f3623]) ).

fof(f1284,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | y = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_106
    | ~ spl0_153 ),
    inference(resolution,[],[f1265,f811]) ).

fof(f3619,plain,
    ( spl0_319
    | ~ spl0_320
    | ~ spl0_106
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1278,f1260,f810,f3616,f3612]) ).

fof(f1278,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | y = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_106
    | ~ spl0_152 ),
    inference(resolution,[],[f1261,f811]) ).

fof(f3610,plain,
    ( spl0_318
    | ~ spl0_113
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1120,f1078,f888,f3608]) ).

fof(f1120,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | member(unordered_pair(X1,X2),y)
        | ~ member(unordered_pair(X1,X2),X0)
        | y = X0 )
    | ~ spl0_113
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f889]) ).

fof(f3606,plain,
    ( spl0_317
    | ~ spl0_108
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f949,f925,f826,f3604]) ).

fof(f3604,plain,
    ( spl0_317
  <=> ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,y)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f949,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,y)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_108
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f932]) ).

fof(f932,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,y)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_108
    | ~ spl0_118 ),
    inference(superposition,[],[f827,f926]) ).

fof(f3602,plain,
    ( spl0_316
    | ~ spl0_108
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f944,f925,f826,f3600]) ).

fof(f3600,plain,
    ( spl0_316
  <=> ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,y)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f944,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,y)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_108
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f937]) ).

fof(f937,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,y)
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_108
    | ~ spl0_118 ),
    inference(superposition,[],[f827,f926]) ).

fof(f3598,plain,
    ( spl0_315
    | ~ spl0_2
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f903,f888,f213,f3596]) ).

fof(f903,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),y)
        | ~ member(regular(regular(X0)),X0)
        | y = X0
        | regular(X0) = y )
    | ~ spl0_2
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f214]) ).

fof(f3594,plain,
    ( spl0_314
    | ~ spl0_51
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f818,f810,f472,f3592]) ).

fof(f818,plain,
    ( ! [X0] :
        ( y = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_51
    | ~ spl0_106 ),
    inference(resolution,[],[f811,f473]) ).

fof(f3590,plain,
    ( ~ spl0_312
    | spl0_313
    | ~ spl0_20
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1192,f1181,f296,f3587,f3583]) ).

fof(f3583,plain,
    ( spl0_312
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f3587,plain,
    ( spl0_313
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f1192,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_20
    | ~ spl0_142 ),
    inference(resolution,[],[f1182,f298]) ).

fof(f3581,plain,
    ( ~ spl0_311
    | ~ spl0_6
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3493,f2248,f233,f3578]) ).

fof(f3578,plain,
    ( spl0_311
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f3493,plain,
    ( ~ inductive(choice)
    | ~ spl0_6
    | ~ spl0_233 ),
    inference(resolution,[],[f2249,f235]) ).

fof(f3576,plain,
    ( ~ spl0_309
    | spl0_310
    | ~ spl0_18
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1188,f1181,f287,f3573,f3569]) ).

fof(f3569,plain,
    ( spl0_309
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f3573,plain,
    ( spl0_310
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f1188,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_18
    | ~ spl0_142 ),
    inference(resolution,[],[f1182,f289]) ).

fof(f3567,plain,
    ( ~ spl0_307
    | spl0_308
    | ~ spl0_17
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1186,f1181,f282,f3564,f3560]) ).

fof(f3560,plain,
    ( spl0_307
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f3564,plain,
    ( spl0_308
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f1186,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_17
    | ~ spl0_142 ),
    inference(resolution,[],[f1182,f284]) ).

fof(f3492,plain,
    ( spl0_306
    | ~ spl0_73
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f3444,f965,f609,f3490]) ).

fof(f3444,plain,
    ( ! [X0,X1] :
        ( ~ member(y,cross_product(X0,X1))
        | member(second(y),X1) )
    | ~ spl0_73
    | ~ spl0_121 ),
    inference(superposition,[],[f610,f967]) ).

fof(f3487,plain,
    ( spl0_304
    | ~ spl0_305
    | ~ spl0_68
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f3443,f965,f583,f3484,f3480]) ).

fof(f3443,plain,
    ( ~ member(y,domain_relation)
    | second(y) = domain_of(first(y))
    | ~ spl0_68
    | ~ spl0_121 ),
    inference(superposition,[],[f584,f967]) ).

fof(f3441,plain,
    ( spl0_121
    | ~ spl0_82
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f2227,f978,f665,f965]) ).

fof(f2227,plain,
    ( y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y))))
    | ~ spl0_82
    | ~ spl0_124 ),
    inference(resolution,[],[f979,f666]) ).

fof(f979,plain,
    ( member(y,cross_product(universal_class,universal_class))
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f978]) ).

fof(f3440,plain,
    ( spl0_303
    | ~ spl0_7
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1543,f1533,f238,f3438]) ).

fof(f3438,plain,
    ( spl0_303
  <=> ! [X2,X0,X1] :
        ( ~ subclass(y,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f1543,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(y,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_178 ),
    inference(superposition,[],[f1534,f239]) ).

fof(f3436,plain,
    ( spl0_302
    | ~ spl0_2
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f947,f925,f213,f3434]) ).

fof(f947,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_2
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f934]) ).

fof(f934,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_118 ),
    inference(superposition,[],[f214,f926]) ).

fof(f3432,plain,
    ( spl0_301
    | ~ spl0_2
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f942,f925,f213,f3430]) ).

fof(f942,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_2
    | ~ spl0_118 ),
    inference(duplicate_literal_removal,[],[f939]) ).

fof(f939,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = y
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_118 ),
    inference(superposition,[],[f214,f926]) ).

fof(f3428,plain,
    ( spl0_300
    | ~ spl0_55
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f843,f831,f492,f3426]) ).

fof(f843,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | y = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_55
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f493]) ).

fof(f3424,plain,
    ( spl0_299
    | ~ spl0_253
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2940,f2834,f2527,f3421]) ).

fof(f3421,plain,
    ( spl0_299
  <=> y = intersection(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f2940,plain,
    ( y = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_253
    | ~ spl0_274 ),
    inference(duplicate_literal_removal,[],[f2923]) ).

fof(f2923,plain,
    ( y = intersection(complement(element_relation),singleton_relation)
    | y = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_253
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f2528]) ).

fof(f3237,plain,
    ( spl0_298
    | ~ spl0_107
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1399,f1351,f814,f3235]) ).

fof(f1399,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,y),X1)
        | member(not_subclass_element(intersection(X0,y),X1),X2)
        | y = X2 )
    | ~ spl0_107
    | ~ spl0_161 ),
    inference(resolution,[],[f1352,f815]) ).

fof(f3233,plain,
    ( spl0_297
    | ~ spl0_107
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1378,f1347,f814,f3231]) ).

fof(f1378,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(y,X0),X1)
        | member(not_subclass_element(intersection(y,X0),X1),X2)
        | y = X2 )
    | ~ spl0_107
    | ~ spl0_160 ),
    inference(resolution,[],[f1348,f815]) ).

fof(f3229,plain,
    ( spl0_296
    | ~ spl0_108
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1271,f1229,f826,f3227]) ).

fof(f3227,plain,
    ( spl0_296
  <=> ! [X0,X1] :
        ( subclass(complement(regular(X0)),X1)
        | ~ member(not_subclass_element(complement(regular(X0)),X1),y)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f1271,plain,
    ( ! [X0,X1] :
        ( subclass(complement(regular(X0)),X1)
        | ~ member(not_subclass_element(complement(regular(X0)),X1),y)
        | y = X0 )
    | ~ spl0_108
    | ~ spl0_145 ),
    inference(resolution,[],[f1230,f827]) ).

fof(f3225,plain,
    ( spl0_295
    | ~ spl0_255
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2938,f2834,f2537,f3222]) ).

fof(f2938,plain,
    ( y = intersection(complement(subset_relation),identity_relation)
    | ~ spl0_255
    | ~ spl0_274 ),
    inference(duplicate_literal_removal,[],[f2932]) ).

fof(f2932,plain,
    ( y = intersection(complement(subset_relation),identity_relation)
    | y = intersection(complement(subset_relation),identity_relation)
    | ~ spl0_255
    | ~ spl0_274 ),
    inference(resolution,[],[f2835,f2538]) ).

fof(f3220,plain,
    ( ~ spl0_293
    | spl0_294
    | ~ spl0_1
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f916,f912,f209,f3217,f3213]) ).

fof(f916,plain,
    ( y = cross_product(unordered_pair(y,y),universal_class)
    | ~ inductive(domain_of(regular(cross_product(unordered_pair(y,y),universal_class))))
    | ~ spl0_1
    | ~ spl0_116 ),
    inference(resolution,[],[f913,f210]) ).

fof(f3211,plain,
    ( spl0_292
    | ~ spl0_39
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f877,f856,f381,f3209]) ).

fof(f877,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_39
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f382]) ).

fof(f3207,plain,
    ( spl0_291
    | ~ spl0_40
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f876,f856,f385,f3205]) ).

fof(f876,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_40
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f386]) ).

fof(f3203,plain,
    ( spl0_290
    | ~ spl0_39
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f863,f852,f381,f3201]) ).

fof(f863,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_39
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f382]) ).

fof(f3199,plain,
    ( spl0_289
    | ~ spl0_40
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f862,f852,f385,f3197]) ).

fof(f862,plain,
    ( ! [X2,X0,X1] :
        ( y = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_40
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f386]) ).

fof(f3144,plain,
    ( spl0_288
    | ~ spl0_35
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2591,f2446,f365,f3142]) ).

fof(f2446,plain,
    ( spl0_247
  <=> ! [X0,X1] :
        ( member(not_subclass_element(y,X0),X1)
        | y = X1
        | subclass(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f2591,plain,
    ( ! [X0] :
        ( y = X0
        | subclass(y,X0) )
    | ~ spl0_35
    | ~ spl0_247 ),
    inference(duplicate_literal_removal,[],[f2565]) ).

fof(f2565,plain,
    ( ! [X0] :
        ( y = X0
        | subclass(y,X0)
        | subclass(y,X0) )
    | ~ spl0_35
    | ~ spl0_247 ),
    inference(resolution,[],[f2447,f366]) ).

fof(f2447,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(y,X0),X1)
        | y = X1
        | subclass(y,X0) )
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f2446]) ).

fof(f3025,plain,
    ( spl0_287
    | ~ spl0_107
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1321,f1287,f814,f3023]) ).

fof(f3023,plain,
    ( spl0_287
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,y)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f1321,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,y)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | y = X2 )
    | ~ spl0_107
    | ~ spl0_154 ),
    inference(resolution,[],[f1288,f815]) ).

fof(f3021,plain,
    ( spl0_286
    | ~ spl0_137
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1227,f1199,f1078,f3019]) ).

fof(f1227,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = y )
    | ~ spl0_137
    | ~ spl0_144 ),
    inference(superposition,[],[f1079,f1200]) ).

fof(f3017,plain,
    ( spl0_285
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f941,f925,f3015]) ).

fof(f3015,plain,
    ( spl0_285
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f941,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_118 ),
    inference(equality_factoring,[],[f926]) ).

fof(f2998,plain,
    ( spl0_284
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f940,f925,f2996]) ).

fof(f940,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = y )
    | ~ spl0_118 ),
    inference(equality_factoring,[],[f926]) ).

fof(f2994,plain,
    ( spl0_283
    | ~ spl0_107
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f880,f856,f814,f2992]) ).

fof(f2992,plain,
    ( spl0_283
  <=> ! [X0,X1] :
        ( y = intersection(X0,y)
        | member(regular(intersection(X0,y)),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f880,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,y)
        | member(regular(intersection(X0,y)),X1)
        | y = X1 )
    | ~ spl0_107
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f815]) ).

fof(f2990,plain,
    ( spl0_282
    | ~ spl0_46
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f873,f856,f424,f2988]) ).

fof(f873,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_46
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f425]) ).

fof(f2986,plain,
    ( spl0_281
    | ~ spl0_107
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f866,f852,f814,f2984]) ).

fof(f2984,plain,
    ( spl0_281
  <=> ! [X0,X1] :
        ( y = intersection(y,X0)
        | member(regular(intersection(y,X0)),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f866,plain,
    ( ! [X0,X1] :
        ( y = intersection(y,X0)
        | member(regular(intersection(y,X0)),X1)
        | y = X1 )
    | ~ spl0_107
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f815]) ).

fof(f2982,plain,
    ( spl0_280
    | ~ spl0_46
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f859,f852,f424,f2980]) ).

fof(f859,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = y
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_46
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f425]) ).

fof(f2978,plain,
    ( spl0_279
    | ~ spl0_106
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f840,f826,f810,f2976]) ).

fof(f2976,plain,
    ( spl0_279
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),y)
        | y = X0
        | y = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f840,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),y)
        | y = X0
        | y = complement(regular(X0)) )
    | ~ spl0_106
    | ~ spl0_108 ),
    inference(resolution,[],[f827,f811]) ).

fof(f2974,plain,
    ( spl0_278
    | ~ spl0_63
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f796,f789,f555,f2972]) ).

fof(f2972,plain,
    ( spl0_278
  <=> ! [X0] :
        ( member(y,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_278])]) ).

fof(f796,plain,
    ( ! [X0] :
        ( member(y,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_63
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f556]) ).

fof(f2945,plain,
    ( spl0_97
    | ~ spl0_131
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f2814,f2805,f1009,f750]) ).

fof(f2814,plain,
    ( member(y,subset_relation)
    | ~ spl0_131
    | ~ spl0_268 ),
    inference(resolution,[],[f2807,f1010]) ).

fof(f2807,plain,
    ( member(y,identity_relation)
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f2805]) ).

fof(f2849,plain,
    ( spl0_276
    | ~ spl0_277
    | ~ spl0_106
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1136,f1089,f810,f2846,f2842]) ).

fof(f1136,plain,
    ( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | y = complement(cross_product(universal_class,universal_class))
    | ~ spl0_106
    | ~ spl0_139 ),
    inference(resolution,[],[f1090,f811]) ).

fof(f2840,plain,
    ( spl0_275
    | ~ spl0_29
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f878,f856,f334,f2838]) ).

fof(f878,plain,
    ( ! [X0,X1] :
        ( y = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_29
    | ~ spl0_112 ),
    inference(resolution,[],[f857,f335]) ).

fof(f2836,plain,
    ( spl0_274
    | ~ spl0_29
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f864,f852,f334,f2834]) ).

fof(f864,plain,
    ( ! [X0,X1] :
        ( y = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_29
    | ~ spl0_111 ),
    inference(resolution,[],[f853,f335]) ).

fof(f2832,plain,
    ( spl0_273
    | ~ spl0_107
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f849,f831,f814,f2830]) ).

fof(f2830,plain,
    ( spl0_273
  <=> ! [X0,X1] :
        ( ~ subclass(X0,y)
        | y = X0
        | member(regular(X0),X1)
        | y = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f849,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,y)
        | y = X0
        | member(regular(X0),X1)
        | y = X1 )
    | ~ spl0_107
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f815]) ).

fof(f2828,plain,
    ( spl0_272
    | ~ spl0_46
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f842,f831,f424,f2826]) ).

fof(f842,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | y = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_46
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f425]) ).

fof(f2824,plain,
    ( spl0_271
    | ~ spl0_35
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f839,f826,f365,f2822]) ).

fof(f839,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),y)
        | y = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_35
    | ~ spl0_108 ),
    inference(resolution,[],[f827,f366]) ).

fof(f2820,plain,
    ( spl0_270
    | ~ spl0_46
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f838,f826,f424,f2818]) ).

fof(f2818,plain,
    ( spl0_270
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,y)
        | y = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f838,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,y)
        | y = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_46
    | ~ spl0_108 ),
    inference(resolution,[],[f827,f425]) ).

fof(f2813,plain,
    ( spl0_269
    | spl0_268
    | ~ spl0_58
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f804,f789,f504,f2805,f2811]) ).

fof(f2811,plain,
    ( spl0_269
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f504,plain,
    ( spl0_58
  <=> ! [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_58])]) ).

fof(f804,plain,
    ( ! [X0] :
        ( member(y,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) )
    | ~ spl0_58
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f505]) ).

fof(f505,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f504]) ).

fof(f2808,plain,
    ( spl0_267
    | spl0_268
    | ~ spl0_59
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f803,f789,f508,f2805,f2802]) ).

fof(f2802,plain,
    ( spl0_267
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f508,plain,
    ( spl0_59
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f803,plain,
    ( ! [X0] :
        ( member(y,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_59
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f509]) ).

fof(f509,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f508]) ).

fof(f2766,plain,
    ( spl0_266
    | ~ spl0_7
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1400,f1351,f238,f2764]) ).

fof(f2764,plain,
    ( spl0_266
  <=> ! [X0,X1] :
        ( member(not_subclass_element(y,X1),regular(X0))
        | subclass(y,X1)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f1400,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(y,X1),regular(X0))
        | subclass(y,X1)
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_161 ),
    inference(superposition,[],[f1352,f239]) ).

fof(f2757,plain,
    ( spl0_264
    | spl0_265
    | ~ spl0_1
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f905,f888,f209,f2754,f2751]) ).

fof(f2751,plain,
    ( spl0_264
  <=> ! [X0] :
        ( ~ member(y,X0)
        | ~ inductive(regular(X0))
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2754,plain,
    ( spl0_265
  <=> member(y,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f905,plain,
    ( ! [X0] :
        ( member(y,y)
        | ~ member(y,X0)
        | y = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_1
    | ~ spl0_113 ),
    inference(resolution,[],[f889,f210]) ).

fof(f2749,plain,
    ( spl0_263
    | ~ spl0_39
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f846,f831,f381,f2747]) ).

fof(f846,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = X0
        | member(regular(X0),X1) )
    | ~ spl0_39
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f382]) ).

fof(f2745,plain,
    ( spl0_262
    | ~ spl0_40
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f845,f831,f385,f2743]) ).

fof(f845,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | y = X0
        | member(regular(X0),X2) )
    | ~ spl0_40
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f386]) ).

fof(f2708,plain,
    ( spl0_261
    | ~ spl0_186
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2525,f2522,f1601,f2706]) ).

fof(f2525,plain,
    ( ! [X0] :
        ( identity_relation = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) )
    | ~ spl0_186
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f2523,f1603]) ).

fof(f2564,plain,
    ( ~ spl0_260
    | spl0_69
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1656,f1601,f587,f2561]) ).

fof(f2561,plain,
    ( spl0_260
  <=> member(identity_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f1656,plain,
    ( ~ member(identity_relation,element_relation)
    | spl0_69
    | ~ spl0_186 ),
    inference(superposition,[],[f588,f1603]) ).

fof(f2558,plain,
    ( spl0_259
    | ~ spl0_16
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1220,f1199,f278,f2556]) ).

fof(f2556,plain,
    ( spl0_259
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f1220,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = y )
    | ~ spl0_16
    | ~ spl0_144 ),
    inference(superposition,[],[f279,f1200]) ).

fof(f2554,plain,
    ( ~ spl0_258
    | ~ spl0_186
    | spl0_257 ),
    inference(avatar_split_clause,[],[f2549,f2545,f1601,f2551]) ).

fof(f2551,plain,
    ( spl0_258
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f2545,plain,
    ( spl0_257
  <=> subclass(universal_class,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f2549,plain,
    ( ~ subclass(universal_class,identity_relation)
    | ~ spl0_186
    | spl0_257 ),
    inference(forward_demodulation,[],[f2547,f1603]) ).

fof(f2547,plain,
    ( ~ subclass(universal_class,y)
    | spl0_257 ),
    inference(avatar_component_clause,[],[f2545]) ).

fof(f2548,plain,
    ( spl0_256
    | ~ spl0_257
    | ~ spl0_107
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1122,f1078,f814,f2545,f2542]) ).

fof(f2542,plain,
    ( spl0_256
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),X2)
        | y = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f1122,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,y)
        | member(unordered_pair(X0,X1),X2)
        | y = X2 )
    | ~ spl0_107
    | ~ spl0_137 ),
    inference(resolution,[],[f1079,f815]) ).

fof(f2539,plain,
    ( spl0_255
    | ~ spl0_112
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1031,f1009,f856,f2537]) ).

fof(f1031,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,identity_relation)),subset_relation)
        | y = intersection(X0,identity_relation) )
    | ~ spl0_112
    | ~ spl0_131 ),
    inference(resolution,[],[f1010,f857]) ).

fof(f2534,plain,
    ( spl0_254
    | ~ spl0_111
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1028,f1009,f852,f2532]) ).

fof(f1028,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | y = intersection(identity_relation,X0) )
    | ~ spl0_111
    | ~ spl0_131 ),
    inference(resolution,[],[f1010,f853]) ).

fof(f2529,plain,
    ( spl0_253
    | ~ spl0_112
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1024,f1005,f856,f2527]) ).

fof(f1024,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | y = intersection(X0,singleton_relation) )
    | ~ spl0_112
    | ~ spl0_130 ),
    inference(resolution,[],[f1006,f857]) ).

fof(f2524,plain,
    ( spl0_252
    | ~ spl0_111
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1021,f1005,f852,f2522]) ).

fof(f1021,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | y = intersection(singleton_relation,X0) )
    | ~ spl0_111
    | ~ spl0_130 ),
    inference(resolution,[],[f1006,f853]) ).

fof(f2510,plain,
    ( spl0_21
    | ~ spl0_8
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1085,f1033,f242,f301]) ).

fof(f1085,plain,
    ( member(y,universal_class)
    | ~ spl0_8
    | ~ spl0_132 ),
    inference(resolution,[],[f1034,f243]) ).

fof(f2493,plain,
    ( spl0_251
    | ~ spl0_168
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2488,f1601,f1428,f2490]) ).

fof(f2490,plain,
    ( spl0_251
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f2488,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_168
    | ~ spl0_186 ),
    inference(forward_demodulation,[],[f1603,f1430]) ).

fof(f2485,plain,
    ( spl0_186
    | spl0_250
    | ~ spl0_50
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f872,f852,f441,f2482,f1601]) ).

fof(f872,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | identity_relation = y
    | ~ spl0_50
    | ~ spl0_111 ),
    inference(superposition,[],[f853,f443]) ).

fof(f2457,plain,
    ( spl0_168
    | spl0_249
    | ~ spl0_49
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f871,f852,f436,f2454,f1428]) ).

fof(f871,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | singleton_relation = y
    | ~ spl0_49
    | ~ spl0_111 ),
    inference(superposition,[],[f853,f438]) ).

fof(f2452,plain,
    ( spl0_248
    | ~ spl0_29
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f847,f831,f334,f2450]) ).

fof(f847,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | y = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_29
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f335]) ).

fof(f2448,plain,
    ( spl0_247
    | ~ spl0_34
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f821,f814,f361,f2446]) ).

fof(f821,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(y,X0),X1)
        | y = X1
        | subclass(y,X0) )
    | ~ spl0_34
    | ~ spl0_107 ),
    inference(resolution,[],[f815,f362]) ).

fof(f2428,plain,
    ( spl0_246
    | ~ spl0_109
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1030,f1009,f831,f2426]) ).

fof(f1030,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ subclass(X0,identity_relation)
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_131 ),
    inference(resolution,[],[f1010,f832]) ).

fof(f2424,plain,
    ( spl0_245
    | ~ spl0_109
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1023,f1005,f831,f2422]) ).

fof(f1023,plain,
    ( ! [X0] :
        ( member(regular(X0),element_relation)
        | ~ subclass(X0,singleton_relation)
        | y = X0 )
    | ~ spl0_109
    | ~ spl0_130 ),
    inference(resolution,[],[f1006,f832]) ).

fof(f2336,plain,
    ( ~ spl0_5
    | ~ spl0_127 ),
    inference(avatar_contradiction_clause,[],[f2333]) ).

fof(f2333,plain,
    ( $false
    | ~ spl0_5
    | ~ spl0_127 ),
    inference(resolution,[],[f993,f230]) ).

fof(f230,plain,
    ( inductive(omega)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f228]) ).

fof(f993,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f992]) ).

fof(f992,plain,
    ( spl0_127
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f2335,plain,
    ( ~ spl0_22
    | ~ spl0_127 ),
    inference(avatar_contradiction_clause,[],[f2334]) ).

fof(f2334,plain,
    ( $false
    | ~ spl0_22
    | ~ spl0_127 ),
    inference(resolution,[],[f993,f307]) ).

fof(f307,plain,
    ( inductive(universal_class)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f2325,plain,
    ( spl0_244
    | ~ spl0_21
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2289,f2279,f301,f2322]) ).

fof(f2289,plain,
    ( member(subset_relation,universal_class)
    | ~ spl0_21
    | ~ spl0_238 ),
    inference(superposition,[],[f302,f2281]) ).

fof(f2319,plain,
    ( spl0_243
    | spl0_241
    | ~ spl0_42
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f799,f789,f393,f2306,f2317]) ).

fof(f2317,plain,
    ( spl0_243
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f799,plain,
    ( ! [X0] :
        ( member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_42
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f394]) ).

fof(f2315,plain,
    ( ~ spl0_242
    | ~ spl0_238
    | spl0_241 ),
    inference(avatar_split_clause,[],[f2310,f2306,f2279,f2312]) ).

fof(f2312,plain,
    ( spl0_242
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f2310,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_238
    | spl0_241 ),
    inference(forward_demodulation,[],[f2307,f2281]) ).

fof(f2309,plain,
    ( spl0_240
    | spl0_241
    | ~ spl0_41
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f798,f789,f389,f2306,f2303]) ).

fof(f2303,plain,
    ( spl0_240
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f798,plain,
    ( ! [X0] :
        ( member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_41
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f390]) ).

fof(f2286,plain,
    ( spl0_238
    | spl0_239
    | ~ spl0_79
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f870,f852,f642,f2283,f2279]) ).

fof(f870,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | subset_relation = y
    | ~ spl0_79
    | ~ spl0_111 ),
    inference(superposition,[],[f853,f644]) ).

fof(f2277,plain,
    ( ~ spl0_237
    | spl0_235
    | ~ spl0_33
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f808,f789,f352,f2263,f2274]) ).

fof(f2274,plain,
    ( spl0_237
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f808,plain,
    ( member(y,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_33
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f354]) ).

fof(f2272,plain,
    ( spl0_236
    | ~ spl0_8
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f2240,f2231,f242,f2269]) ).

fof(f2240,plain,
    ( y = complement(universal_class)
    | ~ spl0_8
    | ~ spl0_230 ),
    inference(resolution,[],[f2232,f243]) ).

fof(f2266,plain,
    ( ~ spl0_234
    | spl0_235
    | ~ spl0_32
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f806,f789,f347,f2263,f2259]) ).

fof(f2259,plain,
    ( spl0_234
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f806,plain,
    ( member(y,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_32
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f349]) ).

fof(f2250,plain,
    ( spl0_233
    | spl0_124
    | ~ spl0_31
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f794,f789,f342,f978,f2248]) ).

fof(f794,plain,
    ( ! [X0] :
        ( member(y,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_31
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f343]) ).

fof(f2246,plain,
    ( spl0_232
    | ~ spl0_6
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f922,f919,f233,f2243]) ).

fof(f2243,plain,
    ( spl0_232
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f922,plain,
    ( single_valued_class(choice)
    | ~ spl0_6
    | ~ spl0_117 ),
    inference(resolution,[],[f920,f235]) ).

fof(f2237,plain,
    ( spl0_231
    | ~ spl0_46
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f2229,f978,f424,f2235]) ).

fof(f2229,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(y,X0) )
    | ~ spl0_46
    | ~ spl0_124 ),
    inference(resolution,[],[f979,f425]) ).

fof(f2233,plain,
    ( spl0_230
    | ~ spl0_106
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f850,f831,f810,f2231]) ).

fof(f850,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = y )
    | ~ spl0_106
    | ~ spl0_109 ),
    inference(duplicate_literal_removal,[],[f841]) ).

fof(f841,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = y
        | complement(X0) = y )
    | ~ spl0_106
    | ~ spl0_109 ),
    inference(resolution,[],[f832,f811]) ).

fof(f2226,plain,
    ( spl0_229
    | spl0_124
    | ~ spl0_26
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f805,f789,f322,f978,f2224]) ).

fof(f2224,plain,
    ( spl0_229
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f805,plain,
    ( ! [X0] :
        ( member(y,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_26
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f323]) ).

fof(f2222,plain,
    ( spl0_227
    | ~ spl0_228
    | ~ spl0_7
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f519,f428,f238,f2219,f2216]) ).

fof(f2216,plain,
    ( spl0_227
  <=> ! [X0] :
        ( member(y,X0)
        | y = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f2219,plain,
    ( spl0_228
  <=> inductive(y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f428,plain,
    ( spl0_47
  <=> ! [X0,X1] :
        ( member(y,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f519,plain,
    ( ! [X0] :
        ( ~ inductive(y)
        | member(y,X0)
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_47 ),
    inference(superposition,[],[f429,f239]) ).

fof(f429,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(y,X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f428]) ).

fof(f2205,plain,
    ( spl0_226
    | ~ spl0_91
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f729,f725,f710,f2203]) ).

fof(f729,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,[],[f726,f711]) ).

fof(f2201,plain,
    ( spl0_225
    | ~ spl0_57
    | ~ spl0_91
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f783,f778,f710,f500,f2199]) ).

fof(f2199,plain,
    ( spl0_225
  <=> ! [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_225])]) ).

fof(f783,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_57
    | ~ spl0_91
    | ~ spl0_103 ),
    inference(forward_demodulation,[],[f781,f501]) ).

fof(f781,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_103 ),
    inference(resolution,[],[f779,f711]) ).

fof(f2188,plain,
    ( spl0_224
    | ~ spl0_34
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f730,f725,f361,f2186]) ).

fof(f730,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_34
    | ~ spl0_94 ),
    inference(resolution,[],[f726,f362]) ).

fof(f2177,plain,
    ( spl0_223
    | ~ spl0_80
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f776,f773,f647,f2175]) ).

fof(f776,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_80
    | ~ spl0_102 ),
    inference(resolution,[],[f774,f648]) ).

fof(f2124,plain,
    ( spl0_222
    | ~ spl0_80
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f771,f767,f647,f2122]) ).

fof(f771,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_80
    | ~ spl0_101 ),
    inference(resolution,[],[f768,f648]) ).

fof(f2120,plain,
    ( spl0_221
    | ~ spl0_80
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f770,f763,f647,f2118]) ).

fof(f770,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_80
    | ~ spl0_100 ),
    inference(resolution,[],[f764,f648]) ).

fof(f2110,plain,
    ( spl0_220
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f782,f778,f261,f2108]) ).

fof(f782,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)
        | y = 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_12
    | ~ spl0_103 ),
    inference(resolution,[],[f779,f262]) ).

fof(f2106,plain,
    ( ~ spl0_219
    | spl0_124
    | ~ spl0_31
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1087,f1033,f342,f978,f2103]) ).

fof(f2103,plain,
    ( spl0_219
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f1087,plain,
    ( member(y,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_31
    | ~ spl0_132 ),
    inference(resolution,[],[f1034,f343]) ).

fof(f2092,plain,
    ( spl0_218
    | ~ spl0_28
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f731,f725,f330,f2090]) ).

fof(f731,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)
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_28
    | ~ spl0_94 ),
    inference(resolution,[],[f726,f331]) ).

fof(f2040,plain,
    ( spl0_217
    | ~ spl0_80
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f668,f665,f647,f2038]) ).

fof(f668,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_80
    | ~ spl0_82 ),
    inference(resolution,[],[f666,f648]) ).

fof(f2001,plain,
    ( spl0_216
    | ~ spl0_46
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f723,f719,f424,f1999]) ).

fof(f723,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_46
    | ~ spl0_93 ),
    inference(resolution,[],[f720,f425]) ).

fof(f1945,plain,
    ( spl0_215
    | ~ spl0_57
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f737,f725,f500,f1943]) ).

fof(f737,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_57
    | ~ spl0_94 ),
    inference(superposition,[],[f726,f501]) ).

fof(f1941,plain,
    ( spl0_214
    | ~ spl0_57
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f734,f725,f500,f1939]) ).

fof(f734,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_57
    | ~ spl0_94 ),
    inference(superposition,[],[f726,f501]) ).

fof(f1920,plain,
    ( spl0_213
    | ~ spl0_34
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f669,f665,f361,f1918]) ).

fof(f669,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_34
    | ~ spl0_82 ),
    inference(resolution,[],[f666,f362]) ).

fof(f1891,plain,
    ( spl0_212
    | ~ spl0_46
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f713,f710,f424,f1889]) ).

fof(f713,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_46
    | ~ spl0_91 ),
    inference(resolution,[],[f711,f425]) ).

fof(f1885,plain,
    ( spl0_211
    | ~ spl0_80
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f744,f741,f647,f1883]) ).

fof(f744,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_80
    | ~ spl0_95 ),
    inference(resolution,[],[f742,f648]) ).

fof(f1881,plain,
    ( spl0_210
    | ~ spl0_28
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f670,f665,f330,f1879]) ).

fof(f1879,plain,
    ( spl0_210
  <=> ! [X0,X1] :
        ( 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)))))))))))
        | ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = y ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f670,plain,
    ( ! [X0,X1] :
        ( 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)))))))))))
        | ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = y )
    | ~ spl0_28
    | ~ spl0_82 ),
    inference(resolution,[],[f666,f331]) ).

fof(f1868,plain,
    ( spl0_209
    | ~ spl0_2
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f732,f725,f213,f1866]) ).

fof(f732,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))
        | y = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_2
    | ~ spl0_94 ),
    inference(resolution,[],[f726,f214]) ).

fof(f1862,plain,
    ( spl0_208
    | ~ spl0_48
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f581,f577,f432,f1860]) ).

fof(f581,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_48
    | ~ spl0_67 ),
    inference(resolution,[],[f578,f433]) ).

fof(f1858,plain,
    ( ~ spl0_205
    | ~ spl0_206
    | spl0_207
    | ~ spl0_77
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f650,f642,f629,f1855,f1851,f1847]) ).

fof(f1847,plain,
    ( spl0_205
  <=> 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_205])]) ).

fof(f1851,plain,
    ( spl0_206
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f1855,plain,
    ( spl0_207
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f629,plain,
    ( spl0_77
  <=> ! [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_77])]) ).

fof(f650,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_77
    | ~ spl0_79 ),
    inference(superposition,[],[f630,f644]) ).

fof(f630,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_77 ),
    inference(avatar_component_clause,[],[f629]) ).

fof(f1843,plain,
    ( spl0_204
    | ~ spl0_80
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f704,f701,f647,f1841]) ).

fof(f704,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_80
    | ~ spl0_89 ),
    inference(resolution,[],[f702,f648]) ).

fof(f1818,plain,
    ( spl0_203
    | ~ spl0_56
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f652,f642,f496,f1816]) ).

fof(f652,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_56
    | ~ spl0_79 ),
    inference(superposition,[],[f497,f644]) ).

fof(f1811,plain,
    ( spl0_202
    | ~ spl0_46
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f659,f647,f424,f1809]) ).

fof(f659,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_46
    | ~ spl0_80 ),
    inference(resolution,[],[f648,f425]) ).

fof(f1807,plain,
    ( spl0_201
    | ~ spl0_48
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f567,f555,f432,f1805]) ).

fof(f1805,plain,
    ( spl0_201
  <=> ! [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_201])]) ).

fof(f567,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_48
    | ~ spl0_63 ),
    inference(resolution,[],[f556,f433]) ).

fof(f1800,plain,
    ( spl0_200
    | ~ spl0_67
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f600,f596,f577,f1798]) ).

fof(f1798,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

fof(f596,plain,
    ( spl0_71
  <=> ! [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_71])]) ).

fof(f600,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_67
    | ~ spl0_71 ),
    inference(resolution,[],[f597,f578]) ).

fof(f597,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f596]) ).

fof(f1761,plain,
    ( spl0_199
    | ~ spl0_21
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1655,f1601,f301,f1758]) ).

fof(f1655,plain,
    ( member(identity_relation,universal_class)
    | ~ spl0_21
    | ~ spl0_186 ),
    inference(superposition,[],[f302,f1603]) ).

fof(f1756,plain,
    ( spl0_198
    | ~ spl0_80
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f691,f683,f647,f1754]) ).

fof(f691,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_80
    | ~ spl0_85 ),
    inference(resolution,[],[f684,f648]) ).

fof(f1752,plain,
    ( spl0_197
    | ~ spl0_46
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f640,f633,f424,f1750]) ).

fof(f633,plain,
    ( spl0_78
  <=> ! [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_78])]) ).

fof(f640,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_46
    | ~ spl0_78 ),
    inference(resolution,[],[f634,f425]) ).

fof(f634,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_78 ),
    inference(avatar_component_clause,[],[f633]) ).

fof(f1748,plain,
    ( spl0_196
    | ~ spl0_46
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f636,f629,f424,f1746]) ).

fof(f636,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_46
    | ~ spl0_77 ),
    inference(resolution,[],[f630,f425]) ).

fof(f1744,plain,
    ( spl0_195
    | ~ spl0_48
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f546,f508,f432,f1742]) ).

fof(f1742,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

fof(f546,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_48
    | ~ spl0_59 ),
    inference(resolution,[],[f509,f433]) ).

fof(f1740,plain,
    ( spl0_194
    | ~ spl0_48
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f545,f504,f432,f1738]) ).

fof(f1738,plain,
    ( spl0_194
  <=> ! [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_194])]) ).

fof(f545,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_48
    | ~ spl0_58 ),
    inference(resolution,[],[f505,f433]) ).

fof(f1652,plain,
    ( spl0_193
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f677,f674,f1650]) ).

fof(f674,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(f677,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,[],[f675]) ).

fof(f675,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,[],[f674]) ).

fof(f1648,plain,
    ( spl0_192
    | ~ spl0_46
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f621,f605,f424,f1646]) ).

fof(f621,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_46
    | ~ spl0_72 ),
    inference(resolution,[],[f606,f425]) ).

fof(f1644,plain,
    ( spl0_191
    | ~ spl0_35
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f531,f496,f365,f1642]) ).

fof(f531,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_35
    | ~ spl0_56 ),
    inference(resolution,[],[f497,f366]) ).

fof(f1640,plain,
    ( spl0_190
    | ~ spl0_34
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f524,f492,f361,f1638]) ).

fof(f524,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_34
    | ~ spl0_55 ),
    inference(resolution,[],[f493,f362]) ).

fof(f1627,plain,
    ( spl0_189
    | ~ spl0_40
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f654,f642,f385,f1625]) ).

fof(f654,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_40
    | ~ spl0_79 ),
    inference(superposition,[],[f386,f644]) ).

fof(f1620,plain,
    ( spl0_188
    | ~ spl0_57
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f637,f629,f500,f1618]) ).

fof(f637,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_57
    | ~ spl0_77 ),
    inference(superposition,[],[f630,f501]) ).

fof(f1608,plain,
    ( spl0_186
    | spl0_187
    | ~ spl0_50
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f886,f856,f441,f1605,f1601]) ).

fof(f886,plain,
    ( member(regular(identity_relation),subset_relation)
    | identity_relation = y
    | ~ spl0_50
    | ~ spl0_112 ),
    inference(superposition,[],[f857,f443]) ).

fof(f1599,plain,
    ( spl0_185
    | ~ spl0_31
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f603,f596,f342,f1597]) ).

fof(f1597,plain,
    ( spl0_185
  <=> ! [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_185])]) ).

fof(f603,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_31
    | ~ spl0_71 ),
    inference(resolution,[],[f597,f343]) ).

fof(f1595,plain,
    ( spl0_184
    | ~ spl0_35
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f489,f472,f365,f1593]) ).

fof(f489,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_35
    | ~ spl0_51 ),
    inference(resolution,[],[f473,f366]) ).

fof(f1591,plain,
    ( spl0_183
    | ~ spl0_42
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f459,f432,f393,f1589]) ).

fof(f459,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_42
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f394]) ).

fof(f1587,plain,
    ( spl0_182
    | ~ spl0_41
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f458,f432,f389,f1585]) ).

fof(f458,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_41
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f390]) ).

fof(f1577,plain,
    ( spl0_181
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f738,f725,f238,f1575]) ).

fof(f738,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(y,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))
        | y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(superposition,[],[f726,f239]) ).

fof(f1568,plain,
    ( spl0_180
    | ~ spl0_12
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f728,f725,f261,f1566]) ).

fof(f728,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)
        | y = 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_12
    | ~ spl0_94 ),
    inference(resolution,[],[f726,f262]) ).

fof(f1539,plain,
    ( spl0_179
    | ~ spl0_46
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f549,f516,f424,f1537]) ).

fof(f516,plain,
    ( spl0_61
  <=> ! [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_61])]) ).

fof(f549,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_46
    | ~ spl0_61 ),
    inference(resolution,[],[f517,f425]) ).

fof(f517,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f516]) ).

fof(f1535,plain,
    ( spl0_178
    | ~ spl0_46
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f530,f496,f424,f1533]) ).

fof(f530,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_46
    | ~ spl0_56 ),
    inference(resolution,[],[f497,f425]) ).

fof(f1531,plain,
    ( spl0_176
    | ~ spl0_177
    | ~ spl0_33
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f466,f432,f352,f1528,f1524]) ).

fof(f1524,plain,
    ( spl0_176
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f466,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_33
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f354]) ).

fof(f1522,plain,
    ( spl0_174
    | ~ spl0_175
    | ~ spl0_32
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f464,f432,f347,f1519,f1515]) ).

fof(f464,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_32
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f349]) ).

fof(f1513,plain,
    ( spl0_173
    | ~ spl0_30
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f462,f432,f338,f1511]) ).

fof(f462,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_30
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f339]) ).

fof(f1506,plain,
    ( spl0_172
    | ~ spl0_28
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f525,f492,f330,f1504]) ).

fof(f525,plain,
    ( ! [X0,X1] :
        ( 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
        | ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = y )
    | ~ spl0_28
    | ~ spl0_55 ),
    inference(resolution,[],[f493,f331]) ).

fof(f1499,plain,
    ( spl0_171
    | ~ spl0_168
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f1495,f1491,f1428,f1497]) ).

fof(f1495,plain,
    ( ! [X2,X0,X1] :
        ( singleton_relation = 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(singleton_relation,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)) )
    | ~ spl0_168
    | ~ spl0_170 ),
    inference(forward_demodulation,[],[f1494,f1430]) ).

fof(f1494,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,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))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_168
    | ~ spl0_170 ),
    inference(forward_demodulation,[],[f1492,f1430]) ).

fof(f1493,plain,
    ( spl0_170
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f735,f725,f238,f1491]) ).

fof(f735,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,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))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(superposition,[],[f726,f239]) ).

fof(f1435,plain,
    ( spl0_168
    | spl0_169
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f885,f856,f436,f1432,f1428]) ).

fof(f885,plain,
    ( member(regular(singleton_relation),element_relation)
    | singleton_relation = y
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(superposition,[],[f857,f438]) ).

fof(f1426,plain,
    ( spl0_167
    | ~ spl0_50
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f534,f496,f441,f1424]) ).

fof(f534,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_50
    | ~ spl0_56 ),
    inference(superposition,[],[f497,f443]) ).

fof(f1422,plain,
    ( spl0_166
    | ~ spl0_49
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f533,f496,f436,f1420]) ).

fof(f533,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_49
    | ~ spl0_56 ),
    inference(superposition,[],[f497,f438]) ).

fof(f1418,plain,
    ( spl0_165
    | ~ spl0_46
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f488,f472,f424,f1416]) ).

fof(f488,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_46
    | ~ spl0_51 ),
    inference(resolution,[],[f473,f425]) ).

fof(f1365,plain,
    ( spl0_164
    | ~ spl0_10
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f602,f596,f251,f1363]) ).

fof(f1363,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

fof(f602,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_10
    | ~ spl0_71 ),
    inference(resolution,[],[f597,f252]) ).

fof(f1361,plain,
    ( spl0_163
    | ~ spl0_26
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f463,f432,f322,f1359]) ).

fof(f463,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_26
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f323]) ).

fof(f1357,plain,
    ( spl0_162
    | ~ spl0_31
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f456,f432,f342,f1355]) ).

fof(f456,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_31
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f343]) ).

fof(f1353,plain,
    ( spl0_161
    | ~ spl0_34
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f418,f385,f361,f1351]) ).

fof(f418,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_34
    | ~ spl0_40 ),
    inference(resolution,[],[f386,f362]) ).

fof(f1349,plain,
    ( spl0_160
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f413,f381,f361,f1347]) ).

fof(f413,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(resolution,[],[f382,f362]) ).

fof(f1339,plain,
    ( spl0_159
    | ~ spl0_1
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f733,f725,f209,f1337]) ).

fof(f733,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),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_1
    | ~ spl0_94 ),
    inference(resolution,[],[f726,f210]) ).

fof(f1306,plain,
    ( spl0_158
    | ~ spl0_63
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f599,f596,f555,f1304]) ).

fof(f1304,plain,
    ( spl0_158
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f599,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_63
    | ~ spl0_71 ),
    inference(resolution,[],[f597,f556]) ).

fof(f1302,plain,
    ( ~ spl0_157
    | spl0_124
    | ~ spl0_20
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f807,f789,f296,f978,f1299]) ).

fof(f1299,plain,
    ( spl0_157
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f807,plain,
    ( member(y,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_20
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f298]) ).

fof(f1297,plain,
    ( spl0_156
    | ~ spl0_38
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f452,f424,f377,f1295]) ).

fof(f452,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_38
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f378]) ).

fof(f1293,plain,
    ( spl0_155
    | ~ spl0_36
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f451,f424,f369,f1291]) ).

fof(f451,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_36
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f370]) ).

fof(f1289,plain,
    ( spl0_154
    | ~ spl0_34
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f445,f424,f361,f1287]) ).

fof(f445,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_34
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f362]) ).

fof(f1266,plain,
    ( spl0_153
    | ~ spl0_39
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f470,f441,f381,f1264]) ).

fof(f470,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_50 ),
    inference(superposition,[],[f382,f443]) ).

fof(f1262,plain,
    ( spl0_152
    | ~ spl0_39
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f468,f436,f381,f1260]) ).

fof(f468,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_39
    | ~ spl0_49 ),
    inference(superposition,[],[f382,f438]) ).

fof(f1258,plain,
    ( spl0_150
    | ~ spl0_151
    | ~ spl0_20
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f465,f432,f296,f1255,f1251]) ).

fof(f465,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_20
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f298]) ).

fof(f1249,plain,
    ( spl0_148
    | ~ spl0_149
    | ~ spl0_18
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f460,f432,f287,f1246,f1242]) ).

fof(f460,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_18
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f289]) ).

fof(f1240,plain,
    ( spl0_146
    | ~ spl0_147
    | ~ spl0_17
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f457,f432,f282,f1237,f1233]) ).

fof(f457,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_17
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f284]) ).

fof(f1231,plain,
    ( spl0_145
    | ~ spl0_29
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f408,f361,f334,f1229]) ).

fof(f408,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_29
    | ~ spl0_34 ),
    inference(resolution,[],[f362,f335]) ).

fof(f1201,plain,
    ( spl0_144
    | ~ spl0_2
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f671,f665,f213,f1199]) ).

fof(f671,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) = y )
    | ~ spl0_2
    | ~ spl0_82 ),
    inference(resolution,[],[f666,f214]) ).

fof(f1197,plain,
    ( ~ spl0_143
    | spl0_124
    | ~ spl0_18
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f800,f789,f287,f978,f1194]) ).

fof(f1194,plain,
    ( spl0_143
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f800,plain,
    ( member(y,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_18
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f289]) ).

fof(f1183,plain,
    ( spl0_142
    | ~ spl0_58
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f623,f617,f504,f1181]) ).

fof(f617,plain,
    ( spl0_75
  <=> ! [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_75])]) ).

fof(f623,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_58
    | ~ spl0_75 ),
    inference(resolution,[],[f618,f505]) ).

fof(f618,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_75 ),
    inference(avatar_component_clause,[],[f617]) ).

fof(f1145,plain,
    ( spl0_141
    | ~ spl0_28
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f419,f385,f330,f1143]) ).

fof(f419,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)
        | ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y )
    | ~ spl0_28
    | ~ spl0_40 ),
    inference(resolution,[],[f386,f331]) ).

fof(f1141,plain,
    ( spl0_140
    | ~ spl0_28
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f414,f381,f330,f1139]) ).

fof(f414,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)
        | ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = y )
    | ~ spl0_28
    | ~ spl0_39 ),
    inference(resolution,[],[f382,f331]) ).

fof(f1091,plain,
    ( spl0_139
    | ~ spl0_39
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f655,f642,f381,f1089]) ).

fof(f655,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_39
    | ~ spl0_79 ),
    inference(superposition,[],[f382,f644]) ).

fof(f1084,plain,
    ( spl0_138
    | ~ spl0_19
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f461,f432,f292,f1082]) ).

fof(f461,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_19
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f293]) ).

fof(f1080,plain,
    ( spl0_137
    | ~ spl0_16
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f450,f424,f278,f1078]) ).

fof(f450,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_16
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f279]) ).

fof(f1068,plain,
    ( spl0_136
    | ~ spl0_28
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f358,f334,f330,f1066]) ).

fof(f358,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)
        | ~ member(complement(X0),universal_class)
        | complement(X0) = y )
    | ~ spl0_28
    | ~ spl0_29 ),
    inference(resolution,[],[f335,f331]) ).

fof(f1061,plain,
    ( spl0_135
    | ~ spl0_8
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f601,f596,f242,f1059]) ).

fof(f1059,plain,
    ( spl0_135
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f601,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_8
    | ~ spl0_71 ),
    inference(resolution,[],[f597,f243]) ).

fof(f1045,plain,
    ( spl0_134
    | ~ spl0_28
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f446,f424,f330,f1043]) ).

fof(f446,plain,
    ( ! [X0,X1] :
        ( ~ 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)
        | ~ member(X0,universal_class)
        | y = X0 )
    | ~ spl0_28
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f331]) ).

fof(f1039,plain,
    ( spl0_133
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f412,f365,f261,f1037]) ).

fof(f412,plain,
    ( ! [X0,X1] :
        ( y = 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))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) )
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f410,f130]) ).

fof(f130,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).

fof(f410,plain,
    ( ! [X0,X1] :
        ( subclass(X0,domain_of(X1))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | y = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1) )
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(resolution,[],[f366,f262]) ).

fof(f1035,plain,
    ( spl0_132
    | ~ spl0_21
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f995,f424,f301,f1033]) ).

fof(f995,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(y,X0) )
    | ~ spl0_21
    | ~ spl0_46 ),
    inference(resolution,[],[f302,f425]) ).

fof(f1011,plain,
    ( spl0_131
    | ~ spl0_40
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f469,f441,f385,f1009]) ).

fof(f469,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_40
    | ~ spl0_50 ),
    inference(superposition,[],[f386,f443]) ).

fof(f1007,plain,
    ( spl0_130
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f467,f436,f385,f1005]) ).

fof(f467,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(superposition,[],[f386,f438]) ).

fof(f1003,plain,
    ( spl0_129
    | ~ spl0_8
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f454,f432,f242,f1001]) ).

fof(f454,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_8
    | ~ spl0_48 ),
    inference(resolution,[],[f433,f243]) ).

fof(f999,plain,
    ( spl0_128
    | ~ spl0_9
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f449,f424,f246,f997]) ).

fof(f997,plain,
    ( spl0_128
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f449,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_9
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f248]) ).

fof(f994,plain,
    ( spl0_127
    | spl0_21
    | ~ spl0_8
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f792,f789,f242,f301,f992]) ).

fof(f792,plain,
    ( ! [X0] :
        ( member(y,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_8
    | ~ spl0_105 ),
    inference(resolution,[],[f790,f243]) ).

fof(f989,plain,
    ( ~ spl0_124
    | spl0_125
    | ~ spl0_126
    | ~ spl0_15
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f359,f342,f273,f986,f982,f978]) ).

fof(f982,plain,
    ( spl0_125
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f273,plain,
    ( spl0_15
  <=> ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(y,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f359,plain,
    ( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | inductive(cross_product(universal_class,universal_class))
    | ~ member(y,cross_product(universal_class,universal_class))
    | ~ spl0_15
    | ~ spl0_31 ),
    inference(resolution,[],[f343,f274]) ).

fof(f274,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(y,X0) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f976,plain,
    ( spl0_122
    | spl0_123
    | ~ spl0_7
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f638,f629,f238,f973,f970]) ).

fof(f638,plain,
    ( ! [X0] :
        ( member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | y = cross_product(X0,universal_class) )
    | ~ spl0_7
    | ~ spl0_77 ),
    inference(superposition,[],[f630,f239]) ).

fof(f968,plain,
    ( spl0_120
    | spl0_121
    | ~ spl0_1
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f672,f665,f209,f965,f962]) ).

fof(f962,plain,
    ( spl0_120
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f672,plain,
    ( ! [X0,X1] :
        ( y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_1
    | ~ spl0_82 ),
    inference(resolution,[],[f666,f210]) ).

fof(f955,plain,
    ( spl0_119
    | ~ spl0_12
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f453,f424,f261,f953]) ).

fof(f453,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X0),X1)
        | member(X2,X1)
        | ~ member(X2,universal_class)
        | y = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) )
    | ~ spl0_12
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f262]) ).

fof(f927,plain,
    ( spl0_118
    | ~ spl0_2
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f526,f492,f213,f925]) ).

fof(f526,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_55 ),
    inference(resolution,[],[f493,f214]) ).

fof(f921,plain,
    ( spl0_117
    | ~ spl0_59
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f547,f512,f508,f919]) ).

fof(f512,plain,
    ( spl0_60
  <=> ! [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_60])]) ).

fof(f547,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_59
    | ~ spl0_60 ),
    inference(resolution,[],[f513,f509]) ).

fof(f513,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f512]) ).

fof(f914,plain,
    ( spl0_116
    | ~ spl0_7
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f259,f255,f238,f912]) ).

fof(f255,plain,
    ( spl0_11
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | y != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f259,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_11 ),
    inference(trivial_inequality_removal,[],[f258]) ).

fof(f258,plain,
    ( ! [X0] :
        ( y != y
        | ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | y = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_7
    | ~ spl0_11 ),
    inference(superposition,[],[f256,f239]) ).

fof(f256,plain,
    ( ! [X0,X4] :
        ( y != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f899,plain,
    ( spl0_115
    | ~ spl0_11
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f540,f500,f255,f897]) ).

fof(f540,plain,
    ( ! [X0,X1] :
        ( y != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_11
    | ~ spl0_57 ),
    inference(superposition,[],[f256,f501]) ).

fof(f895,plain,
    ( ~ spl0_114
    | ~ spl0_1
    | spl0_97 ),
    inference(avatar_split_clause,[],[f829,f750,f209,f892]) ).

fof(f892,plain,
    ( spl0_114
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f829,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_1
    | spl0_97 ),
    inference(resolution,[],[f751,f210]) ).

fof(f890,plain,
    ( spl0_113
    | ~ spl0_7
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f532,f496,f238,f888]) ).

fof(f532,plain,
    ( ! [X0,X1] :
        ( member(X1,y)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_56 ),
    inference(superposition,[],[f497,f239]) ).

fof(f858,plain,
    ( spl0_112
    | ~ spl0_2
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f420,f385,f213,f856]) ).

fof(f420,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_40 ),
    inference(resolution,[],[f386,f214]) ).

fof(f854,plain,
    ( spl0_111
    | ~ spl0_2
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f415,f381,f213,f852]) ).

fof(f415,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = y )
    | ~ spl0_2
    | ~ spl0_39 ),
    inference(resolution,[],[f382,f214]) ).

fof(f837,plain,
    ( spl0_110
    | ~ spl0_1
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f527,f492,f209,f835]) ).

fof(f527,plain,
    ( ! [X0,X1] :
        ( y = X0
        | y = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_1
    | ~ spl0_55 ),
    inference(resolution,[],[f493,f210]) ).

fof(f833,plain,
    ( spl0_109
    | ~ spl0_2
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f447,f424,f213,f831]) ).

fof(f447,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | y = X0 )
    | ~ spl0_2
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f214]) ).

fof(f828,plain,
    ( spl0_108
    | ~ spl0_7
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f422,f385,f238,f826]) ).

fof(f422,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,regular(X0))
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_40 ),
    inference(superposition,[],[f386,f239]) ).

fof(f816,plain,
    ( spl0_107
    | ~ spl0_7
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f417,f381,f238,f814]) ).

fof(f417,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,y)
        | member(X1,X0)
        | y = X0 )
    | ~ spl0_7
    | ~ spl0_39 ),
    inference(superposition,[],[f382,f239]) ).

fof(f812,plain,
    ( spl0_106
    | ~ spl0_2
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f357,f334,f213,f810]) ).

fof(f357,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = y )
    | ~ spl0_2
    | ~ spl0_29 ),
    inference(resolution,[],[f335,f214]) ).

fof(f791,plain,
    ( spl0_105
    | ~ spl0_1
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f448,f424,f209,f789]) ).

fof(f448,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(y,X1)
        | ~ inductive(X0) )
    | ~ spl0_1
    | ~ spl0_46 ),
    inference(resolution,[],[f425,f210]) ).

fof(f787,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f207,f785]) ).

fof(f785,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(f207,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,[],[f206,f130]) ).

fof(f206,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,[],[f205,f130]) ).

fof(f205,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,[],[f204,f130]) ).

fof(f204,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(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,[],[f203,f130]) ).

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(cross_product(universal_class,domain_of(domain_of(flip(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,[],[f202,f130]) ).

fof(f202,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f201,f130]) ).

fof(f201,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,[],[f200,f130]) ).

fof(f200,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,[],[f199,f130]) ).

fof(f199,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,[],[f198,f130]) ).

fof(f198,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f180,f130]) ).

fof(f180,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(f780,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f197,f778]) ).

fof(f197,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,[],[f196,f130]) ).

fof(f196,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,[],[f195,f130]) ).

fof(f195,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,[],[f194,f130]) ).

fof(f194,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,[],[f193,f130]) ).

fof(f193,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,[],[f172,f130]) ).

fof(f172,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(f775,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f192,f773]) ).

fof(f192,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,[],[f171,f130]) ).

fof(f171,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(f769,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f176,f767]) ).

fof(f176,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(f765,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f175,f763]) ).

fof(f175,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(f761,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f160,f759]) ).

fof(f160,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(f757,plain,
    ( spl0_97
    | ~ spl0_98
    | ~ spl0_50
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f566,f484,f441,f754,f750]) ).

fof(f754,plain,
    ( spl0_98
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f484,plain,
    ( spl0_54
  <=> ! [X0,X1] :
        ( member(y,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f566,plain,
    ( ~ inductive(identity_relation)
    | member(y,subset_relation)
    | ~ spl0_50
    | ~ spl0_54 ),
    inference(superposition,[],[f485,f443]) ).

fof(f485,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X1,X0))
        | member(y,X0) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f484]) ).

fof(f748,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f159,f746]) ).

fof(f159,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(f743,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f183,f741]) ).

fof(f183,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,[],[f170]) ).

fof(f170,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(f727,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f174,f725]) ).

fof(f174,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(f721,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f157,f719]) ).

fof(f157,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(f717,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f188,f715]) ).

fof(f188,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,[],[f154,f130]) ).

fof(f154,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(f712,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f179,f710]) ).

fof(f179,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(f708,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f158,f706]) ).

fof(f158,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(f703,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f184,f701]) ).

fof(f184,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,[],[f173]) ).

fof(f173,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(f699,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f156,f697]) ).

fof(f156,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(f695,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f152,f693]) ).

fof(f152,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(f690,plain,
    ( ~ spl0_86
    | ~ spl0_1
    | spl0_69 ),
    inference(avatar_split_clause,[],[f656,f587,f209,f687]) ).

fof(f687,plain,
    ( spl0_86
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f656,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_1
    | spl0_69 ),
    inference(resolution,[],[f588,f210]) ).

fof(f685,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f167,f683]) ).

fof(f167,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(f681,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f177,f679]) ).

fof(f679,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(f177,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(f676,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f178,f674]) ).

fof(f178,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(f667,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f153,f665]) ).

fof(f153,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(f663,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f150,f661]) ).

fof(f150,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(f649,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f166,f647]) ).

fof(f166,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(f645,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f131,f642]) ).

fof(f131,plain,
    subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
    inference(definition_unfolding,[],[f74,f38]) ).

fof(f74,axiom,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).

fof(f635,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f186,f633]) ).

fof(f186,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,[],[f139,f130]) ).

fof(f139,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(f631,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f162,f629]) ).

fof(f162,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(f627,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f155,f625]) ).

fof(f155,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(f619,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f165,f617]) ).

fof(f165,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(f615,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f146,f613]) ).

fof(f146,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(f611,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f145,f609]) ).

fof(f145,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(f607,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f141,f605]) ).

fof(f141,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(f598,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f163,f596]) ).

fof(f163,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(f594,plain,
    ( spl0_69
    | ~ spl0_70
    | ~ spl0_49
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f565,f484,f436,f591,f587]) ).

fof(f591,plain,
    ( spl0_70
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f565,plain,
    ( ~ inductive(singleton_relation)
    | member(y,element_relation)
    | ~ spl0_49
    | ~ spl0_54 ),
    inference(superposition,[],[f485,f438]) ).

fof(f585,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f151,f583]) ).

fof(f151,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(f579,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f185,f577]) ).

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) ),
    inference(forward_demodulation,[],[f135,f130]) ).

fof(f135,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(f575,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f149,f573]) ).

fof(f573,plain,
    ( spl0_66
  <=> ! [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_66])]) ).

fof(f149,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(f571,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f144,f569]) ).

fof(f144,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(f561,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f148,f559]) ).

fof(f559,plain,
    ( spl0_64
  <=> ! [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_64])]) ).

fof(f148,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(f557,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f136,f555]) ).

fof(f136,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(f553,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f79,f551]) ).

fof(f551,plain,
    ( spl0_62
  <=> ! [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_62])]) ).

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(f518,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f187,f516]) ).

fof(f187,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f140,f130]) ).

fof(f140,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(f514,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f138,f512]) ).

fof(f138,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(f510,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f137,f508]) ).

fof(f137,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(f506,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f132,f504]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f502,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f130,f500]) ).

fof(f498,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f23,f496]) ).

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(f494,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f8,f492]) ).

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(f486,plain,
    ( spl0_54
    | ~ spl0_1
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f421,f385,f209,f484]) ).

fof(f421,plain,
    ( ! [X0,X1] :
        ( member(y,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_1
    | ~ spl0_40 ),
    inference(resolution,[],[f386,f210]) ).

fof(f482,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f161,f480]) ).

fof(f480,plain,
    ( spl0_53
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f161,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(f478,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f83,f476]) ).

fof(f476,plain,
    ( spl0_52
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

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(f474,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f25,f472]) ).

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(f444,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f129,f441]) ).

fof(f129,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).

fof(f439,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f104,f436]) ).

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(f434,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f7,f432]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f430,plain,
    ( spl0_47
    | ~ spl0_1
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f416,f381,f209,f428]) ).

fof(f416,plain,
    ( ! [X0,X1] :
        ( member(y,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_1
    | ~ spl0_39 ),
    inference(resolution,[],[f382,f210]) ).

fof(f426,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f1,f424]) ).

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(f407,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f133,f405]) ).

fof(f133,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).

fof(f403,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f110,f401]) ).

fof(f401,plain,
    ( spl0_44
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).

fof(f399,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f88,f397]) ).

fof(f397,plain,
    ( spl0_43
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f395,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f35,f393]) ).

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(f391,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f32,f389]) ).

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(f387,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f22,f385]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f383,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f21,f381]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f379,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f10,f377]) ).

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(f375,plain,
    ( spl0_37
    | ~ spl0_1
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f356,f334,f209,f373]) ).

fof(f373,plain,
    ( spl0_37
  <=> ! [X0] :
        ( ~ member(y,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f356,plain,
    ( ! [X0] :
        ( ~ member(y,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_1
    | ~ spl0_29 ),
    inference(resolution,[],[f335,f210]) ).

fof(f371,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f9,f369]) ).

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(f367,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f3,f365]) ).

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(f363,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f2,f361]) ).

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(f355,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f105,f352]) ).

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(f350,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f95,f347]) ).

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(f344,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f62,f342]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f340,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f57,f338]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f336,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f24,f334]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f332,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f191,f330]) ).

fof(f191,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)
      | y = X1 ),
    inference(forward_demodulation,[],[f190,f130]) ).

fof(f190,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)
      | y = X1 ),
    inference(forward_demodulation,[],[f168,f130]) ).

fof(f168,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | y = 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,f113,f118]) ).

fof(f113,axiom,
    null_class = y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lemma_1_to_restricted_domain_1) ).

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(f328,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f109,f326]) ).

fof(f326,plain,
    ( spl0_27
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).

fof(f324,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f92,f322]) ).

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(f320,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f87,f318]) ).

fof(f318,plain,
    ( spl0_25
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f316,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f86,f314]) ).

fof(f314,plain,
    ( spl0_24
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f312,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f82,f310]) ).

fof(f310,plain,
    ( spl0_23
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f308,plain,
    ( ~ spl0_21
    | spl0_22
    | ~ spl0_8
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f276,f273,f242,f305,f301]) ).

fof(f276,plain,
    ( inductive(universal_class)
    | ~ member(y,universal_class)
    | ~ spl0_8
    | ~ spl0_15 ),
    inference(resolution,[],[f274,f243]) ).

fof(f299,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f98,f296]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f294,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f51,f292]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f290,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f44,f287]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f285,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f18,f282]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f280,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f11,f278]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f275,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f189,f273]) ).

fof(f189,plain,
    ! [X0] :
      ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | inductive(X0)
      | ~ member(y,X0) ),
    inference(forward_demodulation,[],[f164,f130]) ).

fof(f164,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(y,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f113,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(f271,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f78,f269]) ).

fof(f269,plain,
    ( spl0_14
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f267,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f71,f265]) ).

fof(f265,plain,
    ( spl0_13
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f263,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f169,f261]) ).

fof(f169,plain,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | y = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12,f113]) ).

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(f257,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f147,f255]) ).

fof(f147,plain,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | y != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f30,f29,f12,f113]) ).

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(f253,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f181,f251]) ).

fof(f181,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(f249,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f52,f246]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f244,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f4,f242]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f240,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f143,f238]) ).

fof(f143,plain,
    ! [X0] :
      ( y = X0
      | intersection(X0,regular(X0)) = y ),
    inference(definition_unfolding,[],[f67,f113,f113]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f236,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f69,f233]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f231,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f50,f228]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f226,plain,
    ( ~ spl0_4
    | spl0_3 ),
    inference(avatar_split_clause,[],[f221,f217,f223]) ).

fof(f217,plain,
    ( spl0_3
  <=> y = domain_of(intersection(cross_product(y,y),x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f221,plain,
    ( y != domain_of(intersection(x,cross_product(y,y)))
    | spl0_3 ),
    inference(forward_demodulation,[],[f219,f130]) ).

fof(f219,plain,
    ( y != domain_of(intersection(cross_product(y,y),x))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f217]) ).

fof(f220,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f128,f217]) ).

fof(f128,plain,
    y != domain_of(intersection(cross_product(y,y),x)),
    inference(definition_unfolding,[],[f114,f29]) ).

fof(f114,axiom,
    y != domain_of(restrict(x,y,y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lemma_1_to_restricted_domain_2) ).

fof(f215,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f142,f213]) ).

fof(f142,plain,
    ! [X0] :
      ( y = X0
      | member(regular(X0),X0) ),
    inference(definition_unfolding,[],[f66,f113]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f211,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f134,f209]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | member(y,X0) ),
    inference(definition_unfolding,[],[f47,f113]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SET473-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon May 20 12:21:08 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (17083)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35  % (17086)WARNING: value z3 for option sas not known
% 0.11/0.35  % (17084)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35  % (17085)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35  % (17088)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.35  % (17087)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35  % (17086)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35  % (17089)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35  % (17090)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.38  TRYING [1]
% 0.11/0.38  TRYING [2]
% 0.17/0.44  TRYING [3]
% 1.49/0.54  TRYING [1]
% 1.49/0.55  TRYING [2]
% 1.49/0.59  TRYING [4]
% 2.16/0.68  TRYING [3]
% 4.99/1.09  TRYING [5]
% 7.77/1.46  TRYING [1]
% 7.77/1.46  TRYING [2]
% 7.77/1.47  TRYING [3]
% 8.55/1.54  TRYING [4]
% 9.33/1.73  TRYING [4]
% 9.88/1.77  TRYING [5]
% 14.96/2.49  TRYING [6]
% 18.96/3.11  TRYING [6]
% 29.93/4.62  TRYING [7]
% 53.84/8.02  % (17088)First to succeed.
% 54.43/8.10  % (17088)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17083"
% 54.43/8.11  % (17088)Refutation found. Thanks to Tanya!
% 54.43/8.11  % SZS status Unsatisfiable for theBenchmark
% 54.43/8.11  % SZS output start Proof for theBenchmark
% See solution above
% 54.43/8.13  % (17088)------------------------------
% 54.43/8.13  % (17088)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 54.43/8.13  % (17088)Termination reason: Refutation
% 54.43/8.13  
% 54.43/8.13  % (17088)Memory used [KB]: 37045
% 54.43/8.13  % (17088)Time elapsed: 7.753 s
% 54.43/8.13  % (17088)Instructions burned: 15689 (million)
% 54.43/8.13  % (17083)Success in time 7.789 s
%------------------------------------------------------------------------------